Analysis of polling systems with a mixture of exhaustive and gated service disciplines

Queueing analysis is performed for a certain type of multiple-station system attended by a single server in cyclic order. The service discipline at each station may be ‘exhaustive’ or ‘gated’, and staitons with different disciplines can coexist in any order in the system. The mean and second moment of the waiting time at each station are obtained by solving a set of O(N³) and O(N⁴) linear equations, respectively, where N is the number of stations in the system. The paper considers the FCFS (first-come, first-served) and LCFS (last-come, first-served) order of service at each station. By numerical calculation of the mean waiting times (which do not depend on whether the order of service at each station is FCFS or LCFS), it is shown that gated-service stations close downstream from an exhaustive-service station receive favorable treatment, and that exhaustive-service stations close downstream from a gated-service station receive unfavorable treatment.