A rate balance principle and its application to queueing models

A rate balance principle and its application to queueing models

0.00 Avg rating0 Votes
Article ID: iaor20174502
Volume: 87
Issue: 1
Start Page Number: 95
End Page Number: 111
Publication Date: Oct 2017
Journal: Queueing Systems
Authors: , ,
Keywords: queues: applications, queues: theory, markov processes, stochastic processes
Abstract:

We introduce a rate balance principle for general (not necessarily Markovian) stochastic processes. Special attention is given to processes with birth‐and‐death‐like transitions, for which it is shown that for any state n, the rate of two consecutive transitions from n 1 equ1 to n + 1 equ2 coincides with the corresponding rate from n + 1 equ3 to n 1 equ4 . We demonstrate how useful this observation is by deriving well‐known, as well as new, results for non‐memoryless queues with state‐dependent arrival and service processes. We also use the rate balance principle to derive new results for a state‐dependent queue with batch arrivals, which is a model with non‐birth‐and‐death‐like transitions.

Reviews

Required fields are marked *. Your email address will not be published.