Analytical and Scalable Analysis of Transient Tandem Markovian Finite Capacity Queueing Networks

Analytical and Scalable Analysis of Transient Tandem Markovian Finite Capacity Queueing Networks

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Article ID: iaor20173330
Volume: 51
Issue: 3
Start Page Number: 823
End Page Number: 840
Publication Date: Aug 2017
Journal: Transportation Science
Authors: ,
Keywords: markov processes, networks, simulation, networks: flow
Abstract:

This paper proposes an analytical model to approximate the transient aggregate joint queue‐length distribution of tandem finite (space) capacity Markovian networks. The methodology combines ideas from transient aggregation‐disaggregation techniques as well as transient network decomposition methods. The complexity of the proposed method is linear in the number of queues and is independent of the space capacities of the individual queues. This makes it a suitable approach for the analysis of large‐scale networks. The transient joint distributions are validated versus simulation estimates. The model is then used to describe urban traffic dynamics and to address a dynamic traffic signal control problem. The signal plan analysis shows the added value of using joint distributional information, and more generally spatial‐temporal between‐link dependency information, to enhance urban traffic operations. The online appendix is available at https://doi.org/10.1287/trsc.2015.0629.

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