Modeling Vehicular Traffic Flow using M/G/C/C State Dependent Queueing Models

Jain, Rajat; Smith, J. MacGregor

doi:10.1287/trsc.31.4.324

Cited by 132 publications

(87 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, in roadway traffic networks it is well known that the vehicle service time deteriorates as a function of the occupancy on the roadway [7]. In human-based service systems, there is a strong correlation between the volume of work demanded from a human and her/his productivity.…”

Section: Introductionmentioning

confidence: 99%

Busy period analysis of the level dependent PH/PH/1/K queue

Hanbali

2011

Queueing Syst

View full text Add to dashboard Cite

In this paper, we study the transient behavior of a level dependent single server queuing system with a waiting room of finite size during the busy period. The focus is on the level dependent PH/PH/1/K queue. We derive in closed form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. We differentiate between two types of losses: the overflow losses that are due to a full queue and the losses due to an admission controller. For the M/PH/1/K, M/PH/1/K under a threshold policy, and PH/M/1/K queues, we determine simple expressions for their joint transforms. Keywords

show abstract

Section: Introductionmentioning

confidence: 99%

Busy period analysis of the level dependent PH/PH/1/K queue

Hanbali

2011

Queueing Syst

View full text Add to dashboard Cite

show abstract

“…However one can expect this estimate to grow when δ is picked inadequately large, and at the same time reducing perturbation by several orders can lead to 14 increase in computational complexity and the problem becomes less stable. Hence one should seek a compromise between these two conditions when fixing the order of perturbation.…”

Section: N-class Model: Analysis and Resultsmentioning

confidence: 99%

“…Assume that the file size is distributed generally (with CDF G(.)) with mean 1/α..Using the result for M/G/C/C queues with state dependent service in Smith and Jain [14], we have the probability that there…”

Section: General Distribution For File Sizesmentioning

confidence: 99%

Pricing in next generation networks: a queuing model to guarantee QoS

Yacoubi¹,

Emelianenko

Gautam

2003

Performance Evaluation

View full text Add to dashboard Cite

We consider the scenario where users access Next Generation Networks via Network Access Providers (NAP). We assume that users belong to N different classes and the bandwidth received by each class is determined by a user share differentiation (USD) scheme. According to USD, each class is guaranteed a minimum bandwidth and all users accepted into the NAP are allocated the minimum bandwidth corresponding to their class and any remaining bandwidth is shared according to the ratio of the minimum bandwidths of each class. We develop a queueing-based model and solve an optimization problem to determine the minimum bandwidth (defined in USD) for each of the N classes that maximizes the revenue of the NAP, subject to satisfying a request blocking performance guarantee.

show abstract

“…Vandaele et al [46] and Heidemann [28], showed that queueing models can also be used to explain uninterrupted traffic flows and thus offers a more practical approach, useful for sensitivity analysis, forecasts, etc. Jain and Smith [32] describe in their paper a state-dependent M/G/C/C queueing model for traffic flows. Part of their logic is used here to extend our queueing models to state-dependent ones.…”

Section: A Queueing Approachmentioning

confidence: 99%

A Queueing Framework for Routing Problems with Time-dependent Travel Times

Woensel¹,

Kerbache²,

Peremans³

et al. 2006

J Math Model Algor

View full text Add to dashboard Cite

Assigning and scheduling vehicle routes in a dynamic environment is a crucial management problem. Despite numerous publications dealing with efficient scheduling methods for vehicle routing, very few addressed the inherent stochastic and dynamic nature of travel times. In this paper, a vehicle routing problem with time-dependent travel times due to potential traffic congestion is considered. The approach developed introduces the traffic congestion component based on queueing theory. This is an innovative modelling scheme to capture the stochastic behavior of travel times as it generates an analytical expression for the expected travel times as well as for the variance of the travel times. Routing solutions that perform well in the face of the extra complications due to congestion are developed. These more realistic solutions have the potential to reduce real operating costs for a broad range of industries which daily face routing problems. A number of datasets are used to illustrate the appropriateness of the novel approach. Moreover it is shown that static (or time-independent) solutions are often infeasible within a congested traffic environment which is generally the case on European road networks. Finally, the effect of travel time variability (obtained via the queueing approach) is quantified for the different datasets.

show abstract

Modeling Vehicular Traffic Flow using M/G/C/C State Dependent Queueing Models

Cited by 132 publications

References 11 publications

Busy period analysis of the level dependent PH/PH/1/K queue

Busy period analysis of the level dependent PH/PH/1/K queue

Pricing in next generation networks: a queuing model to guarantee QoS

A Queueing Framework for Routing Problems with Time-dependent Travel Times

Contact Info

Product

Resources

About