Technical Note—On Waiting Times for a Queue in Which Customers Require Simultaneous Service from a Random Number of Servers

We consider a queueing system, first introduced by L. Green in 1980, in which customers from a Poisson arrival stream request simultaneous service from a random number of identical servers with exponential service times. Computational formulas for the second moment of time in queue are given, along with tables of these values for selected systems. Numerical results show that the coefficient of variation for time in queue is always greater than 1 and decreases with increasing congestion.