Decomposition Algorithms for Analyzing Transient Phenomena in Multiclass Queueing Networks in Air Transportation

Michael D. Peterson, Dimitris J. Bertsimas and Amedeo R. Odoni
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Michael D. Peterson: McKinsey & Company, Inc., Bedminster, New Jersey
Dimitris J. Bertsimas: Massachusetts Institute of Technology, Cambridge, Massachusetts
Amedeo R. Odoni: Massachusetts Institute of Technology, Cambridge, Massachusetts

Operations Research, 1995, vol. 43, issue 6, 995-1011

Abstract: A previous paper (1992) by the same authors studied the phenomenon of transient congestion in landings at an airport and developed a recursive approach for computing moments of queue lengths and waiting times. This paper extends our approach to a network, developing two approximations based on the prior method. Both approaches work by using delay information estimated at one location to update arrival schedules at other points in the network. We present computational results for a simple 2-node network, comparing the performance of the approximations with an alternative simulation approach. The methods give similar results in light to moderate traffic but show a growing disparity under heavier traffic, where the algorithms underestimate the true magnitude of delay propagation relative to simulation. Finally, to illustrate the usefulness of the modeling, we show how the results may be used to explore the issue of interaction between airports. Although this particular application motivated development of the model, the method is, in principle, applicable to other multiclass queueing networks where service capacity at a station may be modeled as a Markov or semi-Markov process. The model represents a new approach for analyzing transient congestion phenomena in such networks.

Keywords: probability; stochastic model applications; semi-Markov and Markov models of airport capacity; queues; transient results; approximations to compute performance measures in networks; transportation; network models; study of congestion's effects in airline hub-and-spoke networks (search for similar items in EconPapers)
Date: 1995
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