Assessment of Delhi Ncr Traffic Using Queuing Model
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International Journal of Advanced Science and Technology Vol. 29, No. 7, (2020), pp. 5418-5424 Assessment Of Delhi Ncr Traffic Using Queuing Model Himanshu Mittal1) and Naresh Sharma2)* School of Basic and Applied Sciences, GD Goenka University, Gurugram, Haryana, India Emails:1) [email protected]; 2)*[email protected] Abstract Traffic congestion due to the increasing number of vehicles on the road is the prime concern of most of the Indian cities. Higher fuel consumption and generation of unburned hydrocarbons in surrounding necessitates the demand for the appropriate study of traffic movement to minimise the traffic hazards. In this study, the queuing based analytical method is used to analyse the vehicular traffic flow. As the aggregated model have a trivial resolution, M/M/1 queuing model is used to study the traffic approaching Dhaula Kuan intersection for arrival and waiting time to identify the spatial and temporal effects of traffic under various sessions for the day. The methodology adopted reveals the significant factors, causing traffic congestion and will also apply to the broad scenario for determining the traffic flow pattern. Keywords: Queuing model, traffic congestion, arrival time, waiting time. 1. Introduction The development of any city comes up with the traffic woes on the major junctions of the city. The ever increasing traffic results in casualties and also contributes heavily to the country’s mortality rate (Daganzo, 1994; Jain and Smith, 1997). These congested roads are majorly seen in highly populated metropolitan cities like Delhi, India. The stagnation of vehicles on the road for a significant time duration is referred to as traffic jams. There are tremendously varied factors that cause traffic jam, and these factors vary with the location and time of the day. Consumption of excessive fuel, wastage of passenger’s time, generation of unburned hydrocarbons in the atmosphere due to the traffic congestion are the primary concern of most of the cities (Vandaele et al., 2000; Sheu, 2004). Even emergency vehicles do not get sufficient space to travel, which ultimately leads to the loss of human life. Delay induced due to traffic congestion also have a severe impact on individuals as well as on the state's economic profile (Ehlert et al., 2005). The Poisson process is the commonly used technique for the analysis of arriving traffic (Baykal-Gursoy et al., 2008; Adeleke et al., 2009). Queuing model is also based on the Poisson distribution, and it is a commonly used technique for the assessment of skewed behavior of data, for the analysis of flux generated in data and for the design of a mathematical model for the classification of data (Jain and Smith, 1997; Daigle, 2005). Estimation of network traffic using the Queuing model facilitate the imitation of true network and can also be found reliable for suitable for the analysis, designing, and development of network (Adeleke et al., 2009; Mala and Varma, 2016). The probability of the number of vehicles arrived calculated using through Poisson distribution as: Where, P is the probability of arrival of x number of vehicles in t time, 휆 defined as the arrival rate of the vehicle per day. The weak correlation in analytical methods necessities the demand for analysis of actual traffic flow of congested areas. Heidemann (1996) analysed the traffic flow using M/M/1 queuing model for stationary traffic flow and extended the study using the same theory for non-stationary traffic flow (Boxma and Kurkova, 2000; Heidemann, 2001). Jain and Smith (1997) applied to the queuing model to analyse the optimum capacity of the road under various traffic flow conditions. The author illustrated the road space consumed by each vehicle and determined the maximum capacity of flow without affecting the arrival time. Van Woensel and Vandaele (2007) demonstrated the details of traffic flow using the queuing theory design for finite and infinite networks. The queuing theory design through the transient model found successful on small networks (Smith and Cruz, 2005; Van Woensel and Vandaele, 2006). ISSN: 2005-4238 IJAST 5418 Copyright ⓒ 2020 SERSC International Journal of Advanced Science and Technology Vol. 29, No. 7, (2020), pp. 5418-5424 In this paper, the traffic flow of the Dhuala Khan intersection is surveyed and analysed using the queuing theory. The various parameters such as traffic density, number of the vehicle in traffic, length of the vehicle, etc. are evaluated to assess the traffic scenario under different time frames. 2. Methodology 2.1. Queuing Theory and Model Description Queuing theory can be designed using various function elements; however, M/M/1 is the extensively used method of the approach (Purdue, 1973). The queuing theory comprises the Poisson distribution of arrival and service rate referred to as λ and µ, respectively. The arrival rate is defined as vehicles receiving from any channel and involves negative exponentially distributed service time for customers (Baykal-Gursoy et al., 2008). The system is built on the primary assumption that the decision of customers does not depend upon the other customers present in the system. Queuing system works with the large sample size of customers as the small fraction of impact-induced by every single customer on the performance of the system, indicating the utilisation of a small fraction of system resources by a single customer. Queuing theory performs in such a way it responds to each customer on first come first basis as who reaches first for receiving the service and describes the working model of the system (Bhunia et al., 2020). The research utilises the above assumptions of the Queuing model. The theory is design considering that, a customer who will enter the system, would fall in the conventions mentioned above. There would be a significant number of vehicles present on each channel, each vehicle uses a fraction of the total highway resources available, and the independent decision of each car driver to enter the highway. 2.2. Modeling parameters The mean performance of the model (M/M/1) can be determined from the traffic intensity as: For the development of the consistent system, the vehicle handling capacity of the road should always higher than the vehicles approaching the road in the given time. If this condition becomes true, the traffic density will remain equal or less than one always (Boxma and Kurkova, 2000). The usage of a particular channel can also be determined using the outcome of traffic density. Therefore, the probability of the number of the vehicle in the study area at time t would be: 푃0 = 1 − 휌 Where P is the probability of a vehicle. For the n number of vehicles running the model, the probability would become: 푃푛 = 휌푛 ∗ 푃0 The average number of customers, Cs at time t in the n number of vehicles would be: The average time spends by the customer in traffic increases with the traffic intensity. The expected average queue length is calculated as: The total time spent in traffic is estimated as: The waiting time of customers due to the queue length is estimated as: ISSN: 2005-4238 IJAST 5419 Copyright ⓒ 2020 SERSC International Journal of Advanced Science and Technology Vol. 29, No. 7, (2020), pp. 5418-5424 Therefore, each queue would cater to a large number of customer, can be determined as: 3. Study Area Dhaula Kuan intersection, Delhi, India, is selected as the study area due to heavy traffic load over the area. The figure below represents the area where the approaching arrows define the arrival of vehicles. North illustrates the flow from Paharganj; South flow begins from Mahipalpur, East flow from INA, and West directs from Rajouri Garden to Dhaula Kuan intersection. The schematic diagram of the Dhuala Kuan intersection is shown in Figure 1. Figure 1: Schematic representation of Dhaula Kuan Intersection The study involves data collection at the Dhaula Kuan intersection during peak hours of traffic. The data collection is divided into three different time frames as morning, evening, and afternoon. The morning hours are considered from 8:30 to 11:30; afternoon hours are considered as 01:00 to 4:00, and evening hours are defined as 6:30 to 9:30 for consecutive ten days. Afterwards, the calculation of various parameters required for queuing theory is calculated for each day. 4. Results and Discussion The traffic flow at the Dhuala Kuan is being surveyed and analysed to identify the most problematic channel approaching the intersection. Final results and evaluations were made after following the procedure, including traffic flow measurement and traffic congestion analysis. Data evaluation of parameters provided insight about approaching traffic intensity in channels leading to Dhaula Kuan intersection during peak hours of Evening and Morning, respectively. The detailed results of all the parameters of Queuing theory are illustrated in Table 1. Table 1: Traffic analysis at the Dhaula Kuan Intersection Time Time Customer Customer Arrival Service Traffic Spent in Spent in Location Session waiting in waiting in Rate Rate Intensity the the System queue System Queue 흀 µ ρ C퐬 Ct Et Ew ISSN: 2005-4238 IJAST 5420 Copyright ⓒ 2020 SERSC International Journal of Advanced Science and Technology Vol. 29, No. 7, (2020), pp. 5418-5424 INA to Morning 74 82 0.902 9 8 0.1250 0.1128 Dhaula Afternoon 33 55 0.600 2 1 0.0455 0.0273 Kuan Intersection Evening 79 80 0.988 79 78 1.0000 0.9875 Mahipalpur Morning 68 70 0.971 34 33 0.5000 0.4857 to Afternoon 31 64 0.484 1 0 0.0303 0.0147 Dhaula Kuan Evening 78 80 0.975 39 38 0.5000 0.4875 Intersection Rajauri Morning 71 74 0.959 24 23 0.3333 0.3198 Garden to Afternoon 31 51 0.608 2 1 0.0500 0.0304 Dhaula Kuan Evening 81 85 0.953 20 19 0.2500 0.2382 Intersection Pahadganj Morning 60 75 0.800 4 3 0.0667 0.0533 to Dhaula Kuan Afternoon 28 62 0.452 1 0 0.0294 0.0133 Intersection Evening 60 77 0.779 4 3 0.0588 0.0458 4.1.