Determining the exit time distribution for a closed cyclic network

François Baccelli, William A. Massey, Paul E. Wright

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Consider a closed, N-node, cyclic network, where each node has an independent, exponential single server. Using lattice-Bessel functions, we can explicitly solve for the transition probabilities of events that occur prior to one of the nodes becoming empty. This calculation entails associating with this absorbing process a symmetry group that is the semidirect product of simpler groups. As a byproduct, we are able to compute explicitly the entire spectrum for the finite-dimensional matrix generator of this process. When the number of nodes exceeds 1, such a spectrum is no longer purely real. Moreover, we are also able to obtain the quasistationary distribution or the limiting behavior of the network conditioned on no node ever being idle.

Original languageEnglish (US)
Pages (from-to)149-165
Number of pages17
JournalTheoretical Computer Science
Volume125
Issue number1
DOIs
StatePublished - Mar 14 1994
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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