TY - JOUR

T1 - Determining the exit time distribution for a closed cyclic network

AU - Baccelli, François

AU - Massey, William A.

AU - Wright, Paul E.

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1994/3/14

Y1 - 1994/3/14

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0028385880&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028385880&partnerID=8YFLogxK

U2 - 10.1016/0304-3975(94)90298-4

DO - 10.1016/0304-3975(94)90298-4

M3 - Article

AN - SCOPUS:0028385880

VL - 125

SP - 149

EP - 165

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1

ER -