1. A mean-field limit for a class of queueing networks
- Author
-
A. A. Puhalskii, Alexandre Rybko, M. Ya. Kelbert, F. I. Karpelevich, Yu. M. Suhov, and François Baccelli
- Subjects
Discrete mathematics ,Queueing theory ,Boundary problem ,Response time ,Statistical and Nonlinear Physics ,Statistical model ,Statistical mechanics ,Message switching ,chemistry.chemical_compound ,Mean field theory ,chemistry ,Probability distribution ,Mathematical Physics ,Mathematics - Abstract
A model of centralized symmetric message-switched networks is considered, where the messages having a common address must be served in the central node in the order which corresponds to their epochs of arrival to the network. The limitN → ∞ is discussed, whereN is the branching number of the network graph. This procedure is inspired by an analogy with statistical mechanics (the mean-field approximation). The corresponding limit theorems are established and the limiting probability distribution for the network response time is obtained. Properties of this distribution are discussed in terms of an associated boundary problem.
- Published
- 1992