A queueing based traffic flow model

Vandaele, Nico; Woensel, Tom Van; Verbruggen, Aviel

doi:10.1016/s1361-9209(99)00028-0

Cited by 113 publications

(80 citation statements)

References 9 publications

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“…The distance is readily available in the time-independent routing models, but the speed is a new variable that needs to be specified. In this paper, the time-dependent speeds are obtained using queueing models for traffic flows [28,46]. This section is organized as follows: first, the queueing approach to traffic flow is presented, then the procedure to obtain the expected travel time is explained in detail, next the determination of the variance of the travel time is elaborated and finally, the added value of using queueing theory is discussed in detail.…”

Section: Framework For Time-dependent Travel Timesmentioning

confidence: 99%

“…This traditional approach is limited in terms of predictive power and sensitivity analysis. 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.…”

Section: A Queueing Approachmentioning

confidence: 99%

“…This length is then equal to 1/k j and matches the minimal space needed by one vehicle on that road. Each road segment is then considered as a service station, in which vehicles arrive at a certain rate λ and get served at another rate μ [28,46,51]. …”

Section: A Queueing Approachmentioning

confidence: 99%

“…Vandaele et al [46] developed different queueing models. 1 The M/M/1 queueing model (exponential arrival and service rates) is considered as a base case, but due to its specific assumptions regarding the arrival and service processes, it is not useful to describe real-life situations.…”

Section: A Queueing Approachmentioning

confidence: 99%

“…Relaxing both assumptions for the arrival and service processes results in the GI/G/m queueing model. Heidemann [28] and Vandaele et al [46] showed that the speed v can be calculated by dividing the length of the road segment ( ) by the total time in the system (W).…”

Section: A Queueing Approachmentioning

confidence: 99%

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

Woensel¹,

Kerbache²,

Peremans³

et al. 2006

J Math Model Algor

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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.

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Section: Framework For Time-dependent Travel Timesmentioning

confidence: 99%

Section: A Queueing Approachmentioning

confidence: 99%

Section: A Queueing Approachmentioning

confidence: 99%

Section: A Queueing Approachmentioning

confidence: 99%

Section: A Queueing Approachmentioning

confidence: 99%

See 3 more Smart Citations

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

Woensel¹,

Kerbache²,

Peremans³

et al. 2006

J Math Model Algor

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Active Traffic Signal Decisions Using Vector‐Matrix Multiplication

Jang

Jeon

2023

Advanced Intelligent Systems

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A novel methodology in the manner of vector‐matrix multiplication (VMM) architecture is suggested for intelligently determining traffic signal changes to enhance the flow of urban traffic. Unlike the conventional prediction‐based traffic model, a real‐time decision model considering the traffic density at each transport section is established, which simplifies the traffic signal decision process as a convolutional transformation. Compared with a periodically repetitive signal changing system, the suggested VMM system actively optimizes the signal configuration in an irregular shape according to the traffic density distribution, resulting in reduction in the time cost with highly improved decision efficiency. With this system based on particle dynamics, the travel time is reduced by ≈10% at the same pass ratio for different road structures (one‐way, bidirectional, and intersectional transport). The pass ratio and resulting flow dynamics can be controllable using the different transformation matrix selections according to the traffic conditions. In addition, the analog conductance of the memristor device to the transformation matrix elements is applied, maintaining its reduction rate with a deviation tolerance of the VMM process up to ≈50%. It is believed that VMM‐based signal decision platform can lead to great progress for fast and efficient transport in complex urban traffic networks.

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Constructal Pattern Formation in Nature, Pedestrian Motion, and Epidemics Propagation

Miguel¹

2007

Constructal Theory of Social Dynamics

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A queueing based traffic flow model

Abstract: This research was supported by the Environmental Report for Flanders (VMM), the Science Foundation of Flanders (FWO-project G.0063.98) and BOF fund of UFSIA. 2 The authors like to thank Ilse Bilsen and Ruth Creten for their contribution.

Cited by 113 publications

References 9 publications

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

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

Active Traffic Signal Decisions Using Vector‐Matrix Multiplication

Constructal Pattern Formation in Nature, Pedestrian Motion, and Epidemics Propagation

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