A Simple Approximation to the Average Queue Size in the Time-Dependent M/M/1 Queue

1 April 1976

journal article
Published by Association for Computing Machinery (ACM) in Journal of the ACM

Vol. 23 (2) , 361-367
https://doi.org/10.1145/321941.321955

Abstract

The time-dependent equations for the M/M/1 queue can be reduced to a single equation for the expected queue size, but the equation is dependent on P ₀ ( t ), the probability of no jobs in the system. An exact equation for the behavior of P ₀ ( t ) under special conditions is derived and an approximation relating P ₀ ( t ) to Q ( t ), the expected queue size at time t , is derived for the case when the change in queue size is slow compared to the service rate. It is found that the approximation affords a significant improvement over the use of a steady state approximation to the time-dependent queue and is simpler to use than the exact equations.

Keywords

This publication has 1 reference indexed in Scilit:

Air-Terminal Queues under Time-Dependent Conditions
Operations Research, 1972