International Journal of Electronics, Mechanical and Mechatronics Engineering (IJEMME)

PRESIDENT Dr. Mustafa AYDIN Istanbul Aydın University, TR

HONORARY EDITOR Prof. Dr. Hasan SAYGIN Istanbul Aydın University, TR

EDITOR IN CHIEF Prof. Dr. Osman Nuri UÇAN Istanbul Aydın University, Engineering Faculty Electrical-Electronics Engineering Department Florya Yerleskesi, Inonu Caddesi, No.38, Kucukcekmece, Istanbul, Turkey Fax: +90 212 425 57 59 Tel: +90 542 322 91 15, +90 212 425 61 51 E-mail: [email protected]

EDITORIAL BOARD AYDIN Nizamettin Yıldız Technical University, TR BALIK Hasan H. Istanbul Aydin University, TR CATTANI Carlo University of Salerno, ITALY CARLINI Maurizio University “La Tuscia”, ITALY CHAPARRO Luis F. University of Pittsburg, USA DIMIROVSKI Gregory M. SS C. and Methodius University, MAC HARBA Rachid Orleans University, FR JENANNE Rachid Orleans University, FR KONDOZ Ahmet University of Surrey, UK RUIZ Luis Manuel Sanches Universitat Politècnica de València, Spain SIDDIQI Abul Hasan Sharda University, Indian STAVROULAKIS Peter Telecommunication System Ins., GR ADVISORY BOARD AKAN Aydın Istanbul University, TR AKATA Erol Istanbul Aydın University, TR ALTAY Gökmen Bahcesehir University, TR ANARIM, Emin Bosphorus University, TR ASLAN Zafer Istanbul Aydın University, TR ATA Oğuz Istanbul Aydın University, TR BAL Abdullah Yıldız Technical University, TR BİLGİLİ Erdem Piri Reis University, TR CEKIÇ Yalcin Bahçeşehir University, TR CEYLAN Murat Konya Selçuk University, TR DOĞRUEL Murat Marmara University, TR El KAHLOUT Yasser TÜBITAK-MAM, TR ERSOY Aysel Istanbul University, TR GÜNERHAN Huseyin Aegean University, TR GÜNAY Banihan University of Ulster, UK GÜNGÖR Ali Bahçeşehir University, TR HEPBAŞLI Arif Aegean University, TR KALA Ahmet Istanbul University, TR KAR A. Kerim Marmara University, TR KARAMZADEH Saeid Istanbul Aydın University, TR KARAÇUHA Ertuğrul Istanbul Technical University, TR KARAHOCA Adem Bahçeşehir University, TR KARAKOÇ Hikmet Anadolu University,TR KARTAL Mesut Istanbul Technical University, TR KENT Fuad Istanbul Technical University, TR KILIÇ Niyazi Istanbul University,TR KINCAY Olcay Yıldız Technical University, TR KUNTMAN Ayten Istanbul University, TR KOCAASLAN İlhan Istanbul University, TR ÖNER Demir Maltepe University, TR ÖZ Hami Istanbul Aydın University, TR ÖZBAY Yüksel Konya Selçuk University, TR PAKER Selçuk Istanbul Technical University, TR PASTACI Halit Haliç University, TR SAYAN Ömer F. Telecommunications Authority, TR ŞENER Uğur Istanbul Aydın University, TR SİVRİ Nuket Istanbul University, TR SÖNMEZ Ferdi Istanbul Arel University, TR SOYLU Şeref Sakarya University UĞUR Mukden Istanbul University, TR UTLU Zafer Istanbul Aydın University, TR YILMAZ Aziz Air Force Academy, TR YILMAZ Reyat Dokuz Eylül University, TR VISUAL DESIGN & ACADEMIC STUDIES COORDINATION OFFICE Nabi SARIBAŞ - Hakan TERZİ - Nazan ÖZGÜR PRINTED BY Tevfikbey Mahallesi, Dr. Ali Demir Caddesi NO:51 34290 Sefakoy/ISTANBUL, Tel: 0212 624 21 11 - Fax: 0212 624 21 17 E-mail: [email protected] ISSN: 2146-0604 International Journal of Electronics, Mechanical and Mechatronics Engineering (IJEMME) is peer-reviewed journal which provides a platform for publication of original scientific research and applied practice studies. Positioned as a vehicle for academics and practitioners to share field research, the journal aims to appeal to both researchers and academicians. Internationally indexed by EBSCO and DOAJ CONTENTS From Editor Prof. Dr. Osman N. UÇAN

Preparation of a Carbon Fiber Reinforced Epoxy Composite and Increasing The Flight Performance for Radio Controlled Model Helicopters B. Yeşim BÜYÜKAKINCI, Tuğçe ÖZKENAR, Cem GÜLBAHAR 949 Fast and Lossless Image Compression in Chaos-Based Encryption Sajad EINY, Solmaz EINI 955 Design Equations from Geometric Programming Robert C. CREESE 963

Optimizing Bus Lines in Urban Public Transportation by Cost and Trip Calculation Methods: A Software Model Design Ferdi SÖNMEZ 969

From Editor

In this issue of “International Journal of Electronics, Mechanical and Mechatronics Engineering (IJEMME)”, we have especially selected the scientific areas which will cover future prospective Engineering titles such as Robotics, Mechanics, Electronics, Telecommunications, Control systems, System Engineering, Biomedical, and renewable Energy Sources.

We have selected only a few of the manuscripts to be published after a peer review process of many submitted studies. Accepted papers are as follows:

Preparation of a Carbon Fiber Reinforced Epoxy Composite and Increasing The Flight Performance For Radio Controlled Model Helicopters B. Yesim BÜYÜKAKINCI, Tuğçe ÖZKENAR, Cem GÜLBAHAR

Fast and lossless Image compression in chaos-based Encryption Sajad EINY, Solmaz EINI

Design Equations from Geometric Programming Robert C. CREESE

Optimizing Bus Lines In Urban Public Transportation By Cost And Trip Calculation Methods: A Software Model Design Ferdi SÖNMEZ

Prof. Dr. Osman N. UCAN Editor in Chief

Preparation of a Carbon Fiber Reinforced Epoxy Composite and Increasing The Flight Performance for Radio Controlled Model Helicopters Doi: 10.17932/ IAU.IJEMME.m.21460604.2015.5/3.949-953

B. Yeşim BÜYÜKAKINCI1 Tuğçe ÖZKENAR2 Cem GÜLBAHAR3

Abstract Composite-material technologies have matured over the past 40 years to the point where high performance composites are being used to enhance the performance of nearly every new flight vehicle [1]. Carbon fibers have been used to replace metals used in composite materials because its performance-price is changing favorably [2]. They are also lighter and stronger than metals. This is the main reason why carbon fibers are used in composite materials. They also reduce fuel consumption and provide energy efficiency [2]. Furthermore, they have been used in many products, such as cars, airplanes, sporting goods, space vehicles and custom-designed products [2]. In this study, carbon fiber reinforced epoxy composite (CREC) was prepared and the flight performance of a radio controlled model helicopter with CREC chassis was evaluated. According to test flights it was observed that carbon fiber reinforced epoxy composites increase the flight performance of model helicopters.

Keywords:Composites, carbon fiber, flight performance, radio controlled model helicopter

1.Introduction The materials needed to construct theoretrical dimensional stability, high dielectric strength, models conceived by aircraft designers did corrosion resistance, light weight, simplicity not exist for many years [1]. Composite of molding, surface treatment compatibility, materials have allowed engineers to overcome high temperature resistance, transparency, difficulties and now they are frequently high chemical resistance, vibration damping, used in the aircraft industry. They are five acoustic conductivity and sound absorption. times lighter and seven times stronger than These factors have roles in reducing the aluminium. Therefore, they are important operating costs of aircrafts in the long term, to the aviation industry. The most important increasing fuel efficiency and performance benefit of composite materials is their weight, [3,4,5]. which plays a fundamental role in their selection. They provide additional advantages A composite material is formed by combining such as high strength, design flexibility, two or more constituent materials with

1 Istanbul Aydın University, Department of Textile Engineering, Istanbul, Turkey. 2 Istanbul Aydın University, Department of Textile Engineering, Istanbul, Turkey. 3 Istanbul Aydın University, Department of Textile Engineering, Istanbul, Turkey.

949 Preparation of a Carbon Fiber Reinforced Epoxy Composite and Increasing The Flight Performance for Radio Controlled Model Helicopters substantially different physical or chemical properties, resulting in better properties than either constituent can provide independently. But, unlike a metal alloy, the constituents do not dissolve into or blend with each other, they remain separate and distinct within the finished structure [6,7]. One constituent serves as a bonding matrix while the other serves as reinforcement, in the form of fibers within the matrix[1]. In principle, a base matrix is prepared in a mould under high temperature and pressure. Subsequently, an epoxy or resin is poured over the base material, and when the composite is cooled, a strong material is attained [3].

1.1.The manufacturing process Figure 1. In the prepregging process, a resin A common feature of all composite processes is applied to a reinfocement fiber. To saturate is the combination of a resin, a curing agent, the fiber, it is dipped through the liquid and a reinforcing fiber. In general, heat and resin or it is impregnated through heat and pressure are used to shape and cure the mixture pressure. into a finished part. The resin holds the fibers together and transfers the load to the fibers in 1.2.Polymer matrix composite resin the manufactured composite part. The curing systems agent (or hardener) acts as a catalyst in curing Thermoset resins are generally used in the resin into a hard plastic. The reinforcing manufacturing composites. They require fiber gives strength and other properties which addition of a curing agent or hardener and are necessary for the composite. impregnation on to a reinforcing material, followed by a curing step during the The most common manufacturing process manufacturing process of the finished part. is prepregging. In this method, the resin and curing agent are impregnated into the The most common and important class of reinforcing fiber. The prepreg must be reserved epoxy resins widely utilized in the industry in a freezer until used in the manufacturing is formed from reacting epichlorohydrin with process. Cold storage is maintained to prevent bisphenol A. The curing agents or hardeners premature chemical reaction. These prepreg are fundamental ingredients of a composite materials are frequently preferred in the sytem because they control the reaction rate composite industry, especially in the aircraft and determine the performance features of the and aerospace industries (Figure 1). finished part. These compounds must include active sites on their molecules because they serve as catalysts.

950 B. Yeşim BÜYÜKAKINCI, Tuğçe ÖZKENAR, Cem GÜLBAHAR

1.3.Fiber Reinforcements in fibrous form [5]. Today, the polyacrylonitrile Fibers are added to the resin to give strength (PAN)-based carbon fiber is the most utilized to the finished part. They are an integral part precursor in the composite industry [8]. This of the composite system; however they don’t white fiber is produced by extruding and react with the resin. The most frequenly-used processing an acrylonitrile-based polymer, reinforcement materials are carbon fibers[8]. which when integrated with plastic resins produces a carbon fiber composite prepreg Carbon fiber is a very durable material which for fabricating composite structures [11]. has a fibrous structure. The raw material Polyacrylonitrile, a hard, rigid thermoplastic of carbon fiber is acrylic. Carbon fiber is material that is resistive to numerous produced by the combination of nylon and chemicals and solvents, is of low permeability tar [9]. This fiber is manufactured at furnace to gases and slow-burning and is the key temperatures of 1000-2000°C. At these ingredient in high-performance parts used in temperatures, the carbon atoms in the fibers aerospace applications [12]. Its features are are rearranged to provide the properties key to obtaining the high tensile stiffness and necessary for the finished fiber[8]. The carbon tensile strength properties essential in defense fiber manufacturing process comprises four and commercial aircraft applications [11]. chemical stages: 1)The Oxidation step, achieved by heating 2. Material and Method the fibers at lower temperatures in air In this study, CREC material was prepared. (approximately 200-300°C), which allows the Test flights were carried out by using an spun fibers to pick up oxygen molecules and aluminium alloy chassis and a CREC chassis separate from hydrogen. and compared.

2)In carbonization step carbon atoms are 2.1. Materials bonded in a crystalline structure, which • Radio controlled model helicopter: x2; is accomplished by heating the fibers to Align Corp.Ltd approximately 1000-3000°C. • Motor: DJI.920 KV Brushless Motor • Flight Control Board: DJI Naza. M V2 3) Electric surface treatment helps prepare Main Controller the fibers for bonding to resins by adding • Battery: 14.8 Volt 10.000 mah li-po small amounts of oxygen and roughening the • CREC material: Shandong Evergreen surface or electrically coating the fibers [10]. Industries Ltd. • 2024-t3 aluminium (Al) alloy: Zhongfu 4) Coating, where a neutral finish protects Industrial Henan Jiayuan Al Industry Co. the fibers from proximate treatments such Ltd. as prepreg, is performed on fibers that are typically molded with epoxy resin to act as an 2.2. Determination of weight and flight interface between the fiber and resin [4]. performance The 2024-t3 aluminium alloy, which is used in Carbon fibers are manufactured by the construction of passenger aircraft (Figure 2), controlled thermal treatment of organic was cut and mounted onto the radio controlled precursors (polyacrylonitrile, pitch or rayon) model helicopter (Figure 3). The process was

INTERNATIONAL JOURNAL OF ELECTRONICS, MECHANICAL AND MECHATRONICS ENGINEERING Vol.5 Num.2 - 2015 (949-953) 951 Preparation of a Carbon Fiber Reinforced Epoxy Composite and Increasing The Flight Performance for Radio Controlled Model Helicopters repeated for CREC material (Figure 4) on 3.Results and Discussion another radio controlled model helicopter. The weights and flight performances of radio controlled model helicopters were compared (Table 1)

Table 1. The Comparison of CREC and Al Chassis

Carbon fiber Aluminium Difference reinforced alloy in epoxy composite chassis percentage chassis

Figure 2. 2024-t3 Aluminium alloy chassis. Weight (kg) 2.33 1.9 18.45% ↓

Mean flight 13 17.3 33%↑ time (min)

It was observed that the radio controlled model helicopter with CREC chassis was lighter and its flight performance was better Figure 3. Radio controlled model helicopter. than the model helicopter made of aluminium alloy.

4.Conclusion In this study, it was determined that the flight performance of the radio controlled model helicopter was increased by using lightweight CREC material.

Carbon fiber composites have a great future ahead of them and it is a growing market. Composites are used for areas such as Figure 4. Carbon fiber reinforced epoxy aerospace and aviation industry, weapons, composite chassis. rockets and other ammunition industries, urbanism, household appliances, automobiles, The weights of vehicles made with aluminium civil engineering, agriculture and construction alloy chassis and carbon fiber reinforced equipments[4]. epoxy composite chassis were measured and test flights for both vehicles were carried out. Carbon fiber composite materials are important Test flights for both vehicles were repeated to the aircraft industry because they provide a three times and their flight times were lighter weight and greater structural strength determined. when compared to metal alloys. Usage of such materials will reduce fuel consumption,

952 B. Yeşim BÜYÜKAKINCI, Tuğçe ÖZKENAR, Cem GÜLBAHAR improve efficiency and reduce direct operating [8] “OSHA Technical Manual (OTM), costs of aircrafts[3]. Section III: Chapter 1:Polymer Matrix Materials: Advanced Composites”, U.S. REFERENCES Department of Labor -Occupational [1]Day, Dwayne A., “Composites and Safety & Health Administration, http:// Advanced Materials”, US Centennial of web.archive.org/web/20100528112048/ Flight Commision ,http://web.archive. http://www.osha.gov/dts/osta/ org/web/20100528010913/http://www. otm/otm_iii/otm_iii_1.html, 2014 centennialofflight.gov/essay/Evolution_of_ Technology/composites/Tech40.htm,2014 [9]Carbon (fiber), http://en.wikipedia.org/ . wiki/Carbon_(fiber), 2014 [2]Seventekin, N, Oktem, T, Yaman, N., “Properties of Carbon Fibers and Usage [10]http://www.spangpower.com/industry- Possibilities”, Journal of Textile and Apparel, solutions/fibers/carbon-fiber, 2014. N o . 2 , p . 9 0 - 9 5 , 2 0 0 7 . [11]“Polyacrylonitrile (PAN) Carbon [3]Kukreja, B, S.,“Composites in the Aircraft Fibers”, Industrial Capability Assessment Industry”, http://www.appropedia.org/ O U S D ( A T & L ) I n d u s t r i a l P o l i c y , p . 1 , 2 0 0 5 . Composites_in_the_Aircraft_Industry, 2014 [12]http://global.britannica.com/EBchecked/ [4]Demirel, A.,“The Characterisation of topic/468259/polyacrylonitrile-PAN, 2014. Carbon Fiber Reinforced Epoxy Composite Materials”,M.Sc. Thesis,Gazi University Institute of Science and Technology, p.4, 29, 36-39, 2007,Ankara

[5]Khan, M, R, Barron, A,R.,“Carbon Fibers:Opportunities And Challenges”, Advanced Materials & Processes, p.47-49, 20 08.

[6]“Composite Materials”, Dassault Falcon, Focus No.4, p.6, http://www.dassaultfalcon. com/publishingimages/images/media-center/ media-gallery/publications/focus4.pdf,2014

[7] Sharma, S, D., “Analytical Study Of Factors Affecting and Applicatıon of Finite Element Analysis For Heat Transfer Through Fiber Reinforced Composite Materials”, International Journal Of Mechanical Engineering And Robotics Research, India, Vol. 3, No. 3, p.129-133, 2004.

INTERNATIONAL JOURNAL OF ELECTRONICS, MECHANICAL AND MECHATRONICS ENGINEERING Vol.5 Num.2 - 2015 (949-953) 953 Fast and lossless Image compression in chaos-based Encryption

sajad einy1 solmaz eini 2

Abstract The wide use of digital images leads to the necessity of securing them when they enter into an insecure channel. Image cryptography plays a vital role in the modern communication. For telecommunication systems through the internet, various compression and encryption techniques are proposed to satisfy a fast and secure transmission. However these two techniques have been studied separately. In this paper we propose new approach of fast image encryption algorithm with chaos-based encryption system using by cipher structure and in compression process by using a context matching method driven by the correlation between adjacent neighbor mask pixels. With this approach the size of transmission can be reduce and transmission can be secure.

Keywords: Image Compression, Cyrptography, Chaos Based Encryption

In today's heterogeneous network information from a transmitter to a receiver environment, this requires more and mor e (that can be done using an efficient new techniques to meet the increasing needs of a modern society. In recent years, with the compression technique) and a secure rapid development of computer science and transmission of information which can be network technology, people are obtaining, achieved using a powerful encoding using and processing digita l images mor e algorithm. To satisfy these constraints, new frequently. This situation brings us compression and encryption methods convenience, as well as potential threats. How allowing a fast and secure informatio n to protect the information within the digita l transmission are proposed in the literature. images from the attacks of intruders is becoming a more and more serious problem. In case, these methods (compression and Image compression is minimizing the size in encoding) are often developed in an bytes of a graphics file without degrading the independent manner although they are quality of the image to an unacceptable level. strongly connected and one influences the The reduction in file size allows more ima ge s other. Accordingly, we propose to combine to be stored in a given amount of disk or compression with encryption and propose a memory space. It also reduces the time new method of compression and encryption at required for images to be sent over the Internet same time[6-7]. or downloaded from Web pages[1-5]. It is supposed that we transmit important However, for any communication system, it is images to a receiver, preventing non- necessary to take into account two major authorized people from intercepting the requireme nts : a fast transmis s io n to send the images. In order to encrypt the images we Fast and lossless Lossless Image Image compression Compression in chaosin Chaos-Based-based Encryption

Encryption Doi: 10.17932/ IAU.IJEMME.m.21460604.2015.5/3.955-962

sajad einy1 1 Sajadsolmaz EINYeini 2 Solmaz EINI2

Abstract The wide useuse ofof digitaldigital imagesimages leadsleads to to the the necessity necessity of ofsecur securinging them them when when they they enter enter into into an aninsecure insecure channel. channel. Image Image cryptography cryptography plays plays a avital vital role role in in thethe modernmodern communication. ForFor telecommunication systems through the the internet,internet, various various compression compression and and encryption encryption techniques techniques are proposed to satisfy a fast and securesecure transmission. However these two techniques have been studied separately. InIn thisthis paper we propose new approach of fast imageimage encryption algorithm with chaos-basedchaos-based encryption system using by cipher structure and in compression process by using a a context mmatchingatching method driven by the correlation between adjacent neighbor mask pixels. With this approach the size of transmission can be reduce and transmission can be secure.

Keywords: Image Compression, Cyrptography, Chaos Based Encryption Keywords: Image Compression, Cyrptography, Chaos Based Encryption

1 Spatial Information Technology Jawaher Lal Nehro Hyderabad India, Istanbul Aydın University 2 Spatial Information Technology Jawaher Lal Nehro Hyderabad India, Istanbul Aydın University

955 Fast and Lossless Image Compression in Chaos-Based Encryption cover the images with an insignif ica nt ima ge . Depth. In such a case, we take the closest define: In addition we would like to compress the Firstly, we perform prediction using a value from the above range. We compress the (𝛼𝛼1,𝛼𝛼2, 𝛼𝛼3, …, 𝛼𝛼𝑘𝑘) 𝜍𝜍𝑘𝑘(𝛼𝛼̅) = transmitting data, to achieve a high speed predictor selected from a fixed set of 9 simple Residuum symbol that is a difference between 𝑙𝑙,𝑚𝑚 𝑙𝑙,𝑚𝑚 𝑙𝑙,𝑚𝑚 Communica tio ns [8]. For this purpose we the actual and the predicted {𝑥𝑥𝑙𝑙,𝑚𝑚 : 𝑥𝑥1 = 𝛼𝛼1,𝑥𝑥2 = 𝛼𝛼2, 𝑥𝑥3 = linear predictors. Prediction errors are Consist𝑙𝑙,𝑚𝑚 of all the pixels on the value of utilized a compression scheme which also We reorder residual values to 𝜂𝜂 get the 3 𝑘𝑘 𝑘𝑘 reordered to obtain probability distribution 𝛼𝛼 , …, 𝑥𝑥 = 𝛼𝛼 } for sample mean: 𝑥𝑥(𝑖𝑖, 𝑗𝑗) 𝑥𝑥 (𝑖𝑖,𝑗𝑗) 𝑘𝑘 uses multip le predictors. However the expected by the data model. probability distributio n close descriptive by 𝜍𝜍 predictors are generated using local statistics simply picking symbols : first, last, second, (𝛼𝛼1,𝛼𝛼2, 𝛼𝛼3, …, 𝛼𝛼𝑘𝑘) and are used based on a switching algorithm To predict the intensity of a specific pixel X, last but one and so on: 𝑥𝑥|𝛼𝛼 1 which relies on the correlation between pixe ls . we use fast linear predictors up to 3 𝜇𝜇 = 𝑘𝑘 ∑ 𝑥𝑥 ‖𝜍𝜍 (𝛼𝛼̅)‖ 𝑥𝑥𝑥𝑥𝑥𝑥 And in next step, chaos-based image neighbor ing pixels : first left-hand neighbor, 𝜂𝜂 encryption algorithm, in cipher architecture, is second upper neighbor , and third upper-left 𝑥𝑥 (𝑖𝑖,𝑗𝑗) 𝑛𝑛 1) N set of x observation proposed. The flowchar t of the algorithm is neighbor . 2𝑛𝑛(𝑖𝑖, 𝑗𝑗) 𝑓𝑓𝑓𝑓𝑓𝑓 𝑛𝑛(𝑖𝑖,𝑗𝑗) < 2 − 1 2) For each is in sequence of x on replace i: = { 𝑛𝑛 𝑛𝑛 shown in following flowchart. An image is 2(2 − 𝑛𝑛(𝑖𝑖, 𝑗𝑗)) 𝑓𝑓𝑓𝑓𝑓𝑓 𝑛𝑛(𝑖𝑖,𝑗𝑗) > 2 − 1 𝑖𝑖 producing a binary data stream with masking 𝑥𝑥 Lossless compression has eight linear The conditional exception of x set of 3) Let y target amount data of image with a random key stream by a 𝑦𝑦 = [𝑥𝑥𝑖𝑖−𝑛𝑛, …, 𝑥𝑥𝑖𝑖] predictive schemes named JPEG lossless observation in 4) Update all y amounts chaos-based random key stream generator algorithm. condition is: then corresponding encrypted image is Main algorithm of predictors: 𝑖𝑖 𝑦𝑦 1 2 3 formed. The specific details of each 1) First step make no scheme 𝑦𝑦 𝑦𝑦 𝑦𝑦 1 2 3 component are to be discussed in the 2) 1-D predictors 𝐼𝐼 𝑥𝑥 𝑥𝑥 𝑥𝑥 𝐸𝐸[𝑋𝑋|𝑌𝑌 ] = 4 following sections[9]. 𝑋𝑋 𝐼𝐼 𝑦𝑦 The∑ 𝑃𝑃 optimal[𝑋𝑋 = 𝑥𝑥 | value:𝑌𝑌 = 4 𝜂𝜂 1 2, 3 𝑁𝑁 𝑥𝑥 𝑌𝑌 , 𝑌𝑌 𝑌𝑌 , …, 𝑌𝑌 ] 𝑥𝑥 𝜂𝜂(𝑖𝑖,𝑗𝑗) = 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗) (Content bass matching windows) 𝑖𝑖,𝑗𝑗 𝑛𝑛 𝑚𝑚 Recently, Compression schemes have been 3)𝑥𝑥𝜂𝜂 2(-𝑖𝑖D,𝑗𝑗 )predictors= 𝑥𝑥(𝑖𝑖, 𝑗𝑗 − 1) Prediction by particle matching is method is 𝑥𝑥 𝑦𝑦 𝐸𝐸[𝑥𝑥𝑖𝑖,𝑗𝑗|(𝑥𝑥𝑖𝑖−𝑙𝑙,𝑦𝑦𝑗𝑗−𝑚𝑚)𝑙𝑙,𝑚𝑚] = 1 Pseudo-code: greatly developed by various researchers [1]– 𝑥𝑥 (𝑖𝑖,𝑗𝑗) = 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗 − 1) method to predict. The symbol depending on While (not last value of ) do [4]. 𝜂𝜂 pervious. This method is called MARKOV Read neighbors 𝑛𝑛 𝑥𝑥 (𝑖𝑖,𝑗𝑗) = 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗) − 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗 − 1) model in [10-13]. Shorten to 𝛼𝛼4 neighbors of This was introduced in order to solve the + 𝑥𝑥(𝑖𝑖, 𝑗𝑗 − 1) content problems which consist of the separation of 𝜂𝜂 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗) − 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗 − 1) Pixel we can define a set of pixels which While (context amount ( ) < 0 do 𝑥𝑥 (𝑖𝑖,𝑗𝑗) = { } independent sources using observed mixed 2 are neighborhood of as it context. That Escape sequence of 𝑖𝑖,𝑗𝑗 𝑘𝑘 texture without a strong knowledge about + 𝑥𝑥(𝑖𝑖, 𝑗𝑗 − 1) are depending𝑥𝑥 on the scanning and hence 𝜍𝜍 (𝛼𝛼̅) 𝜂𝜂 𝑖𝑖,𝑗𝑗 sources and, in particular lossless 𝑥𝑥(𝑖𝑖, 𝑗𝑗 − 1) − 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗 − 1) operational method.𝑥𝑥 The pixels Calculate average sample 𝑥𝑥 (𝑖𝑖,𝑗𝑗) = { } 1 2 3 𝑘𝑘 compression schemes rely on statistical 2 with set of value (mean𝛼𝛼 ,𝛼𝛼 (, 𝛼𝛼 ,)… , 𝛼𝛼 ) ( ) structure in the data. Lossless compression + 𝑥𝑥 𝑖𝑖 − 1, 𝑗𝑗 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 relay o statistical structure in the data and 𝜂𝜂 𝑥𝑥(𝑖𝑖, 𝑗𝑗 − 1) − 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗) 1 2 3 𝑘𝑘 𝜇𝜇𝑥𝑥|𝛼𝛼 𝑥𝑥 (𝑖𝑖,𝑗𝑗) = { } 𝑥𝑥 , 𝑥𝑥 , 𝑥𝑥 , … , 𝑥𝑥 𝛼𝛼 = work on non-random data contain duplicated In this process is2 the pixel of (i,j) and infor matio n that determine the probability of the value of predictors. Predictor Correction occurring and assigning the smallest part of 𝜂𝜂 𝑥𝑥(𝑖𝑖, 𝑗𝑗) the most common data. If𝑥𝑥 (there𝑖𝑖,𝑗𝑗) is a subtraction operation in a calculation of the predictor, then its value may (Origina l image) (Compress image) This kind of algorithm is used in computing, Model Be out of the nominal range of pixel base for saving space and sending data through the intens ities [0; ], where N denotes web and viewing image online; The algorithm image bit. 𝑛𝑛(𝑖𝑖.𝑗𝑗) work in tow way; prediction and correction- 2 − 1 based conditional average. Figure 1. compression process

956 Sajad EINY, Solmaz EINI cover the images with an insignif ica nt ima ge . Depth. In such a case, we take the closest define: In addition we would like to compress the Firstly, we perform prediction using a value from the above range. We compress the (𝛼𝛼1,𝛼𝛼2, 𝛼𝛼3, …, 𝛼𝛼𝑘𝑘) 𝜍𝜍𝑘𝑘(𝛼𝛼̅) = transmitting data, to achieve a high speed predictor selected from a fixed set of 9 simple Residuum symbol that is a difference between 𝑙𝑙,𝑚𝑚 𝑙𝑙,𝑚𝑚 𝑙𝑙,𝑚𝑚 Communica tio ns [8]. For this purpose we the actual and the predicted {𝑥𝑥𝑙𝑙,𝑚𝑚 : 𝑥𝑥1 = 𝛼𝛼1,𝑥𝑥2 = 𝛼𝛼2, 𝑥𝑥3 = linear predictors. Prediction errors are Consist𝑙𝑙,𝑚𝑚 of all the pixels on the value of utilized a compression scheme which also We reorder residual values to 𝜂𝜂 get the 3 𝑘𝑘 𝑘𝑘 reordered to obtain probability distribution 𝛼𝛼 , …, 𝑥𝑥 = 𝛼𝛼 } for sample mean: 𝑥𝑥(𝑖𝑖, 𝑗𝑗) 𝑥𝑥 (𝑖𝑖,𝑗𝑗) 𝑘𝑘 uses multip le predictors. However the expected by the data model. probability distributio n close descriptive by 𝜍𝜍 predictors are generated using local statistics simply picking symbols : first, last, second, (𝛼𝛼1,𝛼𝛼2, 𝛼𝛼3, …, 𝛼𝛼𝑘𝑘) and are used based on a switching algorithm To predict the intensity of a specific pixel X, last but one and so on: 𝑥𝑥|𝛼𝛼 1 which relies on the correlation between pixe ls . we use fast linear predictors up to 3 𝜇𝜇 = 𝑘𝑘 ∑ 𝑥𝑥 ‖𝜍𝜍 (𝛼𝛼̅)‖ 𝑥𝑥𝑥𝑥𝑥𝑥 And in next step, chaos-based image neighbor ing pixels : first left-hand neighbor, 𝜂𝜂 encryption algorithm, in cipher architecture, is second upper neighbor , and third upper-left 𝑥𝑥 (𝑖𝑖,𝑗𝑗) 𝑛𝑛 1) N set of x observation proposed. The flowchar t of the algorithm is neighbor . 2𝑛𝑛(𝑖𝑖, 𝑗𝑗) 𝑓𝑓𝑓𝑓𝑓𝑓 𝑛𝑛(𝑖𝑖,𝑗𝑗) < 2 − 1 2) For each is in sequence of x on replace i: = { 𝑛𝑛 𝑛𝑛 shown in following flowchart. An image is 2(2 − 𝑛𝑛(𝑖𝑖, 𝑗𝑗)) 𝑓𝑓𝑓𝑓𝑓𝑓 𝑛𝑛(𝑖𝑖,𝑗𝑗) > 2 − 1 𝑖𝑖 producing a binary data stream with masking 𝑥𝑥 Lossless compression has eight linear The conditional exception of x set of 3) Let y target amount data of image with a random key stream by a 𝑦𝑦 = [𝑥𝑥𝑖𝑖−𝑛𝑛, …, 𝑥𝑥𝑖𝑖] predictive schemes named JPEG lossless observation in 4) Update all y amounts chaos-based random key stream generator algorithm. condition is: then corresponding encrypted image is Main algorithm of predictors: 𝑖𝑖 𝑦𝑦 1 2 3 formed. The specific details of each 1) First step make no scheme 𝑦𝑦 𝑦𝑦 𝑦𝑦 1 2 3 component are to be discussed in the 2) 1-D predictors 𝐼𝐼 𝑥𝑥 𝑥𝑥 𝑥𝑥 𝐸𝐸[𝑋𝑋|𝑌𝑌 ] = 4 following sections[9]. 𝑋𝑋 𝐼𝐼 𝑦𝑦 The∑ 𝑃𝑃 optimal[𝑋𝑋 = 𝑥𝑥 | value:𝑌𝑌 = 4 𝜂𝜂 1 2, 3 𝑁𝑁 𝑥𝑥 𝑌𝑌 , 𝑌𝑌 𝑌𝑌 , …, 𝑌𝑌 ] 𝑥𝑥 𝜂𝜂(𝑖𝑖,𝑗𝑗) = 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗) (Content bass matching windows) 𝑖𝑖,𝑗𝑗 𝑛𝑛 𝑚𝑚 Recently, Compression schemes have been 3)𝑥𝑥𝜂𝜂 2(-𝑖𝑖D,𝑗𝑗 )predictors= 𝑥𝑥(𝑖𝑖, 𝑗𝑗 − 1) Prediction by particle matching is method is 𝑥𝑥 𝑦𝑦 𝐸𝐸[𝑥𝑥𝑖𝑖,𝑗𝑗|(𝑥𝑥𝑖𝑖−𝑙𝑙,𝑦𝑦𝑗𝑗−𝑚𝑚)𝑙𝑙,𝑚𝑚] = 1 Pseudo-code: greatly developed by various researchers [1]– 𝑥𝑥 (𝑖𝑖,𝑗𝑗) = 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗 − 1) method to predict. The symbol depending on While (not last value of ) do [4]. 𝜂𝜂 pervious. This method is called MARKOV Read neighbors 𝑛𝑛 𝑥𝑥 (𝑖𝑖,𝑗𝑗) = 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗) − 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗 − 1) model in [10-13]. Shorten to 𝛼𝛼4 neighbors of This was introduced in order to solve the + 𝑥𝑥(𝑖𝑖, 𝑗𝑗 − 1) content problems which consist of the separation of 𝜂𝜂 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗) − 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗 − 1) Pixel we can define a set of pixels which While (context amount ( ) < 0 do 𝑥𝑥 (𝑖𝑖,𝑗𝑗) = { } independent sources using observed mixed 2 are neighborhood of as it context. That Escape sequence of 𝑖𝑖,𝑗𝑗 𝑘𝑘 texture without a strong knowledge about + 𝑥𝑥(𝑖𝑖, 𝑗𝑗 − 1) are depending𝑥𝑥 on the scanning and hence 𝜍𝜍 (𝛼𝛼̅) 𝜂𝜂 𝑖𝑖,𝑗𝑗 sources and, in particular lossless 𝑥𝑥(𝑖𝑖, 𝑗𝑗 − 1) − 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗 − 1) operational method.𝑥𝑥 The pixels Calculate average sample 𝑥𝑥 (𝑖𝑖,𝑗𝑗) = { } 1 2 3 𝑘𝑘 compression schemes rely on statistical 2 with set of value (mean𝛼𝛼 ,𝛼𝛼 (, 𝛼𝛼 ,)… , 𝛼𝛼 ) ( ) structure in the data. Lossless compression + 𝑥𝑥 𝑖𝑖 − 1, 𝑗𝑗 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 𝑖𝑖,𝑗𝑗 relay o statistical structure in the data and 𝜂𝜂 𝑥𝑥(𝑖𝑖, 𝑗𝑗 − 1) − 𝑥𝑥(𝑖𝑖 − 1, 𝑗𝑗) 1 2 3 𝑘𝑘 𝜇𝜇𝑥𝑥|𝛼𝛼 𝑥𝑥 (𝑖𝑖,𝑗𝑗) = { } 𝑥𝑥 , 𝑥𝑥 , 𝑥𝑥 , … , 𝑥𝑥 𝛼𝛼 = work on non-random data contain duplicated In this process is2 the pixel of (i,j) and infor matio n that determine the probability of the value of predictors. Predictor Correction occurring and assigning the smallest part of 𝜂𝜂 𝑥𝑥(𝑖𝑖, 𝑗𝑗) the most common data. 𝑥𝑥If (there𝑖𝑖,𝑗𝑗) is a subtraction operation in a calculation of the predictor, then its value may (Origina l image) (Compress image) This kind of algorithm is used in computing, Model Be out of the nominal range of pixel base for saving space and sending data through the intens ities [0; ], where N denotes web and viewing image online; The algorithm image bit. 𝑛𝑛(𝑖𝑖.𝑗𝑗) work in tow way; prediction and correction- 2 − 1 based conditional average. Figure 1. compression process

INTERNATIONAL JOURNAL OF ELECTRONICS, MECHANICAL AND MECHATRONICS ENGINEERING Vol.5 Num.2 - 2015 (955-962) 957 Fast and Lossless Image Compression in Chaos-Based Encryption

consist of two major parts, serving of init ia l A= Chaos-base image encryption scheme: the key and mixing base upon two different main idea of chaos-based image encryption chaotic maps. system is proposed in the diagram (2) that 12 ⋯ 𝑎𝑎𝑁𝑁 1 𝑎𝑎 ⋯ 0 1 0 12 12 12 0 0 𝑏𝑏 1 + 𝑎𝑎 𝑏𝑏 0 0 0 0 0 0 … ⋱ ⋮ … 0 1 … ⋱ ⋮ Original Encryption ⋮ ⋮ ⋮ 1 0 ⋮ 1 0 𝑀𝑀 𝑁𝑁 𝑀𝑀 image [ 0 0 … 1 ] [𝑏𝑏 0 … 1 + 𝑎𝑎 𝑏𝑏 ] ⋯ 𝑎𝑎𝑁𝑁 (Data stream) (encription data stream) (encript image) 1 0 ⋯ 0 1 0 𝑂𝑂 1 𝑎𝑎23 0 0 0 1 0 32 × 0 𝑏𝑏 … ⋱ ⋮ … 0 1 … ⋱ ⋮ ⋮ ⋮ ⋮ 1 0 ⋮ 1 0 𝑁𝑁−1 𝑀𝑀−1 Where are integer in [0, [0 ] 0.This… 1 ] [0 0 … 1 + 𝑎𝑎 𝑏𝑏 ] 𝑙𝑙−1 (1) With a user key, construct the parameters high-dimensional𝑁𝑁 𝑀𝑀 Cat map, , is used as our (key stream generator) 𝑎𝑎 , 𝑏𝑏 2 needed for the key generator. The post-processing unit for mixing up the init ia l 𝑐𝑐 computational procedures are to be discussed Figure 2. encription procces key stream. ℎ in above.

(2) The image is firstly transformed into a To generating the random key stream , the first A= standard data stream (Fig. 1). Taking an image should be created. For first key the following the useful way for sending secret data without in true color with (N*M) pixels as an example, if each pixel mathematice formolas describe: data integrity is bite sequence as key. 1 1 1 2 13 1 4 15 1 𝑀𝑀 2 3 2 4 (𝑀𝑀−1) ,𝑀𝑀 consists of RGB format, a stream of total 𝐴𝐴Is an𝐴𝐴 matrix𝐴𝐴 M*M𝐴𝐴 𝐴𝐴 with… 𝐴𝐴each𝐴𝐴 𝐴𝐴 mixing… 𝐴𝐴 I th Therefore, adds this to plain text to form of the data can be formed by partitioning the bits and j th dimentio n in details : 𝑖𝑖 𝑖𝑖 𝑗𝑗 cryptogram like bellow chart. obtained from pixels. 𝑐𝑐 𝐴𝐴 𝑥𝑥𝑛𝑛=1 = 𝑓𝑓(𝑥𝑥𝑛𝑛) 3) For each data , it will be masked by the 𝑛𝑛 𝑛𝑛 𝑥𝑥 𝑥𝑥 key stream with the following function: 𝑔𝑔 ( ) 𝑖𝑖𝑖𝑖0 < 𝑙𝑙 < 𝑝𝑝 𝑖𝑖 𝑖𝑖 𝑚𝑚 𝑝𝑝𝑙𝑙 2 + 1 k 𝑖𝑖 = 𝑛𝑛 4) The encrypted data𝑙𝑙 stream is converted𝑐𝑐 = 2 + 1 − 𝑥𝑥 𝑖𝑖 𝑖𝑖 𝑖𝑖−1 𝑖𝑖 𝑖𝑖 ( ) 𝑔𝑔 ( ) 𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑚𝑚 𝑐𝑐 back𝑑𝑑 + 𝑘𝑘into+ 𝑐𝑐 RGB𝑚𝑚𝑚𝑚 𝑚𝑚 format2 for storage or 1 − 𝑝𝑝 In {this formolus p , {1,2,…., } Sequence transmiss io n. Decryption is similar to and the first value of g(0) function. 𝑙𝑙 encryption, except that the following 𝑛𝑛 generator Which can be flooring.𝜖𝜖[0,1 ] This𝑥𝑥 𝜖𝜖this randome 2 decryptions functio n : 0 algorithm𝑥𝑥 is so weak and not good enough due 𝑠𝑠𝑖𝑖 Is decrypting sequence[13- Figure 3. key generator key generator 𝑖𝑖 𝑖𝑖 𝑖𝑖 to its randome process therefore, we are using 15]. 𝑙𝑙 𝐷𝐷̂ = (𝑐𝑐 −𝑘𝑘 − 𝑖𝑖−1 𝑖𝑖 The key can be parameter in f and first state is 𝑑𝑑 )𝑚𝑚𝑚𝑚𝑚𝑚2 𝐷𝐷̂

. high dimentional map to mixing up the Byte-based stream cipher with initia l =k In order to validate our approach several 0 𝑖𝑖 𝑖𝑖−1 𝑖𝑖 𝑖𝑖 𝑖𝑖 𝑖𝑖 𝑖𝑖 sequence generator. This theory in[4] for𝑠𝑠 𝑠𝑠I in= 0,…𝑓𝑓(𝑘𝑘, 𝑠𝑠255 )and, k 0,…,255= 𝑔𝑔(𝑠𝑠 ) equal, 𝑐𝑐 = to𝑚𝑚 ⨁ k simulations are conducted. “Lena” Is serving the porpose 𝑠𝑠[𝑘𝑘] compressed image are encrypted and Cat map is formed by: 0 1 … i 255 decrypted by the proposed method. 512×512 : y=Ax mod 𝑠𝑠[𝑘𝑘] + 𝑘𝑘[𝑖𝑖] ↔ 𝑠𝑠[𝑗𝑗] + 𝑘𝑘[𝑖𝑖] color JPEG format files are used as the 0 1 … j 255 Where x=[ 𝑙𝑙 and origina l images. An example of the 𝑐𝑐 𝑖𝑖 ℎy=[ 2 𝑡𝑡 𝑠𝑠 simulatio ns is shown in Fig. 8. The first row 1 2 3 4, 𝑚𝑚 { 𝑗𝑗 𝑥𝑥 ,𝑥𝑥 , 𝑥𝑥𝑡𝑡 ,𝑥𝑥 …, 𝑥𝑥 ] Figure 4. first key stream 𝑠𝑠 of Fig.4 shows the original source images (a), 1 2 3 [0,4, ] 𝑛𝑛 𝑖𝑖 𝑦𝑦 , 𝑦𝑦 , 𝑦𝑦 , 𝑦𝑦 …𝑙𝑙−1, 𝑦𝑦 ] 𝑘𝑘 𝑖𝑖 𝑗𝑗 958𝑥𝑥 𝑎𝑎𝑎𝑎𝑎𝑎 𝑦𝑦 𝜖𝜖 2 Sajad EINY, Solmaz EINI consist of two major parts, serving of init ia l A= Chaos-base image encryption scheme: the key and mixing base upon two different main idea of chaos-based image encryption chaotic maps. system is proposed in the diagram (2) that 12 ⋯ 𝑎𝑎𝑁𝑁 1 𝑎𝑎 ⋯ 0 1 0 12 12 12 0 0 𝑏𝑏 1 + 𝑎𝑎 𝑏𝑏 0 0 0 0 0 0 … ⋱ ⋮ … 0 1 … ⋱ ⋮ Original Encryption ⋮ ⋮ ⋮ 1 0 ⋮ 1 0 𝑀𝑀 𝑁𝑁 𝑀𝑀 image [ 0 0 … 1 ] [𝑏𝑏 0 … 1 + 𝑎𝑎 𝑏𝑏 ] ⋯ 𝑎𝑎𝑁𝑁 (Data stream) (encription data stream) (encript image) 1 0 ⋯ 0 1 0 𝑂𝑂 1 𝑎𝑎23 0 0 0 1 0 32 × 0 𝑏𝑏 … ⋱ ⋮ … 0 1 … ⋱ ⋮ ⋮ ⋮ ⋮ 1 0 ⋮ 1 0 𝑁𝑁−1 𝑀𝑀−1 Where are integer in [0, [0 ] 0.This… 1 ] [0 0 … 1 + 𝑎𝑎 𝑏𝑏 ] 𝑙𝑙−1 (1) With a user key, construct the parameters high-dimensional𝑁𝑁 𝑀𝑀 Cat map, , is used as our (key stream generator) 𝑎𝑎 , 𝑏𝑏 2 needed for the key generator. The post-processing unit for mixing𝑐𝑐 up the init ia l Figure 2. encription procces key stream. ℎ computational procedures are to be discussed in above. (2) The image is firstly transformed into a To generating the random key stream , the first A= standard data stream (Fig. 1). Taking an image should be created. For first key the following the useful way for sending secret data without in true color with (N*M) pixels as an example, if each pixel mathematice formolas describe: data integrity is bite sequence as key. 1 1 1 2 13 1 4 15 1 𝑀𝑀 2 3 2 4 (𝑀𝑀−1) ,𝑀𝑀 consists of RGB format, a stream of total 𝐴𝐴Is an𝐴𝐴 matrix𝐴𝐴 M*M𝐴𝐴 𝐴𝐴 with… 𝐴𝐴each𝐴𝐴 𝐴𝐴 mixing… 𝐴𝐴 I th Therefore, adds this to plain text to form of the data can be formed by partitioning the bits and j th dimentio n in details : 𝑖𝑖 𝑖𝑖 𝑗𝑗 cryptogram like bellow chart. obtained from pixels. 𝑐𝑐 𝐴𝐴 𝑥𝑥𝑛𝑛=1 = 𝑓𝑓(𝑥𝑥𝑛𝑛) 3) For each data , it will be masked by the 𝑛𝑛 𝑛𝑛 𝑥𝑥 𝑥𝑥 key stream with the following function: 𝑔𝑔 ( ) 𝑖𝑖𝑖𝑖0 < 𝑙𝑙 < 𝑝𝑝 𝑖𝑖 𝑖𝑖 𝑚𝑚 𝑝𝑝𝑙𝑙 2 + 1 k 𝑖𝑖 = 𝑛𝑛 4) The encrypted data𝑙𝑙 stream is converted𝑐𝑐 = 2 + 1 − 𝑥𝑥 𝑖𝑖 𝑖𝑖 𝑖𝑖−1 𝑖𝑖 𝑖𝑖 ( ) 𝑔𝑔 ( ) 𝑜𝑜𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑚𝑚 𝑐𝑐 back𝑑𝑑 + 𝑘𝑘into+ 𝑐𝑐 RGB𝑚𝑚𝑚𝑚 𝑚𝑚 format2 for storage or 1 − 𝑝𝑝 In {this formolus p , {1,2,…., } Sequence transmiss io n. Decryption is similar to and the first value of g(0) function. 𝑙𝑙 encryption, except that the following 𝑛𝑛 generator Which can be flooring.𝜖𝜖[0,1 ] This𝑥𝑥 𝜖𝜖this randome 2 decryptions functio n : 0 algorithm𝑥𝑥 is so weak and not good enough due 𝑠𝑠𝑖𝑖 Is decrypting sequence[13- Figure 3. key generator key generator 𝑖𝑖 𝑖𝑖 𝑖𝑖 to its randome process therefore, we are using 15]. 𝑙𝑙 𝐷𝐷̂ = (𝑐𝑐 −𝑘𝑘 − 𝑖𝑖−1 𝑖𝑖 The key can be parameter in f and first state is 𝑑𝑑 )𝑚𝑚𝑚𝑚𝑚𝑚2 𝐷𝐷̂

. high dimentional map to mixing up the Byte-based stream cipher with initia l =k In order to validate our approach several 0 𝑖𝑖 𝑖𝑖−1 𝑖𝑖 𝑖𝑖 𝑖𝑖 𝑖𝑖 𝑖𝑖 sequence generator. This theory in[4] for𝑠𝑠 𝑠𝑠I in= 0,…𝑓𝑓(𝑘𝑘, 𝑠𝑠255 )and, k 0,…,255= 𝑔𝑔(𝑠𝑠 ) equal, 𝑐𝑐 = to𝑚𝑚 ⨁ k simulations are conducted. “Lena” Is serving the porpose 𝑠𝑠[𝑘𝑘] compressed image are encrypted and Cat map is formed by: 0 1 … i 255 decrypted by the proposed method. 512×512 : y=Ax mod 𝑠𝑠[𝑘𝑘] + 𝑘𝑘[𝑖𝑖] ↔ 𝑠𝑠[𝑗𝑗] + 𝑘𝑘[𝑖𝑖] color JPEG format files are used as the 0 1 … j 255 Where x=[ 𝑙𝑙 and origina l images. An example of the 𝑐𝑐 𝑖𝑖 ℎy=[ 2 𝑡𝑡 𝑠𝑠 simulatio ns is shown in Fig. 8. The first row 1 2 3 4, 𝑚𝑚 { 𝑗𝑗 𝑥𝑥 ,𝑥𝑥 , 𝑥𝑥𝑡𝑡 ,𝑥𝑥 …, 𝑥𝑥 ] Figure 4. first key stream 𝑠𝑠 of Fig.4 shows the original source images (a), 1 2 3 [0,4, ] 𝑛𝑛 𝑖𝑖 𝑦𝑦 , 𝑦𝑦 , 𝑦𝑦 , 𝑦𝑦 …𝑙𝑙−1, 𝑦𝑦 ] 𝑘𝑘 𝑖𝑖 𝑗𝑗 𝑥𝑥 𝑎𝑎𝑎𝑎𝑎𝑎 𝑦𝑦 𝜖𝜖 2 INTERNATIONAL JOURNAL OF ELECTRONICS, MECHANICAL AND MECHATRONICS ENGINEERING Vol.5 Num.2 - 2015 (955-962) 959 Fast and Lossless Image Compression in Chaos-Based Encryption the images in the second row were obtained for the embedding text ensures the protection Annual Allerton Conf., Oct. 2002, pp. by applying optimize chaotic to the of data against any intruder attack. In addition, 576–585. compressed image in (b), and the last row the user has been given the freedom of corresponds the reconstructed images which choosing the key and using it by anyway s/he [8] T. J. Richardson and R. L. Urbanke, the receiver can obtain (c). After execution of likes. Further research over the proposed “The capacity of low-density cat map and applying chaotic algorithm to the method has also been discussed so that studies paritycheck codes under message- compressed components with the random key on this Stream can be continued smoothly. passing decoding,” IEEE Trans. generator, we can get the source images. Inform. Theory, vol. 47, pp. 599–618, Feb. 2001. The quality of the reconstructed images, [1] “HDCP specification rev 1.3,” Dec. however, is not as same as the original ones, 2006. [9] W. Hong, T. Chen, and C. Shiu, because compression cut off higher frequency “Lossless Steganography for components. Moreover, the order of the Figure 4c. recovered image [2] M. Johnson, P. Ishwar, V. M. AMBTC-Compressed Images”, IEEE outputs is not always same as that of the Prabhakaran, D. Schonberg, and K. Congress on Image and Signal origina l images. In this test the below table shows ability of this Ramchandran, “On compressing Processing, Vol. 2, pp. 13-17, July algorithm: encrypted data,” in IEEE Trans. Signal 2008, DOI: 10.1109/CISP.2008.638. Ite ms value Processing, Oct. 2004, vol. 52, pp. PSNR 78.04 2992–3006. [10] A.M. Fard, M.-R. Akbarzadeh-T, and MCSE 0.002 F. Varasteh-A, “A New Genetic ENTROPY 7.62 [3] D. Slepian and J. K. Wolf, “Noiseless Algorithm Approach for Secure JPEG The picture of histogram shows no different coding of correlated information Steganography”, IEEE Internatio na l between original image and recovered image. sources,” IEEE Trans. Inform. Theory, Conference on Engineering of vol. 19, pp. 471–480, Jul. 1973. Intelligent Systems, pp. 1-6, September 2006, DOI: [4] C. Shannon, “Communication theory 10.1109/ICEIS.2006.1703168. of secrecy systems,” in Bell System Technical Journal , 1949, vol. 28, pp. [11] M. Ishaque, and S.A. Sattar, “Quality 656–715. Based JPEG Steganography Using Balanced Embedding Technique”, Figure 4a. Orginalimage [5] F. Kschischang, B. Frey, and H. IEEE International Conference on Loeliger, “Factor graphs and the sum Emerging Trends in Engineering and product algorithm,” in IEEE Trans. Technology, pp. 215-221, January Inform. Theory, Feb. 2001, vol. 47, 2010, DOI: Figure 5. histogram diagram pp. 498–519. 10.1109/ICETET.2009.188.

Conclusio n: [6] R. G. Gallager, Low Density Parity [12] M. Hasan and K. M. Nur, “A Lossless In this paper, we presented a novel image Check Codes, Ph.D. thesis, MIT, Image Compression Technique using encryption technique for compressed domain. Cambridge, MA, 1963. Location Based Approach ”, Our proposed technique can work efficiently International Journal of Scientific and and independently regardless of the image [7] D. Schonberg, K. Ramchandran, and Technology Research (IJSTR), vol. 1, size, quality and dimens io n. The experime n ta l S. S. Pradhan, “LDPC codes can issue. 2, March 2012. results shown in this paper proved that the approach the Slepian Wolf bound for encryption of the proposed method is general binary sources,” in 40th [13] M. D. Lema and O. R. Mitchel, extremely high if the relative compression “Absolute Moment Block Truncation Figure 4b. encripted and copressed ratio is compromised. Double layer of security Coding and its Application to Color

960 Sajad EINY, Solmaz EINI the images in the second row were obtained for the embedding text ensures the protection Annual Allerton Conf., Oct. 2002, pp. by applying optimize chaotic to the of data against any intruder attack. In addition, 576–585. compressed image in (b), and the last row the user has been given the freedom of corresponds the reconstructed images which choosing the key and using it by anyway s/he [8] T. J. Richardson and R. L. Urbanke, the receiver can obtain (c). After execution of likes. Further research over the proposed “The capacity of low-density cat map and applying chaotic algorithm to the method has also been discussed so that studies paritycheck codes under message- compressed components with the random key on this Stream can be continued smoothly. passing decoding,” IEEE Trans. generator, we can get the source images. Inform. Theory, vol. 47, pp. 599–618, Feb. 2001. The quality of the reconstructed images, [1] “HDCP specification rev 1.3,” Dec. however, is not as same as the original ones, 2006. [9] W. Hong, T. Chen, and C. Shiu, because compression cut off higher frequency “Lossless Steganography for components. Moreover, the order of the Figure 4c. recovered image [2] M. Johnson, P. Ishwar, V. M. AMBTC-Compressed Images”, IEEE outputs is not always same as that of the Prabhakaran, D. Schonberg, and K. Congress on Image and Signal origina l images. In this test the below table shows ability of this Ramchandran, “On compressing Processing, Vol. 2, pp. 13-17, July algorithm: encrypted data,” in IEEE Trans. Signal 2008, DOI: 10.1109/CISP.2008.638. Ite ms value Processing, Oct. 2004, vol. 52, pp. PSNR 78.04 2992–3006. [10] A.M. Fard, M.-R. Akbarzadeh-T, and MCSE 0.002 F. Varasteh-A, “A New Genetic ENTROPY 7.62 [3] D. Slepian and J. K. Wolf, “Noiseless Algorithm Approach for Secure JPEG The picture of histogram shows no different coding of correlated information Steganography”, IEEE Internatio na l between original image and recovered image. sources,” IEEE Trans. Inform. Theory, Conference on Engineering of vol. 19, pp. 471–480, Jul. 1973. Intelligent Systems, pp. 1-6, September 2006, DOI: [4] C. Shannon, “Communication theory 10.1109/ICEIS.2006.1703168. of secrecy systems,” in Bell System Technical Journal , 1949, vol. 28, pp. [11] M. Ishaque, and S.A. Sattar, “Quality 656–715. Based JPEG Steganography Using Balanced Embedding Technique”, Figure 4a. Orginalimage [5] F. Kschischang, B. Frey, and H. IEEE International Conference on Loeliger, “Factor graphs and the sum Emerging Trends in Engineering and product algorithm,” in IEEE Trans. Technology, pp. 215-221, January Inform. Theory, Feb. 2001, vol. 47, 2010, DOI: Figure 5. histogram diagram pp. 498–519. 10.1109/ICETET.2009.188.

INTERNATIONAL JOURNAL OF ELECTRONICS, MECHANICAL AND MECHATRONICS ENGINEERING Vol.5 Num.2 - 2015 (955-962) 961 Images”, IEEE Transactions on communications, Vol. 32, Number.10, pp. 1148-1157, 1984, DOI: 10.1109/TCOM.1984.1095973.

[14] Z. Zhao and L. Tang , “High Capacity Reversible Data Hiding in AMBTC - Compressed Images ”, Internatio nal Journal of Digital Content Technology and its Applications, Vol. 6, Number 2, February 2012.

[15] C. Velasco, M. Nakano, H. Perez, R. Martinez, and K. Yamaguchi, “Adaptive JPEG Steganography using Convolutional Codes and Synchronization Bits in DCT Domain”, IEEE Internatio na l Midwe s t Symposium on Circuits and Systems , pp. 842-847, September 2009, DOI: 10.1109/MWSCAS.2009.5235899.

962 Images”, IEEE Transactions on Design Equations from Geometric Programming communications, Vol. 32, Number.10, Doi:Robert 10.17932/ C. IAU.IJEMME.m.21460604.2015.5/3.963-968CREESE pp. 1148-1157, 1984, DOI:

10.1109/TCOM.1984.1095973. Robert C. CREESE1

[14] Z. Zhao and L. Tang , “High Capacity Geometric programming is an optimization tool that permits the development of design Reversible Data Hiding in AMBTC - Abstractrelationships. Most researchers do not develop the design relationships, but only solve the specific Compressed Images ”, Internatio nal Geometricoptimization programming problem for is a an set optimization of specific inputtool that parameters permits the and development a new solutio of n design must relationships. be develop e d Journal of Digital Content Technology for any changes. and its Applications, Vol. 6, Number Most researchers do not develop the design relationships, but only solve the specific optimization 2, February 2012. problem for a set of specific input parameters and a new solution must be developed for any changes. For some problems with few degrees of difficulty, design relations can be developed which given [15] C. Velasco, M. Nakano, H. Perez, R. Foran insight some problemsinto the importance with few degrees of the input of difficulty, constants . design An example relations from can abe previous developed paper which using given the Martinez, and K. Yamaguchi, anCobb insight-Douglas into theproduction importance function of the is input used constants. to illustrate An the example development from a ofprevious design paper relationships. using the “Adaptive JPEG Steganography using Cobb-Douglas production function is used to illustrate the development of design relationships. Convolutional Codes and Keywords: Geometric Programming, Design Equation Development, Cobb-Douglas production Synchronization Bits in DCT Keywords: Geometric Programming, Design Equation Development, Cobb-Douglas production function Domain”, IEEE Internatio na l Midwe s t function Symposium on Circuits and Systems , pp. 842-847, September 2009, DOI: 10.1109/MWSCAS.2009.5235899. Clarence Zener is credited as being the father a dual formula tio n. The primal proble m of geometric programming with the formulatio n is somewhat simila r to the publishing of the paper "A mathematical aid primal formula tio n in linear programmin g, in optimizing engineering designs" in the and is often solved by traditional search Proceedings of the National Academy of methods. The dual formulation is harder to Science[1] in 1961. He is better known for formulate, but is much easier to solve. The the invention of the Zener diode. He later co- authored with Richard Duffin and Elmor design equations can be found by utilizing the Peterson the book "Geometric primal-dual relationships. The example Programming"[2] in 1967 published by John presented will be with zero degrees of Wiley. Several books have been written diffic ulty to illustrate the solution procedure about geometric programming, but fe w for finding the design equations. It is easie r consider or emphasize the development of to determine the design equations for cost design equations. models than it is for profit models.

The mathematics of geometric programming The example presented is that of Ibrahim are rather complex and presented in more Guney and Ersoy Oz in the paper " An detail in the references presented[3-5]. Applicatio n of Geometric Programming "[ 6 ] Geometric programming is similar to line a r in Vol. 2 of the Internal Journal of programming in that it has both a primal and Electronics, Mechanical and Mathematics

1 Professor Emeritus, Industrial and Management Systems Engineering, Benjamin M. Statler College of Engineering and Mineral Resources, West Virginia University, West Virginia, USA, [email protected]

963 Design Equations from Geometric Programming

Engineering. This example concerns the M Tm σ ω σ minimiza tio n of production costs for a fixe d d(ω) = σ [ ∏ ∏ (Cmtωm0 /ωmt) mt mt ] production level using the Cobb-Douglas (2) production function. m=0 t=1

The basic formulations of the primal and dual for m = 0,1,2,...M and t = 1,2,....Tm will be shown and then the example will be presented following the steps of the where formulations. One of the requirements for σ = signum function for objective function geometric programming is that the terms ( 1 for minimiza tio n and -1 fo r used are posynomials, that is, they are maximiza tio n) positive polynomials. That prohibits σmt = signum function for dual constraints functions such as the sin(x) and fractiona l (± 1) powers that cannot be expanded, such as (2 + Cmt > 0 positive constant coefficients 3.3 4x) . ωm0 = dual variables from the line a r inequality constraints The primal problem is formula ted as: ωmt = dual variables of dual constraints σmt = signum function for dual constraints Tm N ω00 = 1 mtn Ym(x) =∑σmtCmt ∏ x for m=0,1,2..M The dual is formulated from four conditions (1) t=1 n=1 First, a normality condition is expressed by: where Tm σmt = ±1 (signum function to indicate sign ∑ σ0t ω0t = σ where σ = ±1 of (3) term ) t=1 Cmt > 0 positive constant coefficients Ym(x) ≤1 for the constraints, m=1,2,... M and Y0(x) = objective function σ0t = signum of dual objective function terms ω0t = dual variables for dual objective The dual formula tio n initia lly appears mor e function terms complex, but it results in several line a r equations which are easier to solve. The dual The second conditions are the N orthogonal objective function is not linear and is solve d conditions after the dual variables have been determined from the dual formulation model. The dual M Tm objective function is :

964 Robert C. CREESE

Engineering. This example concerns the M Tm ∑ ∑ σmt amtn ωmt = 0 Once the dual variables are determined, the σ ω σ minimiza tio n of production costs for a fixe d d(ω) = σ [ ∏ ∏ (Cmtωm0 /ωmt) mt mt ] (4) primal variables can be determined from the production level using the Cobb-Douglas (2) m=0 t=1 relationships between the primal and dual production function. m=0 t=1 variables. As in linear programming, the where primal and dual objective functions must be The basic formulations of the primal and dual for m = 0,1,2,...M and t = 1,2,....Tm σmt = signum of constraint term equal and thus Y0(x) and d(ω) are equal. The will be shown and then the example will be amtn = exponent of design variable term in two equations relating the primal and dua l presented following the steps of the where primal for determining the primal variables are: formulations. One of the requirements for σ = signum function for objective function ωmt = dual variable of dual constraint geometric programming is that the terms ( 1 for minimiza tio n and -1 fo r N mtn used are posynomials, that is, they are maximiza tio n) The third condition is the T non-negativit y C0t ∏ xn = ω0t σ d(ω) (8) positive polynomials. That prohibits σmt = signum function for dual constraints conditions that require that the dual variables n=1 functions such as the sin(x) and fractiona l (± 1) must not be negative, that is: powers that cannot be expanded, such as (2 + Cmt > 0 positive constant coefficients and 3.3 4x) . ωm0 = dual variables from the line a r ωmt ≥ 0 for m= 0,1,2,.M and t=1,2,3,..Tm inequality (5) N mtn constraints Cmt ∏ xn = ωmt / ωm0 (9) The primal problem is formula ted as: ωmt = dual variables of dual constraints The fourth condition is the M linear n=1 σmt = signum function for dual constraints inequality constraints expressed by: Tm N ω00 = 1 for t=1,2,...Tm and m = 1,2,...M mtn Ym(x) =∑σmtCmt ∏ x for m=0,1,2..M The dual is formulated from four conditions Tm (1) ωm0 = σm ∑ σmt ωmt ≥ 0 (6) t=1 n=1 First, a normality condition is expressed by: t=1 The initia l formula tio n is to minimize labo r where Tm The complexity of a problem is indicated by and capital costs to obtain a specific output σmt = ±1 (signum function to indicate sign ∑ σ0t ω0t = σ where σ = ±1 the number of degrees of difficulty(D). The level. The model by Guney and Oz() is of (3) higher the degree of difficulty, the more slightly modified and can be stated in its term ) t=1 difficult the problem is to solve. The formula primal form as: Cmt > 0 positive constant coefficients for determining the degrees of difficulty is: Ym(x) ≤1 for the constraints, m=1,2,... M and Y(x) = r1x1 + r2x2 (10) Y0(x) = objective function σ0t = signum of dual objective function terms D = T - (N + 1) (7) ω0t = dual variables for dual objective subject to the Cobb-Douglas production The dual formula tio n initia lly appears mor e function terms where constraint complex, but it results in several line a r T = number of terms in the primal α β equations which are easier to solve. The dual The second conditions are the N orthogonal formulatio n q = A x1 x2 (11) objective function is not linear and is solve d conditions N=number of orthogonal conditions (which after the dual variables have been determined is equivale nt to the number of primal where from the dual formulation model. The dual M Tm variables) x1 = labor amount objective function is : r1 = labor rate

INTERNATIONAL JOURNAL OF ELECTRONICS, MECHANICAL AND MECHATRONICS ENGINEERING Vol.5 Num.2 - 2015 (963-968) 965 Design Equations from Geometric Programming

x2 = capital amount Eqn 4 (x1) ω01 -α ω11 = 0 r2 = capital rate (14) q = desired output level Eqn 4 (x2) ω01 -β ω 11 = 0 A = total productivity factor (15) α = labor elasticity β = capital elasticity Solving Eqns 13-15 for the dual variables one obtains: The constraints must be written in the form of inequalities with the right hand side being ω01 = (α / (α + β )) (16) unity and thus the constraint becomes: ω02 = (β / (α + β )) (17) -α -β (q/A) x1 x2 ≤ 1 (12 ) ω11 = (1 / (α + β )) (18) Thus the primal objective function is given in Eqn. 10 and Eqn 12.is the constraint. The number of degrees of difficulty using Eqn 7 Now ω10 can be determined using Eqn 6 and is: is

D = 3 - (2 + 1) = 0 ω10 = σ10 ∑ σmt ωmt = 1*(1 * (1/(α + β))) = 1/(α + β) (19) The degrees of freedom must be greater than or equal to zero. The dual objective function of Eqn 2 can now be determined and is: Since all the terms in Eqns. 10 and 12 are (1*( α/(α+β)) positive, the signum values are all positive , d(ω)= 1* [{r1*1/(α/(α+β))} * (1*( β/(α+β)) (1*/(α+β)) 1 that is {r2*1/(β/(α+β))} * {q/A} ] (20) σ00 = 1 (objective function is minimiza tio n) Note that both ω11 and ω 10 are equal. Now σ01 = 1 using the primal-dual relationship of Eqn. 8 σ02 = 1 for the two terms of the objective functio n, σ11 = 1 one obtains: σ10 = 1 (RHS of constraint is positive) r1x1 = (α(α +β)) *1* d(ω) (21) The dual can be formulated using Eqns.3, 4 and 6 as: r2x2 = (β(α +β)) *1* d(ω) (22) Eqn 3 ω01 + ω 02 =1 Solving Eqns. 21 and 22 for x1 one obtains: (13) x1 = (α/β) (r2 / r1 ) x2 (23)

966 Robert C. CREESE

x2 = capital amount Eqn 4 (x1) ω01 -α ω11 = 0 Now using Eqn 22 in Eqn 11and solving for Table 1. Yearly Input Data for Estimate r2 = capital rate (14) x2: Calculations q = desired output level Eqn 4 (x2) ω01 -β ω 11 = 0 (1/(α + β)) (-α/(α + β)) A = total productivity factor (15) x2 = (q/A) (αr2/βr1) (24) Year Production Labor Capital α = labor elasticity Index q Index Index β = capital elasticity Solving Eqns 13-15 for the dual variables Using Eqn 24 in Eqn 21 x1 is found to be r1 r2 one obtains: 2006 118.4 121.88 114.32 The constraints must be written in the form 2007 124.9 137.80 122.32 (1/(α + β)) (β(α + β)) of inequalities with the right hand side being ω01 = (α / (α + β )) (16) x1 = (q/A) (αr2/βr1) (25) 2008 115.6 153.85 140.06 unity and thus the constraint becomes: 2009 96.4 158.53 131.48 ω02 = (β / (α + β )) (17) The primal objective function can now be -α -β (q/A) x1 x2 ≤ 1 (12 ) determined from the primal variables and The results for x1 and x2, the labor and capital ω11 = (1 / (α + β )) (18) Eqn 10 becomes estimates, were in complete agreement with Thus the primal objective function is given in those of Guney and Oz[6] so only one set (1/(α + β)) (β(α + β)) Eqn. 10 and Eqn 12.is the constraint. The Y(x) = r1 * (q/A) (αr2/βr1) + are included in results given inTable 2. The (1/(α + β)) (-α/(α + β)) number of degrees of difficulty using Eqn 7 Now ω10 can be determined using Eqn 6 and r2 * (q/A) (αr2/βr1) primal and dual values of the objective is: is (26) function from Equations 20 and 26 are identical as expected and although the D = 3 - (2 + 1) = 0 ω10 = σ10 ∑ σmt ωmt = 1*(1 * (1/(α + β))) Equations 20 and 26 have quite different objective function was not given in the = 1/(α + β) (19) appearances, but the numerical values will be reference[6], it would most likely have been The degrees of freedom must be greater than the same. the same. In the model equations presented, or equal to zero. The dual objective function of Eqn 2 can now the values for A, α, and β from the Cobb- be determined and is: Douglas production equation could be varied Since all the terms in Eqns. 10 and 12 are The equations developed were used to and a sensitivity analysis of these parameters (1*( α/(α+β)) positive, the signum values are all positive , d(ω)= 1* [{r1*1/(α/(α+β))} * compare with the data reported by Guney and could be evaluated and would not require (1*( β/(α+β)) (1*/(α+β)) 1 that is {r2*1/(β/(α+β))} * {q/A} ] Oz[6] on the construction sector in Turkey. resolving the adjusted problem. (20) The input values are given in Table 1 and the σ00 = 1 (objective function is output values are in Table 2. The input minimiza tio n) Note that both ω11 and ω 10 are equal. Now values of A, α, and β were fixed at 1.0, 0.53, σ01 = 1 using the primal-dual relationship of Eqn. 8 and 0.47 for all four reported cases. σ02 = 1 for the two terms of the objective functio n, σ11 = 1 one obtains: σ10 = 1 (RHS of constraint is positive) r1x1 = (α(α +β)) *1* d(ω) (21) The dual can be formulated using Eqns.3, 4 and 6 as: r2x2 = (β(α +β)) *1* d(ω) (22) Eqn 3 ω01 + ω 02 =1 Solving Eqns. 21 and 22 for x1 one obtains: (13) x1 = (α/β) (r2 / r1 ) x2 (23)

INTERNATIONAL JOURNAL OF ELECTRONICS, MECHANICAL AND MECHATRONICS ENGINEERING Vol.5 Num.2 - 2015 (963-968) 967 OPTIMIZING BUS LINES in URBAN PUBLIC TRANSPORTATION by COST and Table 2. Out put Values of Model for TRIP CALCULATION METHODS: A SOFTWARE MODEL DESIGN Estimates. [1] Clarence Zener, "A Mathematical Aid in Optimizing Engineering Designs", Ferdi Sönmez Yea Labor Capita Primal Dual Proceedings of the National Academy of r Estima l Total Total Sciences, vol. 47, pp 537-539. Abstract te Estima Cost Cost Planning of a public transport system in an ordered way is the key which offers potential users a x1 te (Y) d(ω) [2] Duffin, R.J., Peterson, E.L. Zener. C.M., x2 Geometric Programming - Theory and mode of transport. To attract travelers from other modes of transport, sufficiently attractive 200 121.56 114.93 27955. 27955. Applications, John Wiley & Sons, New York overall journey times must be provided, so reducing traffic congestion and obtaining delivered 6 11 11 1967 benefits like road safety and lower atmospheric and noise pollution. The congestion that close with 200 124.96 124.84 32488. 32488. 7 98 98 [3] Wilde, D.J. Beightler, C.S., increasing demand is becoming a part of our lives and it is complicating our lives. Some work is 200 117.03 114.00 33973. 33973. Fundamentals of Optimization, Prentic e - done to reduce the traffic congestion. If we want to provide an efficient and balanced layout in 8 0 08 08 Hall, Englewood Cliffs, New Jersey, pp 99- public transport system, we must place the right stop at the right places. Hence, we consider some 200 93..41 99.88 27941. 27941. 133, 1967. 8 39 39 components like cost, security, noise pollution, etc. In this study, it is aimed to solve a set covering [4] Zener, C., Engineering Design by problem for locating the smallest number possible of bus stops. Geometric Programming, John Wiley & The development of design equations for a Sons, New York 1971. Keywords: Bus Stop Spacing, Bi-Level Optimization Model, Trip Demand, O-D Matrix. geometric programming model of from data [5] Beightler, C. and Phillips, D.T. Applied of the construction sector in Turkey. These Geometric Programming, John Wiley & design equations ( Eqns. 20,24,25,and 26) Purpose of this work is to make an optimal problem we use the estimation method [2, 3]. give the solutions for the model outputs and Sons, New York 1976. bus stop location and spacing model which Once a decision is made to modify the the model does not need to be resolved. The minimizes the operator cost of all the design equations for the variables x1 and x2 [6] I. Guney, E. Oz, " An Application of transport system, examine the equilibrium location of bus stops in an area then changes can then be used to determine the total cost to Geometric Programming", International travel costs by installing the route under will be made to the initia l conditio ns [1] on travel costs among the studied O-D (Origin– which travelers in all the system base their meet the desired production level. Journal of Electronics, Mechanical, and modal choice decision. Mechatronics Engineering, vol. 2, pp 157- Destination Matrix) pairs, stated by the travel distribution [1, 2]. Firstly, we calculate 161, 2012 The design equations also permit easy operator cost, later we will compare these Operators can use these data. It is aimed to analysis of the impact of the Cobb-Douglas costs. We will determine analysis of the ensure traveling comfortably [4, 5] and safe elasticity exponents and total productivity [7] Creese, R.C., Geometric Programming operator cost between two routes and identify movement for passengers from a place to factor upon the total cost. The development for Design and Cost Optimization, routes that cause the most cost [1, 2, 3]. Our another. of design equations takes considerable effort, Morgan&Claypool Publishers, pp7-10, 103- focus will be on optimizing these routes. If we need to change stops, we will change stop but the equations permit a more rapid 113, 2011 places. We need to put the best stops on the Trip generation determines the frequency of analysis of the impact of the input variables most appropriate places and to solve this origins or destinations of trips in each zone upon the output. by trip purpose, as a function of land uses and

968 OPTIMIZING BUS LINES in URBAN PUBLIC TRANSPORTATION by COST and Table 2. Out put Values of Model for OptimizingTRIP CALCULATION Bus METHODS:Lines in UrbanA SOFTWARE Public MODEL Transportation DESIGN by Estimates. [1] Clarence Zener, "A Mathematical Aid in Cost and Trip Calculation Methods: A Software Model Optimizing Engineering Designs", Ferdi Sönmez Yea Labor Capita Primal Dual Proceedings of the National Academy of Design Doi: 10.17932/ IAU.IJEMME.m.21460604.2015.5/3.969-977 r Estima l Total Total Sciences, vol. 47, pp 537-539. Abstract te Estima Cost Cost FerdiPlanning SÖNMEZ of a public1 transport system in an ordered way is the key which offers potential users a x1 te (Y) d(ω) [2] Duffin, R.J., Peterson, E.L. Zener. C.M., x2 Geometric Programming - Theory and mode of transport. To attract travelers from other modes of transport, sufficiently attractive 200 121.56 114.93 27955. 27955. Applications, John Wiley & Sons, New York Abstractoverall journey times must be provided, so reducing traffic congestion and obtaining delivered 6 11 11 1967 Planningbenefits like of roada public safety transport and lower system atmospheric in an ordered and noise way pollution. is the key The which congestion offers potentialthat close users with 200 124.96 124.84 32488. 32488. a mode of transport. To attract travelers from other modes of transport, sufficiently attractive 7 98 98 [3] Wilde, D.J. Beightler, C.S., overallincreasing journey demand times is becomingmust be provided, a part of soour reducing lives and traffic it is complicating congestion ourand lives.obtaining Some delivered work is 200 117.03 114.00 33973. 33973. Fundamentals of Optimization, Prentic e - benefitsdone to reducelike road the safety traffic and congestion. lower atmospheric If we want and to noise provide pollution. an efficient The congestion and balanced that closelayout within 8 0 08 08 Hall, Englewood Cliffs, New Jersey, pp 99- increasing demand is becoming a part of our lives and it is complicating our lives. Some work is donepublic to transport reduce the system, traffic we congestion.must place theIf righwe wantt stop to at provide the right an places. efficient Hence and, webalanced consider layout some in 200 93..41 99.88 27941. 27941. 133, 1967. public transport system, we must place the right stop at the right places. Hence, we consider some 8 39 39 components like cost, security, noise pollution, etc. In this study, it is aimed to solve a set covering components like cost, security, noise pollution, etc. In this study, it is aimed to solve a set covering [4] Zener, C., Engineering Design by problem for locating the smallest number possible of bus stops. problem for locating the smallest number possible of bus stops. Geometric Programming, John Wiley & The development of design equations for a Sons, New York 1971. Keywords:Keywords: Bus Stop Spacing, Bi-LevelBi-Level Optimization Model, Trip Demand,Demand, O-DO-D Matrix.Matrix. geometric programming model of from data [5] Beightler, C. and Phillips, D.T. Applied of the construction sector in Turkey. These Geometric Programming, John Wiley & design equations ( Eqns. 20,24,25,and 26) Purpose of this work is to make an optimal problem we use the estimation method [2, 3]. give the solutions for the model outputs and Sons, New York 1976. bus stop location and spacing model which Once a decision is made to modify the the model does not need to be resolved. The minimizes the operator cost of all the design equations for the variables x1 and x2 [6] I. Guney, E. Oz, " An Application of transport system, examine the equilibrium location of bus stops in an area then changes can then be used to determine the total cost to Geometric Programming", International travel costs by installing the route under will be made to the initia l conditio ns [1] on travel costs among the studied O-D (Origin– which travelers in all the system base their meet the desired production level. Journal of Electronics, Mechanical, and modal choice decision. Mechatronics Engineering, vol. 2, pp 157- Destination Matrix) pairs, stated by the travel distribution [1, 2]. Firstly, we calculate 161, 2012 The design equations also permit easy operator cost, later we will compare these Operators can use these data. It is aimed to analysis of the impact of the Cobb-Douglas costs. We will determine analysis of the ensure traveling comfortably [4, 5] and safe elasticity exponents and total productivity [7] Creese, R.C., Geometric Programming operator cost between two routes and identify movement for passengers from a place to factor upon the total cost. The development for Design and Cost Optimization, routes that cause the most cost [1, 2, 3]. Our another. of design equations takes considerable effort, Morgan&Claypool Publishers, pp7-10, 103- focus will be on optimizing these routes. If we need to change stops, we will change stop but the equations permit a more rapid 113, 2011 places. We need to put the best stops on the Trip generation determines the frequency of analysis of the impact of the input variables most appropriate places and to solve this origins or destinations of trips in each zone upon the output. by trip purpose, as a function of land uses and

1 İstanbul Arel University, Department of Computer Engineering, e-mail: [email protected]

969 Optimizing Bus Lines in Urban Public Transportation by Cost and Trip Calculation Methods: A Software Model Design household demographics, and other socio- = unit cost per kilometer covered by bus economic factors [1, 4, 5]. Transportation The vertical portion of the matrix show the type k ( per km) 𝑘𝑘 0 planning [1] is reached by O-D matrix. Trip origin and the destination of the matrix show 𝐶𝐶𝐶𝐶= mute variable worth 1 if bus type k is 𝑂𝑂𝑂𝑂 ≤ 𝑂𝑂𝐶𝐶 𝑙𝑙 𝑡𝑡𝑡𝑡 0 distrubtion step of transportation planning is down time in Figure 2. Examinatio n starts assigned to route l and 0 if not. ∑( ⁄ 𝑙𝑙) ≤ 𝑓𝑓𝑓𝑓𝑓𝑓 , 𝛿𝛿𝑘𝑘,𝑙𝑙 𝑙𝑙 ℎ done modelling by these using matrix. with the first line. Firstly, if you go fr o m The cost of buses being stationary with the Where, the first constraint defines the 𝑚𝑚𝑚𝑚𝑚𝑚 𝑙𝑙 𝑚𝑚𝑚𝑚𝑚𝑚 An illustration of the O-D matrix is given in origin 1 to destinatio n 1, distance is equal to engine running (CR) will be depend on the 𝐹𝐹characteristics≤ 𝑓𝑓 ≤ 𝐹𝐹 of the∀ binary𝑙𝑙 variables and Figure 1. 0. Secondly, if you go from origin 1 to time they spend at the bus stop dealing with the rest of the constraints represent the group destination 2, distance is 35. We process the 𝑘𝑘,𝑙𝑙 passenger. This value is calculated [1] as: of operational constraints which need𝛿𝛿 to be opposite this condition. So if you go from imple me nted in the model, such as maximu m destination 2 to origin 1, distance is equal to (3) 𝑠𝑠𝑠𝑠 operator cost (OC), fleet restriction, and 35 or if you go from destination 2 to origin 3, 𝑡𝑡 𝑙𝑙 𝑘𝑘 𝑘𝑘 𝑘𝑘,𝑙𝑙 𝑙𝑙 𝐶𝐶𝐶𝐶 = ( ⁄ ) ∑ ∑ 𝐶𝐶𝐶𝐶 𝛿𝛿 𝑌𝑌 maximum and minimum allowed frequenc ie s distance is equal to 32. It continues like this Where, 60 [1, 7, 8]. for other numbers (1-6). When we add = average time for passengers getting on and off the bus (min per passenger) Once and for all, we will calculate OC by the automatically line in Excel, distance values 𝑠𝑠𝑠𝑠 𝑡𝑡 equation below; are reached. Typically, the distance is twice =unit cost per hour of bus type k standing

that of time. Time is calculated with this stil with engine running ( per hour) 𝐶𝐶𝐶𝐶𝑘𝑘 OC= CK + CR+ CF+ CP infor matio n. = journey demand on line l (passengers per hour) (6) Figure 1: An Illustration of the O-D Matrix 𝑙𝑙 (Üçer, 2009) 𝑌𝑌 = mute variable worth 1 if bus type k is assigned to route l and 0 if not In detail, be showed as follows. 𝛿𝛿𝑘𝑘,𝑙𝑙 Here, T ij = Trips from origin i to destination j. For example; if the passanger comes from The personnel cost [1, 7] (CP) is : OC= origin 1 to destinatio n i, trip will be a T 11. In ∑𝑙𝑙 ∑𝑘𝑘 𝐿𝐿𝑙𝑙 𝑓𝑓𝑙𝑙𝐶𝐶𝐶𝐶𝑘𝑘𝛿𝛿𝑘𝑘,𝑙𝑙 + this project O-D matrix values are used. 𝑙𝑙 𝑠𝑠𝑠𝑠 (4) 𝑙𝑙 𝑘𝑘 𝑡𝑡𝑡𝑡 𝑡𝑡 𝑙𝑙 𝑘𝑘 𝑘𝑘 𝑘𝑘,𝑙𝑙 𝑙𝑙 Generally, O-D matrix values are reached 𝐶𝐶𝐶𝐶 = 𝐶𝐶𝐶𝐶∑ ∑ ( ⁄ 𝑙𝑙) ( ⁄ ) ∑ ∑ 𝐶𝐶𝐶𝐶 𝛿𝛿 𝑌𝑌 + Where, ℎ 6 0 𝑙𝑙 with survey [4,5]. But for this project data is 𝑙𝑙 𝑘𝑘 𝑡𝑡𝑡𝑡 𝑘𝑘 𝑘𝑘,𝑙𝑙 ∑ ∑ 𝑙𝑙 = is the unit cost per hour of the staff ( (( ⁄ℎ ) . 𝐶𝐶𝐶𝐶 . 𝛿𝛿 + received from IETT (General Directorate of Figure 3: Examples of Network (Üçer, 𝑙𝑙 per hour) 𝑙𝑙 𝑘𝑘 𝑡𝑡𝑡𝑡 Istanbul Electricity, Tramway and Tunnel) 2009) 𝐶𝐶𝐶𝐶∑ ∑ ( ⁄ 𝑙𝑙) 𝐶𝐶𝐶𝐶=is the time of a round trip (min) ℎ Information Technologies Section. Values 3. =is the headway on route l (min) = The general aim of this article is to provide are used within the equations. The follow ing Figure 3 shows the cost between routes. For 𝑙𝑙 𝑡𝑡𝑡𝑡 detailed trip reports that can be used by the example is given for a better undertanding of instance, the green route is preferred then the 𝑙𝑙 ℎ 1⁄ 𝑙𝑙 operators, and provide the means need to find O-D Matrix. cost is 13. P1, P2, P3, P4, P5 are calculated. The total financial fixed cost [1, 2, 4, 7] 𝑓𝑓(CF) the stops that need to be optimized. This figure allows to find the shortest is: distance. 𝑙𝑙 (5) 𝑙𝑙 𝑘𝑘 𝑡𝑡𝑡𝑡 𝑘𝑘 𝑘𝑘 , 𝑙𝑙 Our model is independent and totally self- 𝐶𝐶𝐶𝐶 = ∑ ∑ (( 𝑙𝑙) . 𝐶𝐶𝐶𝐶 . 𝛿𝛿 ⁄ℎ contained, and not a part of any other The total cost of the kilometers covered (CK) Where, program [9]. MySQL database with PHP will be calculated [1, 2, 5, 7] as: Unit fixed cost per hour of bus type k ( per hour) language is used. This work is exploited by 𝑘𝑘 𝐶𝐶𝐶𝐶=is= the time of a round trip (min) gmapV3 API support. We also used HTML 5 (2) 𝑙𝑙 𝑘𝑘 𝑙𝑙 𝑙𝑙 𝑘𝑘 𝑘𝑘,𝑙𝑙 and jscript for interfaces development. The 𝐶𝐶𝐶𝐶Where,= ∑ ∑ 𝐿𝐿 𝑓𝑓 𝐶𝐶𝐶𝐶 𝛿𝛿 𝑙𝑙=is the headway on route l (min) = 𝑡𝑡𝑡𝑡 parameters and variables used in the = length of route l (km per bus) 𝑙𝑙 = mute variable worth 1 if bus type k is ℎ 1 𝑙𝑙 calculations [1, 2, 4, 7, 8, 9, 10] and their =frequency of route l (bus per hour) ⁄𝑓𝑓 𝑙𝑙 assigned to route l and 0 if not. definitions are shown in Table 1. 𝐿𝐿 𝛿𝛿𝑘𝑘,𝑙𝑙 Figure 2: Example of an O-D Matrix 𝑓𝑓𝑙𝑙 𝛿𝛿𝑘𝑘,𝑙𝑙 ∈ (0,1) 970 Ferdi SÖNMEZ household demographics, and other socio- = unit cost per kilometer covered by bus economic factors [1, 4, 5]. Transportation The vertical portion of the matrix show the type k ( per km) 𝑘𝑘 0 planning [1] is reached by O-D matrix. Trip origin and the destination of the matrix show 𝐶𝐶𝐶𝐶= mute variable worth 1 if bus type k is 𝑂𝑂𝑂𝑂 ≤ 𝑂𝑂𝐶𝐶 𝑙𝑙 𝑡𝑡𝑡𝑡 0 distrubtion step of transportation planning is down time in Figure 2. Examinatio n starts assigned to route l and 0 if not. ∑( ⁄ 𝑙𝑙) ≤ 𝑓𝑓𝑓𝑓𝑓𝑓 , 𝛿𝛿𝑘𝑘,𝑙𝑙 𝑙𝑙 ℎ done modelling by these using matrix. with the first line. Firstly, if you go fr o m The cost of buses being stationary with the Where, the first constraint defines the 𝑚𝑚𝑚𝑚𝑚𝑚 𝑙𝑙 𝑚𝑚𝑚𝑚𝑚𝑚 An illustration of the O-D matrix is given in origin 1 to destinatio n 1, distance is equal to engine running (CR) will be depend on the 𝐹𝐹characteristics≤ 𝑓𝑓 ≤ 𝐹𝐹 of the∀ binary𝑙𝑙 variables and Figure 1. 0. Secondly, if you go from origin 1 to time they spend at the bus stop dealing with the rest of the constraints represent the group destination 2, distance is 35. We process the 𝑘𝑘,𝑙𝑙 passenger. This value is calculated [1] as: of operational constraints which need𝛿𝛿 to be opposite this condition. So if you go from imple me nted in the model, such as maximu m destination 2 to origin 1, distance is equal to (3) 𝑠𝑠𝑠𝑠 operator cost (OC), fleet restriction, and 35 or if you go from destination 2 to origin 3, 𝑡𝑡 𝑙𝑙 𝑘𝑘 𝑘𝑘 𝑘𝑘,𝑙𝑙 𝑙𝑙 𝐶𝐶𝐶𝐶 = ( ⁄ ) ∑ ∑ 𝐶𝐶𝐶𝐶 𝛿𝛿 𝑌𝑌 maximum and minimum allowed frequenc ie s distance is equal to 32. It continues like this Where, 60 [1, 7, 8]. for other numbers (1-6). When we add = average time for passengers getting on and off the bus (min per passenger) Once and for all, we will calculate OC by the automatically line in Excel, distance values 𝑠𝑠𝑠𝑠 𝑡𝑡 equation below; are reached. Typically, the distance is twice =unit cost per hour of bus type k standing that of time. Time is calculated with this stil with engine running ( per hour) 𝐶𝐶𝐶𝐶𝑘𝑘 OC= CK + CR+ CF+ CP infor matio n. = journey demand on line l (passengers per hour) (6) Figure 1: An Illustration of the O-D Matrix 𝑙𝑙 (Üçer, 2009) 𝑌𝑌 = mute variable worth 1 if bus type k is assigned to route l and 0 if not In detail, be showed as follows. 𝛿𝛿𝑘𝑘,𝑙𝑙 Here, T ij = Trips from origin i to destination j. For example; if the passanger comes from The personnel cost [1, 7] (CP) is : OC= origin 1 to destinatio n i, trip will be a T 11. In ∑𝑙𝑙 ∑𝑘𝑘 𝐿𝐿𝑙𝑙 𝑓𝑓𝑙𝑙𝐶𝐶𝐶𝐶𝑘𝑘𝛿𝛿𝑘𝑘,𝑙𝑙 + this project O-D matrix values are used. 𝑙𝑙 𝑠𝑠𝑠𝑠 (4) 𝑙𝑙 𝑘𝑘 𝑡𝑡𝑡𝑡 𝑡𝑡 𝑙𝑙 𝑘𝑘 𝑘𝑘 𝑘𝑘,𝑙𝑙 𝑙𝑙 Generally, O-D matrix values are reached 𝐶𝐶𝐶𝐶 = 𝐶𝐶𝐶𝐶∑ ∑ ( ⁄ 𝑙𝑙) ( ⁄ ) ∑ ∑ 𝐶𝐶𝐶𝐶 𝛿𝛿 𝑌𝑌 + Where, ℎ 6 0 𝑙𝑙 with survey [4,5]. But for this project data is 𝑙𝑙 𝑘𝑘 𝑡𝑡𝑡𝑡 𝑘𝑘 𝑘𝑘,𝑙𝑙 ∑ ∑ 𝑙𝑙 = is the unit cost per hour of the staff ( (( ⁄ℎ ) . 𝐶𝐶𝐶𝐶 . 𝛿𝛿 + received from IETT (General Directorate of Figure 3: Examples of Network (Üçer, 𝑙𝑙 per hour) 𝑙𝑙 𝑘𝑘 𝑡𝑡𝑡𝑡 Istanbul Electricity, Tramway and Tunnel) 2009) 𝐶𝐶𝐶𝐶∑ ∑ ( ⁄ 𝑙𝑙) 𝐶𝐶𝐶𝐶=is the time of a round trip (min) ℎ Information Technologies Section. Values 3. =is the headway on route l (min) = The general aim of this article is to provide are used within the equations. The follow ing Figure 3 shows the cost between routes. For 𝑙𝑙 𝑡𝑡𝑡𝑡 detailed trip reports that can be used by the example is given for a better undertanding of instance, the green route is preferred then the 𝑙𝑙 ℎ 1⁄ 𝑙𝑙 operators, and provide the means need to find O-D Matrix. cost is 13. P1, P2, P3, P4, P5 are calculated. The total financial fixed cost [1, 2, 4, 7] 𝑓𝑓(CF) the stops that need to be optimized. This figure allows to find the shortest is: distance. 𝑙𝑙 (5) 𝑙𝑙 𝑘𝑘 𝑡𝑡𝑡𝑡 𝑘𝑘 𝑘𝑘 , 𝑙𝑙 Our model is independent and totally self- 𝐶𝐶𝐶𝐶 = ∑ ∑ (( 𝑙𝑙) . 𝐶𝐶𝐶𝐶 . 𝛿𝛿 ⁄ℎ contained, and not a part of any other The total cost of the kilometers covered (CK) Where, program [9]. MySQL database with PHP will be calculated [1, 2, 5, 7] as: Unit fixed cost per hour of bus type k ( per hour) language is used. This work is exploited by 𝑘𝑘 𝐶𝐶𝐶𝐶=is= the time of a round trip (min) gmapV3 API support. We also used HTML 5 (2) 𝑙𝑙 𝑘𝑘 𝑙𝑙 𝑙𝑙 𝑘𝑘 𝑘𝑘,𝑙𝑙 and jscript for interfaces development. The 𝐶𝐶𝐶𝐶Where,= ∑ ∑ 𝐿𝐿 𝑓𝑓 𝐶𝐶𝐶𝐶 𝛿𝛿 𝑙𝑙=is the headway on route l (min) = 𝑡𝑡𝑡𝑡 parameters and variables used in the = length of route l (km per bus) 𝑙𝑙 = mute variable worth 1 if bus type k is ℎ 1 𝑙𝑙 calculations [1, 2, 4, 7, 8, 9, 10] and their =frequency of route l (bus per hour) ⁄𝑓𝑓 𝑙𝑙 assigned to route l and 0 if not. definitions are shown in Table 1. 𝐿𝐿 𝛿𝛿𝑘𝑘,𝑙𝑙 Figure 2: Example of an O-D Matrix 𝑓𝑓𝑙𝑙 𝛿𝛿𝑘𝑘,𝑙𝑙 ∈ (0,1) INTERNATIONAL JOURNAL OF ELECTRONICS, MECHANICAL AND MECHATRONICS ENGINEERING Vol.5 Num.2 - 2015 (969-977) 971 Optimizing Bus Lines in Urban Public Transportation by Cost and Trip Calculation Methods: A Software Model Design

kilometer covered by bus k Figure 4 is the map page of our software ( per hour). İt is thought model. Here, the user first (a) select the line Below there is a map (Figure 4) showing the as fuel. you want to know the cost of the part. Then route from the origin to the destination along avgpassenger The average passenger users will want to select the button (b). with the routes stops [10, 11, 12]. Details number Calculate the operator cost of the program. concerning the stops and the route [1, 13, 14] busname Bus name When users pressed the button (b), stops are will be shown on the right of the map. busid Bus ID ordered, such as in figure (d). The user will be able to see the shape and then the line stops ctraveltime Value of car travel time Table 1 : Variables Used in the Model totaltravelt Total car travel time (e). The name of the line that selected shown orderino Order no in the section (e). In part (f) has a CK value. Figure 5: The Total Financial Name of Description tcost The data will be used the CK is determined as the total cost of the bus Fixed Cost Graph Variable operator cost calculatio n. as we know it. (g) Include the value of the CP Dname driver’s name Operator cost include CF section. This is the cost paid to the driver. In CK altering graph of all line according to bus totaltmvehic is equal to total time in equation. CF equation part (h) takes place in the CF which is a fixed as follows in Figure 6. This graph show total cost. The fixed cost portion of the vehicle fuel vehicle in the database include unit cost of the kilometers covered. is at the forefront. If the CR motor runs but vehictm Value of time in vehic le fixed cost per hour of bus k k does not move occurring is the cost of the car waittm is equal to value of waiting type k ( CF per. hour)CF = (i). In part (j) seems to be the OC (Operator time in the database lname driver’s surname cost) value by which the operator is able to avgwaittm is equal to average waiting time Time find the optimal line. The operator will reach driver Every bus must have one time it by making the change on the stops. In the Stop line Stop line driver. This makes easy to find bus by identifying the section (k) the name of the stop code and stop name stop name coordinate information are shown. By using driver. stop code stop code section (c) it is possible to zoom out the map DID Driver’s identifica tio n access time in the database is equal to like you want the user part will be able to Figure 6: Total Cost of the Kilometers number. total access time value clearly see the area which is choice of users. Covered Graph tottript The total time it takes the total access total access time time bus to do a complete trip. CR altering graph of all line according to bus direction Direction (from Frequency Frequency CF values of all line according to bus as as follows. CR is unit cost per hour of bus origina tio n to destinatio n) Line name Line name follows. In Figure 5 shows that total fixed type k standing still with engine running (

Line name Line name cost for each bus. We see that HAT A has the per hour), Figure 7 show us CR graph. Here,

Line code Line code maximum cost, as shown in the graph. The we take into account part that is time for district district user who wants to look at events in terms of passengers getting on and off the bus Manager Every district must have a fixed costs in HAT A, the user should change (minutes per passenger). Numbers express manager. on the HAT A. the bus name. Horizontal line express the CR personalsost The cost paid to person. values according to each line. x coordinate x coordinate y coordinate y coordinate Linelength length of the line. ocost The data will be used in the operator cost calculation. Operator cost includes CK equation. CK Figure 4: Map Page equation include = unit cost per CKk. k 972 CK Ferdi SÖNMEZ kilometer covered by bus k Figure 4 is the map page of our software ( per hour). İt is thought model. Here, the user first (a) select the line Below there is a map (Figure 4) showing the as fuel. you want to know the cost of the part. Then route from the origin to the destination along avgpassenger The average passenger users will want to select the button (b). with the routes stops [10, 11, 12]. Details number Calculate the operator cost of the program. concerning the stops and the route [1, 13, 14] busname Bus name When users pressed the button (b), stops are will be shown on the right of the map. busid Bus ID ordered, such as in figure (d). The user will be able to see the shape and then the line stops ctraveltime Value of car travel time Table 1 : Variables Used in the Model totaltravelt Total car travel time (e). The name of the line that selected shown orderino Order no in the section (e). In part (f) has a CK value. Figure 5: The Total Financial Name of Description tcost The data will be used the CK is determined as the total cost of the bus Fixed Cost Graph Variable operator cost calculatio n. as we know it. (g) Include the value of the CP Dname driver’s name Operator cost include CF section. This is the cost paid to the driver. In CK altering graph of all line according to bus totaltmvehic is equal to total time in equation. CF equation part (h) takes place in the CF which is a fixed as follows in Figure 6. This graph show total cost. The fixed cost portion of the vehicle fuel vehicle in the database include unit cost of the kilometers covered. is at the forefront. If the CR motor runs but vehictm Value of time in vehic le fixed cost per hour of bus k k does not move occurring is the cost of the car waittm is equal to value of waiting type k ( CF per. hour)CF = (i). In part (j) seems to be the OC (Operator time in the database lname driver’s surname cost) value by which the operator is able to avgwaittm is equal to average waiting time Time find the optimal line. The operator will reach time driver Every bus must have one driver. This makes easy to it by making the change on the stops. In the Stop line Stop line section (k) the name of the stop code and stop name stop name find bus by identifying the driver. coordinate information are shown. By using stop code stop code section (c) it is possible to zoom out the map access time in the database is equal to DID Driver’s identifica tio n Figure 6: Total Cost of the Kilometers number. like you want the user part will be able to total access time value clearly see the area which is choice of users. Covered Graph tottript The total time it takes the total access total access time time bus to do a complete trip. CR altering graph of all line according to bus Frequency Frequency direction Direction (from as follows. CR is unit cost per hour of bus origina tio n to destinatio n) CF values of all line according to bus as Line name Line name follows. In Figure 5 shows that total fixed type k standing still with engine running (

Line name Line name cost for each bus. We see that HAT A has the per hour), Figure 7 show us CR graph. Here,

the HAT X. When we removed stops from Figure 7: The Cost of Bus Standing Still HAT X, HAT A is our new line. Then cost with Engine Running Graph account made for the HAT A. HAT A and

HAT X the only difference from occurring Figure 11: Comparison Total Cost of the CP altering graph of all line according to bus also are the stops. We just pulled the stops from HAT X. Other variables remained the Kilometers Covered Graph as follows. In Figure 8, it is defined the paid same. Stops were used as a variable. The to the driver that the total cost calculation is CR value graph that is in the between HAT A Figure 14: Comparison all Cost Graph performed and the chart has been drawn. charts below includes the reached results of our investigations. and HAT X (Figure 12). Each number corresponds to one line. Here, the values are examined individually in a Software model compares CF value that is cumulative manner. between HAT A and HAT X, as follows; (Figure 10) Result of an operator cost graph as follow in Figure 15. Fixed costs that is also occurring on the HAT X are more likely to HAT A. The numbers in Figure 8: The Personel Cost Graph the horizontal column is buses. Fixed costs

are as shown in vertical space. According to Figure 12: Comparison the Cost of Bus

the fixed cost, a user must choose HAT A. Standing Still with Engine Running Graph

The goal of our model is to find the line 4.2 Comparison of the Results which has the lowest cost. Here, at HAT A Figure 13 shows the variation of the cost paid

we saw lower cost. to the driver. The difference between the two lines as seen below.

Figure 15: Operator Cost Graph

As a result, we can see all values above Figure 10: Comparison the Total Financial graph. The graph examine changing cost values. Operator will compare all values Fixed Cost Graph about graph in Figure 15, later will decide Figure 9: Diferent Line Variations CK value graph that is in the between HAT A Figure 13: Comparison the Personel line where user want to optimize [12, 14, 15]. HAT A and HAT X is compared by above and HAT X, as follows in Figure 11. This Cost Graph The above lines were investigated in Figure graph show us total bus costs. The numbers graph. User can see all data. For example we 9. With different colors from each other, each from 1 to 24 refers to the buses on here. compare HAT A and HAT X lines, we see line has its own unique costs were calculated. that operator cost of HAT A is 1595992,41

974 Ferdi SÖNMEZ

As a result of this calculatio n, the follo w in g According to graph, HAT X has the most We come through as follows with charts reached. cost. information mentioned above. CP-CK-CR- CF graph; also refers to the lines from 1 to 9 Here we will consider Figure 9. We will in Figure 14. examine by comparing HAT X (Line X) and HAT A (Line A). Normally the HAT X is our route (Figure 9). We removed some stops on the HAT X. When we removed stops from Figure 7: The Cost of Bus Standing Still HAT X, HAT A is our new line. Then cost with Engine Running Graph account made for the HAT A. HAT A and HAT X the only difference from occurring Figure 11: Comparison Total Cost of the CP altering graph of all line according to bus also are the stops. We just pulled the stops from HAT X. Other variables remained the Kilometers Covered Graph as follows. In Figure 8, it is defined the paid same. Stops were used as a variable. The to the driver that the total cost calculation is CR value graph that is in the between HAT A Figure 14: Comparison all Cost Graph performed and the chart has been drawn. charts below includes the reached results of our investigations. and HAT X (Figure 12). Each number corresponds to one line. Here, the values are examined individually in a Software model compares CF value that is cumulative manner. between HAT A and HAT X, as follows; (Figure 10) Result of an operator cost graph as follow in Figure 15. Fixed costs that is also occurring on the HAT X are more likely to HAT A. The numbers in Figure 8: The Personel Cost Graph the horizontal column is buses. Fixed costs are as shown in vertical space. According to Figure 12: Comparison the Cost of Bus the fixed cost, a user must choose HAT A. Standing Still with Engine Running Graph

The goal of our model is to find the line 4.2 Comparison of the Results which has the lowest cost. Here, at HAT A Figure 13 shows the variation of the cost paid we saw lower cost. to the driver. The difference between the two lines as seen below.

Figure 15: Operator Cost Graph

INTERNATIONAL JOURNAL OF ELECTRONICS, MECHANICAL AND MECHATRONICS ENGINEERING Vol.5 Num.2 - 2015 (969-977) 975 Optimizing Bus Lines in Urban Public Transportation by Cost and Trip Calculation Methods: A Software Model Design and HAT X is 20340115,43. Operator they left a very big difference, therefore it has Transportation Science, 27, pp.133–147, decides [14, 15] routes and stops by looking been determined that. 1993. at these results. The calculation of user cost values that [8] dell’Olio, L., Ibeas, A., Moura, J.L. A bi- occurred at each stop is a subject of another level mathematica l programming model to O-D traffic demand matrix is an impor ta nt study. In this context, it is planned to perform locate bus stops and optimize frequencies. source of data for the equilibrium this calculation and show these values for Journal of Transportation Research Board, assignment. So, O-D traffic demands is each bus stop. Being able to observe stops on 1971, pp. 23–31, 2006. important for a reliable estimate of the their cost values is an important concern for calculations we make. In this study, the passengers. In this context, it is planned to [9] Bard, J.F. Practical Bilevel Programming: traffic calculation according to the perform calculation of both user and operator Algorithms and Applicatio ns. Kluwe r assignments made, and as a result is provided costs in a software model in a future work. Academic Publishers, Dordrecht., 1998. to detect the most optimal stop. Over the years, socio-economic factors that will be due [10] Gleason, J.M.Set covering approach to to the change and improvement in the data [1] Ibeas, Á., Alonso, B., Sainz, O. the location of Express bus stops. Omega 3, obtained, the developed model can be made Optimizing Bus Stop Spacing in Urban 605-608, 1973. with the update of the data is provided Areas. Transportation Research Part E, 46, renewed at any moment. pp. 446-458, 2010. [11] Kraft, W.H., Boardman T.J. Location of bus stops. Journal of tramsportation Our study include 283 drivers, 8 lines, 110 [2] Bowerman, G., Hall, B., Calamai, P. A engineering 98 (TE1), pp.103-116, 1972. stops and 283 buses. The values that occurr at multi-objective optimization approach to the stops were examined individually. school bus routing problems. Transportation [12] Räsänen, M. Functionality of a bus stop Graphs were obtained with from occurring Research Part A 28 (5), pp.107–123, 1995. at exit or merging lanes and its impact on values. Making comparisons are provided driver bahavior. Traffic Engineering and between two lines. [3] Ceder, A., Wilson, N.H.M. Bus network Control, 47 (1), pp. 29-32, 2006. design. Transportation Research Part B 20, Separate cost accounts for the cost of the pp.331–334, 1986. [13] Üçer, F. Ulusal karayolu sisteminin ağ operator are reviewed. By the way, cost güvenilir liği yaklaşımı ile incelenmes i. PhD functions are affected by the volume of [4] Ceder, A., Prashker, J.N., Stern, J.I. An Thesis. Balıkesir Univers ity, C ivil traffic. algorithm to evaluate public transportation Engineering, 2009. for minimizing passenger walking distance. As a result of the equations that are used on Applied Mathematical Modelling, 7(1), [14] Cea, J.D., Fernández, J.E., Dekock, V., the value of the cost of an operator has been pp.19-24, 1983. Soto, A. Solving network equilibrium reached. These values were compared with problems on multimodal urban transportation all lines comparison results are shown in the [5] Ceder, A. Bus frequency determinatio n networks with multiple user classes. graphs. Even the cost of any changes using passenger count data. Transportatio n Transport Reviews, 25(3), pp.293-317, 2005. affecting the whole of the line was calculated. Research Part A, 18, pp.439–453, 1984. We want to optimize costs that occur even [15] Farahani, R.Z., Miandoabchi, E., Szeto, after the changes we made a comparison was [6] Chriqui, C., Robilland, P. Common bus W.Y., Rashidi, H. A review of urban made of the cost of old. lines. Transportation Science, 9, pp.115–121, transportation network design problems, 1975. European Journal of Operational Research, In traffic assignment, which is done by 229, 2, pp.281-302, 2013. raising the calculated travel time from the [7] De Cea, J., Fernandez, J.E. Transit proposed method works well with each other, assignment for congested public transport systems: an equilibr ium mode l.

976 Ferdi SÖNMEZ and HAT X is 20340115,43. Operator they left a very big difference, therefore it has Transportation Science, 27, pp.133–147, decides [14, 15] routes and stops by looking been determined that. 1993. at these results. The calculation of user cost values that [8] dell’Olio, L., Ibeas, A., Moura, J.L. A bi- occurred at each stop is a subject of another level mathematica l programming model to O-D traffic demand matrix is an impor ta nt study. In this context, it is planned to perform locate bus stops and optimize frequencies. source of data for the equilibrium this calculation and show these values for Journal of Transportation Research Board, assignment. So, O-D traffic demands is each bus stop. Being able to observe stops on 1971, pp. 23–31, 2006. important for a reliable estimate of the their cost values is an important concern for calculations we make. In this study, the passengers. In this context, it is planned to [9] Bard, J.F. Practical Bilevel Programming: traffic calculation according to the perform calculation of both user and operator Algorithms and Applicatio ns. Kluwe r assignments made, and as a result is provided costs in a software model in a future work. Academic Publishers, Dordrecht., 1998. to detect the most optimal stop. Over the years, socio-economic factors that will be due [10] Gleason, J.M.Set covering approach to to the change and improvement in the data [1] Ibeas, Á., Alonso, B., Sainz, O. the location of Express bus stops. Omega 3, obtained, the developed model can be made Optimizing Bus Stop Spacing in Urban 605-608, 1973. with the update of the data is provided Areas. Transportation Research Part E, 46, renewed at any moment. pp. 446-458, 2010. [11] Kraft, W.H., Boardman T.J. Location of bus stops. Journal of tramsportation Our study include 283 drivers, 8 lines, 110 [2] Bowerman, G., Hall, B., Calamai, P. A engineering 98 (TE1), pp.103-116, 1972. stops and 283 buses. The values that occurr at multi-objective optimization approach to the stops were examined individually. school bus routing problems. Transportation [12] Räsänen, M. Functionality of a bus stop Graphs were obtained with from occurring Research Part A 28 (5), pp.107–123, 1995. at exit or merging lanes and its impact on values. Making comparisons are provided driver bahavior. Traffic Engineering and between two lines. [3] Ceder, A., Wilson, N.H.M. Bus network Control, 47 (1), pp. 29-32, 2006. design. Transportation Research Part B 20, Separate cost accounts for the cost of the pp.331–334, 1986. [13] Üçer, F. Ulusal karayolu sisteminin ağ operator are reviewed. By the way, cost güvenilir liği yaklaşımı ile incelenmes i. PhD functions are affected by the volume of [4] Ceder, A., Prashker, J.N., Stern, J.I. An Thesis. Balıkesir Univers ity, C ivil traffic. algorithm to evaluate public transportation Engineering, 2009. for minimizing passenger walking distance. As a result of the equations that are used on Applied Mathematical Modelling, 7(1), [14] Cea, J.D., Fernández, J.E., Dekock, V., the value of the cost of an operator has been pp.19-24, 1983. Soto, A. Solving network equilibrium reached. These values were compared with problems on multimodal urban transportation all lines comparison results are shown in the [5] Ceder, A. Bus frequency determinatio n networks with multiple user classes. graphs. Even the cost of any changes using passenger count data. Transportatio n Transport Reviews, 25(3), pp.293-317, 2005. affecting the whole of the line was calculated. Research Part A, 18, pp.439–453, 1984. We want to optimize costs that occur even [15] Farahani, R.Z., Miandoabchi, E., Szeto, after the changes we made a comparison was [6] Chriqui, C., Robilland, P. Common bus W.Y., Rashidi, H. A review of urban made of the cost of old. lines. Transportation Science, 9, pp.115–121, transportation network design problems, 1975. European Journal of Operational Research, In traffic assignment, which is done by 229, 2, pp.281-302, 2013. raising the calculated travel time from the [7] De Cea, J., Fernandez, J.E. Transit proposed method works well with each other, assignment for congested public transport systems: an equilibr ium mode l.

INTERNATIONAL JOURNAL OF ELECTRONICS, MECHANICAL AND MECHATRONICS ENGINEERING Vol.5 Num.2 - 2015 (969-977) 977

INTERNATIONAL JOURNAL OF ELECTRONICS, MECHANICAL AND MECHATRONICS ENGINEERING

SUBMISSION INSTRUCTIONS The scope of International Journal of Electronics, Mechanical and Mechatronics Engineering (IJEMME) covers the novel scientific papers about Electronics, Image Processing, Information Theory, Electrical Systems, Power Electronics, Control Theory, Embedded Systems, Robotics, Motion Control, Stochastic Modeling, System Design, Multidisciplinary Engineering, Computer Engineering, Optical Engineering, Design Optimization, Material Science, Metamaterials, Heat and Mass Transfer, Kinematics, Dynamics, Thermo-Dynamics, Energy and Applications, Renew- able Energy, Environmental Impacts, Structural Analysis, Fluid Dynamics and related topics of the above subjects.

IJEMME is an international periodical published triple a year (February, July and October). Man- uscripts reporting on original theoretical and/or experimental work and tutorial expositions of permanent reference value are welcome. IJEMME Editorial Board is authorized to accept/reject the manuscripts based on the evaluation of international experts. The papers should be written in English. The manuscript should be sent in electronic submission via [email protected]

SUBMISSION INSTRUCTIONS OF MANUSCRIPTS.

Page Design: Text body area is (195mm x 275mm). 30 mm margin from top, 20 mm from down and 25 mm margin should be left on right/left sides.

Title: should be in 16 pt. bold, capital letters with Times New Roman font in Microsoft Word format. Authors’ names, affiliations, e-mail addresses should follow the title after double line spacing with authors’ names and surnames in lower case except first letters in 14 pt, the rest is 10 pt. italic.

Abstract: should not exceed 200 words with the word “Abstract” in 10 pt. italic, bold, abstract text in 9 pt. italic, all in Times New Roman font in Microsoft Word format.

Keywords: not exceeding 5 should be in bold.

Document Character: Subtitles should be in 10 pt. bold, capital letters and text body 10 pt. both with Times New Roman font in Microsoft Word format. The manuscripts should be written on a single column, be double spaced with single line spacing between paragraphs. The subtitle of the first section should start after a single space following the keywords, the other subtitles also with a single line space following the text, there should also be single line spacing between the previous text and the subtitle.

CONCLUSION section should have a title written in 1o pt. bold, capital letters and the text in 10 pt. all in Times New Roman font in Microsoft Word format. REFERENCE numbers should be given in brackets as illustrated below: Referencing books:

[1] Özsu M., T, Valduriez, P., Principles of Distributed Database Systems, Prentice Hall, New Jersey, 128-136,1991.

Referencing papers:

[2] G. Altay, O. N., Ucan, “Heuristic Construction of High-Rate Linear Block Codes,” Interna- tional Journal of Electronics and Communications (AEU), vol. 60, pp.663-666, 2006.

Page number is to be placed at the top left corner of each page with pencil. Length of the Manuscript should not exceed 20 pages excluding Figures and Tables.

INSTRUCTIONS ABOUT THE ACCEPTED MANUSCRIPTS: Page Design: Text body area is (195mm x 275mm). 30 mm margin from top, 20 mm from down and 25 mm margins should be left on right/left sides.

Title: should be in 16 pt. bold, capital letters with Times New Roman font in Microsoft Word format. Authors’ names, affiliations, e-mail addresses should follow the title after double line spacing with authors’ names in lower case and surnames in capital letter in 14 pt. the rest in 10 pt. in the same format.

Abstract: should not exceed 200 words with the word “Abstract” in 12 pt. italic, bold, abstract text in 9 pt. italic, all in Times New Roman font in Microsoft Word format.

Keywords: not exceeding 5 should be in 9 pt. bold.

Document Character: Subtitles should be in 10 pt. bold, capital letters and text body 10 pt. both with Times New Roman font in Microsoft Word format. The manuscripts should be written on two columns, be single spaced with single line spacing between paragraphs. The subtitle of the first section should start after a single space following the keywords, the other subtitles also with a single line space following the text, there should also be single line spacing between the previous text and the subtitle.

SECTIONS: Formulas should be numbered sequentially. Referring to formulas should be as Eqn (.). Figures and Tables should be placed into the text body and captions for both should be 10 pt. Table numbers and captions should be placed before the Table. If necessary, both columns may be used for large Figures and Tables.

CONCLUSION section should have a title written in 12 pt. bold, capital letters and the text in 10 pt. all in Times New Roman font in Microsoft Word format. Conclusion should not be a version of the Abstract. REFERENCE numbers should be given in brackets as illustrated below:

Referencing books: [1] Özsu M., T, Valduriez, P., Principles of Distributed Database Systems, Prentice Hall, New Jersey, 128-136,1991.

Referencing papers:

[2]G. Altay, O. N., Ucan, “Heuristic Construction of High-Rate Linear Block Codes,” Internation- al Journal of Electronics and Communications (AEU), vol. 60, pp.663-666, 2006.

SHORT BIOGRAPHY of the authors should follow references after a single line space, names in 9 pt. surnames in 9 pt. and the text in 9 pt. The text should not exceed 100 words.

CORRESPONDENCE ADDRESS:

Editor in Chief

Prof. Dr. Osman N. UÇAN Engineering Faculty Electrical and Electronics Engineering Department Inonu Caddesi, No.38, Florya, Istanbul, TURKEY E-mail : [email protected] Web : www.aydin.edu.tr/eng/ijemme

Prepared by Instructor: Saeid KARAMZADEH Engineering Faculty Electrical and Electronics Engineering Department Inonu Caddesi, No.38, Florya, Istanbul, TURKEY E-mail: [email protected]

Published by Istanbul Aydın University