Symmetric queues served in cyclic order

Consider a symmetrical system of n queues served in cyclic order by a single server. It is shown that the stationary number of customers in the system is distributed as the sum of three independent random variables, one being the stationary number of customers in a standard M/G/1 queue. This fact is used to establish an upper bound for the mean waiting time for the case where at most k customers are served at each queue per visit by the server. This approach is also used to rederive the mean waiting times for the cases of exhaustive service, gated service, and serve at most one customer at each queue per visit by the server.