Heavy traffic analysis of a transportation network model

We study a model of a stochastic transportation system introduced by Crane. By adapting constructions of multidimensional reflected Brownian motion (RBM) that have since been developed for feedforward queueing networks, we generalize Crane's original functional central limit theorem results to...

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Bibliographic Details
Published in:Journal of applied probability 1996-09, Vol.33 (3), p.870-885
Main Authors: Peterson, William P., Wein, Lawrence M.
Format: Article
Language:English
Subjects:
Applied sciences
Brownian motion
Covariance matrices
Exact sciences and technology
Limit theorems
Mathematical models
Mathematical vectors
Mathematics
Modeling
Motor vehicle traffic
Operational research and scientific management
Operational research. Management science
Passengers
Probability
Probability and statistics
Probability theory and stochastic processes
Queuing theory
Queuing theory. Traffic theory
Research Papers
Sciences and techniques of general use
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
Studies
Traffic
Transportation
Transportation networks
Vehicle capacity
Vehicles
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Summary:We study a model of a stochastic transportation system introduced by Crane. By adapting constructions of multidimensional reflected Brownian motion (RBM) that have since been developed for feedforward queueing networks, we generalize Crane's original functional central limit theorem results to a full vector setting, giving an explicit development for the case in which all terminals in the model experience heavy traffic conditions. We investigate product form conditions for the stationary distribution of our resulting RBM limit, and contrast our results for transportation networks with those for traditional queueing network models.
ISSN:0021-9002
1475-6072
DOI:10.2307/3215365