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Mathematical Problems in Engineering
Volume 7, Issue 5, Pages 433-454
http://dx.doi.org/10.1155/S1024123X01001727

Transient analysis of a queue where potential customers are discouraged by queue length

Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

Copyright © 2001 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

The transient solution is obtained analytically using continued fractions for a state-dependent birth-death queue in which potential customers are discouraged by the queue length. This queueing system is then compared with the well-known infinite server queueing system which has the same steady state solution as the model under consideration, whereas their transient solutions are different. A natural measure of speed of convergence of the mean number in the system to its stationarity is also computed.