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

This paper considers a cyclic-service system with a class of limited service policies that consists of exhaustive limited, gated limited and general decrementing policies. Under these policies, the number of customers served consecutively during a server visit is limited by a vector of integers. The major results in this paper are derivations of expected amount of work left in the queues at the server departures for these three policies. Exact expressions of weighted sum of mean waiting times, known as pseudo-conservation laws, are subsequently obtained. The conservation laws for this class of policies contain unknown boundary probabilities. The authors estimate these probabilities using corresponding server vacation models. Numerical results presented for the exhaustive limited policy are noted to be very accurate compared with simulation results. Moreover, the authors have obtained analytical bounds for the weighted sums. Finally, they present a conservation law with mixed service policies, and mean waiting times for symmetric systems.