A priority M/G/1 queue with application to voice/data communication

A single server queue, with two types of customers having different Poisson arrival rates and different general service distributions, is considered in which only one type of customer can be buffered. The customers that cannot be buffered are assumed to have preemptive priority over the other customers. The customers that can be buffered belong to several priority classes in which service is provided according to a non-preemptive priority discipline among the classes. The Laplace-Stieltjes transform of the queueing and system times for different priority classes and some resulting performance measures are obtained using level crossing methods. This model has applications to integrated voice/data transmission and to systems where the service medium is subject to breakdowns.