Several models, including those based on queueing theory; exist for predicting traffic queue size at signalized intersections. However, the traffic characteristics such as speed, density, flow, and congestion are so diverse that a tailor-made model, where the computation of the parameters could be done at each signal at regular intervals seems the most appropriate one. A vacation queueing model as in Lioris et al. (Lioris J, Pedarsani R, Tascikaraoglu FY, Varaiya P, Transp Res Part C Emerging Technol 77:292–305, 2017) falls in this category. In the above model, it is assumed that the arrival of vehicles is according to a Poisson process with parameter λ and their service time follows an exponential distribution with parameter μ. The server (traffic signal), goes on single vacations (red signal) after a random duration (green signal), which is exponentially distributed with parameter υ1. Each vacation duration follows an exponential distribution with parameter υ2. Steady state analytic expression for the average number of vehicles and the delay at the signal can then be obtained in terms of the above parameters. However, depending on the per minute vehicle arrival rate λ, the underlying Markov chain may take several minutes to reach the steady state. Hence, the steady state measures may vary from reality. The present study shows that even the transient measures don’t give a better prediction. Motie & Savla (Motie M, Savla K, IFAC-PapersOnLine. Elsevier B.V, 2017) applied a pure birth process for the red period and an M/D/1/N queue for the green period of the traffic signal. Transient study of their combined model showed better performance, compared to the steady state analysis of the Lioris et al. (Lioris J, Pedarsani R, Tascikaraoglu FY, Varaiya P, Transp Res Part C Emerging Technol 77:292–305, 2017) model. Our study shows that an Mt/Mt/1 queue gives a similar performance as the Motie & Savla (Motie M, Savla K, IFAC-PapersOnLine. Elsevier B.V, 2017) model. Capturing the traffic at a signal in Kerala, India, we compared the performance of the transient Lioris et al. (Lioris J, Pedarsani R, Tascikaraoglu FY, Varaiya P, Transp Res Part C Emerging Technol 77:292–305, 2017), Motie & Savla (Motie, M., & Savla, K., IFAC-PapersOnLine. Elsevier B.V, <publisher-loc>, 2017), and the Mt/Mt/1 queueing models. Our results suggest that the performance of the Motie & Savla (Motie M, Savla K, IFAC-PapersOnLine. Elsevier B.V, 2017) and the Mt/Mt/1 queueing models are similar; whereas the performance of the vacation queueing model deviates from reality.</publisher-loc>

Comparison of Vacation and Mt/Mt/1 Queueing Models for Traffic Flow at Signalized Intersections

会议论文
发表日期：

2025年

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Reya Kuruvila,
Narayanan C. Viswanath

摘要

Several models, including those based on queueing theory; exist for predicting traffic queue size at signalized intersections. However, the traffic characteristics such as speed, density, flow, and congestion are so diverse that a tailor-made model, where the computation of the parameters could be done at each signal at regular intervals seems the most appropriate one. A vacation queueing model as in Lioris et al. (Lioris J, Pedarsani R, Tascikaraoglu FY, Varaiya P, Transp Res Part C Emerging Technol 77:292–305, 2017) falls in this category. In the above model, it is assumed that the arrival of vehicles is according to a Poisson process with parameter λ and their service time follows an exponential distribution with parameter μ. The server (traffic signal), goes on single vacations (red signal) after a random duration (green signal), which is exponentially distributed with parameter υ1. Each vacation duration follows an exponential distribution with parameter υ2. Steady state analytic expression for the average number of vehicles and the delay at the signal can then be obtained in terms of the above parameters. However, depending on the per minute vehicle arrival rate λ, the underlying Markov chain may take several minutes to reach the steady state. Hence, the steady state measures may vary from reality. The present study shows that even the transient measures don’t give a better prediction. Motie & Savla (Motie M, Savla K, IFAC-PapersOnLine. Elsevier B.V, 2017) applied a pure birth process for the red period and an M/D/1/N queue for the green period of the traffic signal. Transient study of their combined model showed better performance, compared to the steady state analysis of the Lioris et al. (Lioris J, Pedarsani R, Tascikaraoglu FY, Varaiya P, Transp Res Part C Emerging Technol 77:292–305, 2017) model. Our study shows that an Mt/Mt/1 queue gives a similar performance as the Motie & Savla (Motie M, Savla K, IFAC-PapersOnLine. Elsevier B.V, 2017) model. Capturing the traffic at a signal in Kerala, India, we compared the performance of the transient Lioris et al. (Lioris J, Pedarsani R, Tascikaraoglu FY, Varaiya P, Transp Res Part C Emerging Technol 77:292–305, 2017), Motie & Savla (Motie, M., & Savla, K., IFAC-PapersOnLine. Elsevier B.V, , 2017), and the Mt/Mt/1 queueing models. Our results suggest that the performance of the Motie & Savla (Motie M, Savla K, IFAC-PapersOnLine. Elsevier B.V, 2017) and the Mt/Mt/1 queueing models are similar; whereas the performance of the vacation queueing model deviates from reality.