Analysis of symmetric nonexhaustive polling with multiple servers

An analysis of polling schemes with multiple servers is presented where the service discipline at each station is assumed to be of the nonexhaustive (limited) type, i.e. no more than one customer can be removed from a station per visit of a server. The times spent by servers to walk from station to station are assumed to be nonzero and are modeled by independent, identically distributed random variables. The arrival processes at each queue are assumed to be Poisson, and serving times are modeled with independent, identically distributed random variables with arbitrary PDF. The case in which at most one server and the case in which any number of servers can simultaneously attend a queue are separately considered. Under the assumption of balanced traffic (equal arrival rates at all stations), several results concerning the cycle analysis and the stability of such schemes are obtained. A simple, explicit expression that gives an approximation for the steady-state average customer waiting time is derived