Multiserver multiqueue systems with limited service and zero walk time

A study of multiserver multiqueue systems, i.e., queuing systems comprising a set of waiting lines where customers arrive to be served by a pool of servers, is described. Servers cyclically move from one queue to another, and provide service to at most one waiting customer per visit to a queue. Such (1-limited) multiserver polling models are analyzed. Attention is restricted to the case where the movement of the servers from queue to queue takes place in zero time. Two different server utilization policies are considered, and exact results are presented for the average customer waiting time and delay in the simpler case, while simple upper and lower bounds and a very accurate approximation are proposed for the more complex policy. In both cases systems are assumed to be symmetrical, arrivals are taken to be Poisson, and service times exponential.<>