Assessment of Delhi Ncr Traffic Using Queuing Model

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

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:

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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

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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. Morning Session Calculation of traffic intensity reveals the traffic situation over an area where if the value approaches equivalent to 0.5, then it states the stable traffic situation with variable traffic flow. At the same time, the unstable traffic flow resulted when the value inclines towards 1. The traffic intensity of all the channels is shown in Figure 2. For the traffic flow from Paharganj to the Dhuala Kuan, the arrival rate and service rate are determined as 60 and 75 respectively, signifying traffic intensity as 0.80, which reveals somewhat stable situation, but without smooth traffic flow. Whereas, other locations shows the critical state of traffic. The evaluation of traffic flow from INA to the Dhuala Kuan indicates the heavy traffic intensity as 0.908 (observed arrival rate (74) and service rate (82). However, the highly unstable and critical condition of traffic flow is observed while directing from Mahipalpur and Rajouri Garden to the Dhuala Kuan as traffic intensity was calculated as 0.971 and 0.959, respectively, approaching to 1.

4.2. Afternoon Session Comparatively, stable traffic flow is observed during the afternoon for the vehicular flow from all of the directional sites to the study area, with respect, the flow found during morning and evening sessions. The most stable traffic situation with smooth traffic flow ensues for the vehicular movement from Paharganj in comparison to other channels leading to the study area for Morning and Afternoon sessions, describing traffic intensity as 0.452 calculated after dividing observed arrival rate (28) to the service rate (62). Traffic intensity of flow from INA to Dhaula Kuan and Mahipalpur to Dhaula Kuan is calculated as 0.60 (observed arrival and service rate as 33 and 55 respectively) and 0.484 (arrival and service rate observed as 31 and 64 respectively). Such traffic flow represents an improved situation, on comparing with another channel (West) directing towards the Dhuala Kuan during the afternoon. Rajouri Garden carries traffic flow to the Dhuala Kuan represents a stable traffic flow situation but without smooth flow, described after calculating their traffic intensity as 0.608.

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Traffic Density 1.000 Tra 0.800 ffic De 0.600 nsi ty 0.400

0.200

0.000 M Aft Ev M Aft Ev M Aft Ev M Aft Ev or er eni or er eni or er eni or er eni nin no ng nin no ng nin no ng nin no ng g on g on g on g on

INA to Dhuala Kuan Mahipalpur to Dhuala Rajauri Garden to Pahadganj to Dhaula Kuan Dhaula Kuan Kuan Different Channels

Figure2: Traffic density of Dhuala Kuan intersection for various channels

Time Spend in Queue 1.0000 Morning

Ti 0.8000 Afternoon me sp 0.6000 Evening en 0.4000 d 0.2000

0.0000 INA Mahipalpur Rajouri Garden Pahadganj Different Channels

Figure 3: Time spent in traffic at Dhuala Kuan intersection

4.3. Evening Session The most stable and securable traffic flow situation with the smooth vehicular flow is observed along the path of Paharganj to the Dhuala Kuan during evening sessions while comparing with other directional routes in all three sessions. Traffic intensity is calculated as 0.779 using respective arrival rate (60) and service rate (77), which states the least value of traffic intensity as compared to others. On the contrary, maximum traffic intensity (0.988) with a huge traffic load is observed for the flow from INA to Dhaula Kuan, stating the worst condition of traffic on the route during the evening, after comparing with all other channels for all three sessions. This route states the seriously unstable and critical traffic situation followed by the

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Mahipalpur having traffic intensity of 0.975. INA also has the maximum time spent by vehicles in traffic, as shown in Figure 3. The traffic route from Rajouri Garden to the Dhuala Kuan also reveals the unstable traffic flow where the traffic intensity observed as 0.953 is found slightly lesser than Mahipalpur and INA channel, but still on higher side. Thus, the traffic flow situation is stable without smooth flow was only found in Paharganj to the Dhaula Kuan during the evening session.

4.4. Outcome of the Study From the above results, the primary outcome is made that some channels leading to the study area show traffic intensity approaching to 1, indicating the proximity of the arrival rate to the respective service rate. INA and Mahipalpur routes directing towards intersection are found as the most overcrowded routes during the morning and evening sessions followed by Rajouri Garden. On the contrary, traffic congestion is found to be smooth with stable traffic system directing from Paharganj to the Dhaula Kuan intersection during the evening. The primary reasons behind the above results support the observations made in the study area like unauthorised parking, and roadside hawkers increase the rate of traffic congestion over an area. Along with this, there are wavering time intervals observed between the signals given by servers like traffic police signals, which disturbs the traffic flow intensity across the area. Another outcome is prepared when it is found that commercial transport drivers park and off/on load passengers at the unauthorised places in proximity with intersections, impede the traffic flow, and destabilises the traffic situation. With disturbed traffic situations and heavy vehicular load, pollution becomes the major concern as increasing with the rapid rate for the area and even the city.

5. Conclusion The study comprises of assessment of traffic congestion at Dhaula Kuan intersection of Delhi, India. Dhaula Kuan receives the heavy traffic flow throughout the day from all the directions. The traffic merging at Dhuala Kuan intersection from all the four directions are surveyed and analysed to calculate the traffic intensity, time spends by vehicle in traffic and time spent by vehicle in a queue, the number of the vehicles waiting in traffic and the number of vehicles in queue. Queuing theory is applied for the assessment of traffic flow from each side approaching Dhuala Kuan. Results of queuing theory represent there is significant variation in traffic flow during a different period of a single day. There is a need to design separate lanes for the various group of vehicles to avoid congestion for the management of the heavy traffic, especially in morning and evening hours with the properly visible direction and warning signs to assists the driver. Queuing theory comes out as a useful tool and would be an effective technique for the planning of Smart cities. The design of alternative routes or the provision of crossover at the junction helps in the frequent and easy movement of traffic; moreover, the available carriageway should be free from any hindrances like roadside hawkers, and unauthorised parking.

References 1. A. Ehlert, M.G.H Bell, S. Grosso (2005). The optimisation of traffic count locations in road networks. Transportation Research Part B. 2. C.F. Daganzo, (1994). The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory, Transportation Research – Part B 4, 269–287. 3. D. Heidemann, (2001). A queueing theory model of nonstationary traffic flow. Transportation Science, 35(4), 405–412. 4. J. MacGregor Smith, F.R.B Cruz (2005). The buffer allocation problem for general finite buffer queueing networks. IIE Transactions, 37(4), 343–365. 5. J.-B. Sheu,(2004). A sequential detection approach to real-time freeway incident detection and characterisation, European Journal of Operational Research, 157, 471–485. 6. J. N. Daigle, (2005). Queueing Theory with Applications to Packet Telecommunication, ISBN: 0-387-22857-8, Springer, Boston, USA, 2005.

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7. M. Baykal-Gursoy, W. Xiao (2008). Modeling traffic flow interrupted by incidents. European Journal of Operational Research, 195, 127-138. 8. Mala, S.P. Varma (2016). Minimisation of Traffic Congestion by Using Queueing Theory, IOSR Journal of Mathematics (IOSR-JM), 12(1), 116-122. 9. N. Vandaele, T.V. Woensel, A. Verbruggen (2000). A queueing based traffic flow model, Transportation Research Part D 5, 121–135. 10. O.J. Boxma, I.A. Kurkova (2000). The M/M/1 queue in a heavy-tailed random environment. Statistica Neerlandica, 54 (2), 221–236. 11. P. Purdue, (1973). The M/M/1 queue in a Markovian environment, Operations Research 22, 562– 569. 12. R. Adeleke, O.D.Ogunwale, O.Y. Halid, (2009). Application of Queueing Theory to Waiting Time of Out-Patients in Hospitals, Pacific Journal of Science and Technology, 10(2), 270-274 13. R. Jain, J.M. Smith, (1997). Modeling vehicular traffic flow using M/G/C/C state dependent queueing models, Transportation Science 31 (4), 324–336. 14. A. K. Bhunia, L. Sahoo, A.A. Shaikh, (2020). Queueing theory. Advanced Optimisation and Operations Research, Optimizationa and its applications, 153, 403-486 15. D. Heidemann, (1996). A queueing theory approach to speed- flow-density relationships. J.-B. Lesort, ed. Transportation and Traffic Theory—Proceedings of the 13th International Symposium on Transportation and Traffic Theory. Elsevier Science, Oxford/New York/Tokyo, 103–118. 16. T. Van Woensel, N. Vandaele, (2007). Modeling traffic flows with queueing models: A review. Asia-Pacific Journal of Operational Research, 24(04), 435–461. 17. T. Van Woensel, N. Vandaele, (2006). Empirical validation of a queueing approach to uninterrupted traffic flows. 4OR, 4(1), 59–72.

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