Transient solution of the virtual waiting tune of a single-server queue and its applications

The major emphasis in the study of general single-server queues has been towards analysis of their steady-state behavior. In many practical situations, however, the knowledge of the steady-state solution is not sufficient. This paper presents an approach for obtaining the transient solution of a single-server queueing system. Treating the virtual waiting time at any instant as a random variable, its expected value and the distribution function are given. The use of this approach requires less restrictive assumptions than those essential for prior techniques. Examples using this approach for practical problems are given.