Pseudo-conservation laws in cyclic-server, multiqueue systems with a class of limited service policies

A multiqueue system with a cyclic server and a class of limited service policies is discussed. In particular, exhaustive limited (EL), gated limited, and general decrementing service policies are investigated. The derivations of the expected amount of work left in the queue at the server departures for these three policies are given. These results are all in terms of unknown boundary probabilities. Corresponding server vacation models are used to estimate these unknown probabilities. Pseudoconservation laws for these policies are subsequently obtained. Numerical results obtained for the EL policy are noted to be very accurate compared with simulation results. Conservation laws with mixed service policies, and exact expressions of mean waiting times in symmetric systems are given