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February, 1993 Travel and Sojourn Times in Stochastic Networks
Kwang Ho Kook, Richard F. Serfozo
Ann. Appl. Probab. 3(1): 228-252 (February, 1993). DOI: 10.1214/aoap/1177005517

Abstract

This study concerns travel times in a stochastic network in which units move among the nodes that process the units. The network may be closed or open, there may be several types of units and the processing at each node may depend on the numbers of units at the other nodes. This is a Jackson network when the nodes operate independently. The travel time on a "route" in this network is the time it takes for an arbitrary unit to traverse one of a series of nodes that constitute the route, when the network is in equilibrium. An example is the time for a unit to move from one set of nodes to another. We present an expression for the expectation of a general travel time. We also characterize the distribution of the travel time, and the sojourn times at the nodes, on an overtake-free path. This includes the known results on the product-form distribution of sojourn times at the nodes on overtake-free paths in Jackson networks.

Citation

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Kwang Ho Kook. Richard F. Serfozo. "Travel and Sojourn Times in Stochastic Networks." Ann. Appl. Probab. 3 (1) 228 - 252, February, 1993. https://doi.org/10.1214/aoap/1177005517

Information

Published: February, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0771.60069
MathSciNet: MR1202525
Digital Object Identifier: 10.1214/aoap/1177005517

Subjects:
Primary: 60K20
Secondary: 60F15 , 60K25

Keywords: Little's law , Markov process , Palm probability , passage time , queueing service system , sojourn time , Stochastic network , Strong law of large numbers , travel time

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.3 • No. 1 • February, 1993
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