Journal of Applied Mathematics and Stochastic Analysis
Volume 5 (1992), Issue 2, Pages 177-192
doi:10.1155/S1048953392000157
On a first passage problem in general queueing systems with multiple vacations
Department of Applied Mathematics, Florida Institute of Technology, Melbourne 32901, FL, USA
Received 1 September 1991; Revised 1 January 1992
Copyright © 1992 Jewgeni H. Dshalalow. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The author studies a generalized single-server queueing system with
bulk arrivals and batch service, where the server takes vacations each time the
queue level falls below r(≥1) in accordance with the multiple vacation
discipline. The input to the system is assumed to be a compound Poisson
process modulated by the system and the service is assumed to be state dependent. One of the essential part in the analysis of the system is the employment
of new techniques related to the first excess level processes. A preliminary
analysis of such processes and recent results of the author on modulated processes enabled the author to obtain all major characteristics for the queueing
process explicitly. Various examples and applications are discussed.