The Time-Dependent Problem for a Queue with Preemptive Priorities

Use is made of the Laplace transform to study the two-dimensional preemptive priority queuing problem with exponential arrival and service times. The method of generating functions is used to solve the difference equations so obtained. In the section “The Differential-Difference Equations for the System” the transform of the generating function of the queuing process is given and the moments of the distribution of the nonpriority queue length derived from this. An explicit solution is given only for the case of equal service rates, the general case requiring only additional calculation. The distribution of the length of a busy period for the nonpriority queue is studied later.