Waiting-time approximations in multiqueue systems with cyclic service

This study is devoted to mean waiting-time approximations in a single-server multi-queue model with cyclic service and zero switching times of the server between consecutive queues. Two different service disciplines are considered: exhaustive service and (ordinary cyclic) nonexhaustive service. For both disciplines it is shown how estimates of the mean waiting times at the various queues can be obtained when no explicit information on arrival intensities and service-time distributions is available, while only the utilizations at the queues and the lengths of the busy periods of the system can be measured. In the exhaustive case, a known mean waiting-time approximation is shown to be suitable for our purposes; in the nonexhaustive case, a new approximation has been derived which is simple and yet more accurate than existing approximations. Extensive simulation validates the approximation methods

Waiting-time approximations for cyclic-service systems with switchover times

Mean waiting-time approximations are derived for a single-server multi-queue system with nonexhaustive cyclic service. Nonzero switchover times of the server between consecutive queues are assumed. The main tool used in the derivation is a pseudo-conservation law recently found by Watson (1984). The approximation is simpler and, as extensive simulations show, more accurate than existing approximations. Moreover, it gives very good insight into the qualitative behaviour of cyclic-service queueing systems