Stationary waiting time distribution of a queue in which customers require a random number of servers

The authors consider the multiserver queueing system studied originally by L. Green in which customers request service from a random number of identical servers. They provide a matrix-geometric formulation of the problem, present a simple means for computing the stationary probability vector, and propose an algorithm based on randomization for computing the waiting time distribution. The authors also give a numerical example and discuss issues involved in extending the formulation to include customer priority classes.