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Journal of Applied Mathematics and Simulation
Volume 1, Issue 1, Pages 41-55
http://dx.doi.org/10.1155/S1048953388000048

On a multi-channel transportation loss system with controlled input and controlled service

University of Pittsburgh at Bradford, Campus Drive, Bradford, PA 16701, USA

Copyright © 1987 Hindawi Publishing Corporation. 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

A multi-channel loss queueing system is investigated. The input stream is a controlled point process. The service in each of m parallel channels depends on the state of the system at certain moments of time when input and service may be controlled. To obtain explicitly the limiting distribution of the main process (Zt) (the number of busy channels) in equilibrium, an auxiliary three dimensional process with two additional components (one of them is a semi-Markov process) is treated as semi-regenerative process. An optimization problem is discussed. Simple expressions for an objective function are derived.