Stationary Waiting Time Distribution of a Queue in Which Customers Require a Random Number of Servers

We consider the multiserver queueing system studied originally by L. Green (1980) in which customers request service from a random number of identical servers. We 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. We also give a numerical example and discuss issues involved in extending the formulation to include customer priority classes.