International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 3, Pages 593-600
doi:10.1155/S0161171292000759
On a single-server queue with fixed accumulation level, state dependent service, and semi-Markov modulated input flow
Department of Applied Mathematics, Florida Institute of Technology, Melbourne 32901, FL, USA
Received 29 July 1991
Copyright © 1992 Jewgeni H. Dshalalow and Gary Russell. 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 authors study the queueing process in a single-server queueing system with state dependent service and with the input modulated by a semi-Markov process embedded in the queueing process. It is also assumed that the server capacity is r≥1 and that any service act will not begin until the queue accumulates at least r units. In this model, therefore, idle periods also depend upon the queue length.
The authors establish an ergodicity criterion for the queueing process and evaluate explicitly its stationary distribution and other characteristics of the system, such as the mean service cycle, intensity of the system, intensity of the input stream, distribution of the idle period, and the mean busy period. Various special cases are treated.