The departure process for queueing systems with batch arrival of customers

The departure process for queueing systems with batch arrival of customers

0.00 Avg rating0 Votes
Article ID: iaor2010913
Volume: 24
Issue: 2
Start Page Number: 246
End Page Number: 263
Publication Date: Apr 2008
Journal: Stochastic Models
Authors:
Keywords: batch queues, GI/G/1 queues
Abstract:

In the article, a single-server queueing system of GI/G/1 type with batch arrival of customers, individual service and unlimited queue is considered. We denote by h(t) the departure process that at any fixed moment t takes on a random value equal to the number of customers completely served during [0, t].A system of integral equations on a half-axis [0,8] is written for probabilities under two different initial conditions. Hence some general results for the departure process in transient state are obtained. The results are written in terms of Laplace-Stieltjes transforms of distribution functions F1 and F2 of interarrival and service times respectively, and using factors of a certain factorization identity of Wiener-Hopf type connected with F1 and F2.

Reviews

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 Your email address will not be published.