Approximate mean waiting times in transient GI/G/1 queues

In this paper we give an approximation method for obtaining the probability the server is busy and the mean waiting time as seen by the nth arriving customer for the GI/G/1 queueing system. Transient behavior is the key issue of the method. The approximation consists of a pair of recursion formulae whose state variables are the probability of delay and the mean waiting time. Any initial state may be prescribed for the 0th arriving customer. Programming is very easy, and the computation is rapid. The procedure is useful for rush-hour analyses and for studying the recovery of a system from temporary overload.