A Simple Approximation to the Average Queue Size in the Time-Dependent M
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 PO(t), the probability of no jobs in the system. An exact equation for the behavior of PO(t) under special conditions is derived and an approximation relating PO(t) to Q(t), the expected queue size at time t, is found 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. 16 pp. Ref.