An Analysis of Telecommunication Queuing System and Making More Efficient with Empirical Distribution of Service Time and Inter

IJSTE - International Journal of Science Technology & Engineering | Volume 2 | Issue 01 | July 2015 ISSN (online): 2349-784X An Analysis of Telecommunication Queuing System and Making More Efficient with Empirical Distribution of Service Time and Inter-

arrival Time (F-I-F-O Service)

Subhra Narayan Bose UG Student Department of Electronics and Communication Engineering Kalyani Government Engineering College

Abstract

A queue is a line of people or things to be handled in a sequential order. It is a sequence of objects that are waiting to be processed. Queuing theory is the study of queues for managing process and objects. Simulation has been applied successfully for modelling small and large complex systems and understanding queuing behaviour. Analysis of the models helps to increases the performance of the system. In this paper we analyze various models of the Single server queuing system with necessary implementation using Microsoft Excel and Matlab Software. For better understanding we have considered a Virtual Telecommunication System, is presented with help of Microsoft Excel. Empirical distribution of Service Time and Inter-arrival Time of call has an impact on the performance of Queuing models. Examples include: A Telecommunication System staffing a call centre and measuring system parameters like average time that a call spend in the system ,average waiting time for those calls which are waiting. Numerous problems and more motivate the development of a queuing theory. Queuing theory as discussed in this paper is organized and a simulation of queuing system and the necessary mathematical tools are developed to analyze them. Finally, we illustrate the use of these models through various communication applications. Keywords: Entity, Arrival Time, Waiting Time, Queuing Model, Service Time, Discrete-Event Simulation ______

I. INTRODUCTION

The first step in building a simulator is to decide the level of detail with which the simulation model will represent the real system. This may be only an approximation as we may only want the simulation model to capture the details that are important from our point of view. Based on the details that have been incorporated in the simulator, it should operate in exactly the same fashion as the real system. We can then sample the parameters of the simulator in exactly same way we would have sampled the parameters of the real system. These parameters are then reported back by the simulator in an appropriate fashion, i.e. averaged values and/or min/max values. Suitable statistical tests are needed to give confidence levels indicating the degree of confidence which we can ascribe to the results of the simulation. The real system will have its functional entities (i.e. its components) and will have some defined interactions and interdependencies between them as a function of time. For example, if the system to be simulated is a Queuing Network then its functional entities will be the individual queues, their buffers and servers, the external arrivals, the departures from the system and the way the jobs are routed from one queue to the next. These will interact with each other as a function of time depending on the various events that can happen in the system. It should be noted that one would typically simplify the system being studied in order to construct the simulator. However, the simulator should be realistic enough so that its behaviour correlates well with that of the actual system. In this paper we will consider Discrete Event Simulation model. A Discrete-Event Simulation approach focuses only on the system changes that happen when an event actually occurs. The time interval between events can be safely ignored as the system will not change during this time. After processing the current event, the simulator forwards the system clock to the next event time. Simulation moves from the current event to the event occurring next on the event list that is suitably generated and updated for the system.. A. Queuing Process: Customers requiring service are generated over time by an input source. Here we analyze different scenarios of a single model server based on FIFO, first in first out queuing Process The required service is then performed for the incoming calls (Entity) by the service mechanism, after which the outgoing leaves the queuing system. . Simulation can be done based on various tools which can be either physical or conceptual.

An Analysis of Telecommunication Queuing System and Making More Efficient with Empirical Distribution of Service Time and Inter-arrival Time (F-I-F-O Service) (IJSTE/ Volume 2 / Issue 01 / 027)

Fig. 1: Modelling of Queuing System.

B. Entity Arrival & Service Model: The Poisson process is the canonical traffic process model. We omit the definition of the stationary version and immediately define the no stationary version. The stochastic process A = {A(t) | −∞ < t < ∞} is nonhomogeneous Poisson with mean rate function λ if it has independent Poisson increments. This means that for all s < t we assume that the increment A(t)−A(s) for the interval (s, t ] has a Poisson distribution or

for all non-negative integers n. Finally, we assume that the process has the independent increment property, i.e. for all mutually disjoint intervals (s1, t1], (s2, t2], . . . , (sk, tk],the random variables. [2]

II. RELATED WORK

We have developed a call centre simulation model with assumption that we are dealing with finite number of calls including all incoming and outgoing calls and nonzero probability Using relationship between Poisson Distributions and Binomial distribution we can convert this problem with calls into consideration that securing inter-arrival time and call waiting time have binomial distribution. Our interests is one finding system parameter and do the experiment for various skewness of distribution to determine the desired empirical distribution for which Telecommunication System will face less delay as well as more efficiently can perform functions There are nine possible case of performing this problem in Microsoft Excel 1) Inter-arrival Time of call in system is negatively skewed and Service Time of that is negatively skewed ; 2) Inter-arrival Time of call in system is negatively skewed and Service Time of that is non- skewed; 3) Inter-arrival Time of call in system s negatively skewed and Service Time of that is positively skewed; 4) Inter-arrival Time of call in system is non- skewed and Service Time of that is negatively skewed 5) Inter-arrival Time of call in system is non- skewed and Service Time of that is non- skewed ; 6) Inter-arrival Time of call in system is non- skewed and Service Time of that is positively skewed; 7) Inter-arrival Time of call in system is positively skewed and Service Time of that is negatively skewed; 8) Inter-arrival Time of call in system is positively skewed and Service Time of that is non- skewed ; 9) Inter-arrival Time of call in system is positively skewed and Service Time of that is positively skewed; We have done our experiment with all above cases but presented only 3 cases in this paper, and final result is recapitulated by tabular Format with various distributions having various skewness.

An Analysis of Telecommunication Queuing System and Making More Efficient with Empirical Distribution of Service Time and Inter-arrival Time (F-I-F-O Service) (IJSTE/ Volume 2 / Issue 01 / 027)

A. Calls Having Negatively Skewed Inter-Arrival Time & Negatively Skewed Service Time:

Fig. 2: Both IAT and ST are negatively skewed binomial distribution

Fig. 3(a): Inter-Arrival Time Distribution

Fig. 3(b): Service Time Distribution

Fig 3: Both IAT and ST are negatively skewed binomial distribution via histogram

An Analysis of Telecommunication Queuing System and Making More Efficient with Empirical Distribution of Service Time and Inter-arrival Time (F-I-F-O Service) (IJSTE/ Volume 2 / Issue 01 / 027)

B. Calls Having Negatively Skewed Inter-Arrival Time & Positively Skewed Service Time :

Fig 4: Negatively skewed IAT and positively skewed ST (binomial distribution)

Fig. 5(a): Inter-Arrival Time Distribution

Fig. 5(b): Service Time Distribution

Fig 5: IAT negatively skewed and ST positively skewed binomial distribution via histogram

An Analysis of Telecommunication Queuing System and Making More Efficient with Empirical Distribution of Service Time and Inter-arrival Time (F-I-F-O Service) (IJSTE/ Volume 2 / Issue 01 / 027)

C. Calls Having Non Skewed Inter-Arrival Time & Positively Skewed Service Time:

Fig 6: Non-skewed IAT and Positively skewed ST ( binomial distribution)

Fig. 7(a): Inter-Arrival Time Distribution

Fig. 7(b): Service Time Distribution

Fig 7: IAT non-skewed and ST positively skewed binomial distribution via histogram

An Analysis of Telecommunication Queuing System and Making More Efficient with Empirical Distribution of Service Time and Inter-arrival Time (F-I-F-O Service) (IJSTE/ Volume 2 / Issue 01 / 027)

III. TABLE OF DATA WITH DECREASING AVERAGE TIME IN SYSTEM

Fig. 8: Table of Data with Decreasing Average Time In System

IV. CONCLUSION

We have now in a position to make a conclusion depending on data enlisted above. If we choose Negatively Skewed binomial distribution of Inter-arrival Time of a call and Non-skewed binomial distribution of Service Time, then we can achieve more efficient system in terms of Average time of a call spent in a Tele-Communication Queuing System . On the other hand Tele- communication System having Inter-arrival Time of a call non-skewed binomial distribution and Service Time is positively skew binomial distribution Then the overall system become worse n performance

ACKNOWLEDGEMENT

I would like to thank Dr. Prasanta Pathak (Member-Secretary International Statistical Education Centre (ISEC) Indian Statistical Institute and associate professor of Sampling and Official statistics Unit (SOSU-ISI KOLKATA) ) for giving Me chance to do this project and also would like to thank my mother Mrs. Sumita Bose for encouraging me .

REFERENCES

[1] Benny Mathew, Manoj Kumar Nambir “ A TUTORIAL ON MODELLING CALL CENTRES USING DISCRETE EVENT SIMULATION”. [2] Salman Akhtar and Muhammad Latif “Exploiting Simulation for Call Centre Optimization” Proceedings of the World Congress on Engineering 2010 Vol III WCE 2010, June 30 - July 2, 2010, London, U.K. [3] Prof. Dr. Mesut Güneş ▪ Ch. 2 Simulation Examples, Freie Universität Berlin [4] Simulation Techniques for Queues and Queueing Networks (National Programme on Technology Enhanced learning –Dr. Sa"njay Kumar Bose IIT Gwahati ) [5] "QUEUING THEORY AND ITS APPLICATIONS IN THE TELECOMMUNICATIONS NETWORKS”-by Giovanni Giambene Dipartimento di Ingegneria dell'Informazione, Università degli Studi di Siena,Via Roma, 56 - 53100 Siena, Ital. [6] Moshe Zukerman, EE Department,City University of Hong Kong-“Introduction to Queueing Theory and Stochastic Teletraffic Models”