Throughput estimation in cyclic queueing networks with blocking

Abstract

The paper presents a new approach for estimating the throughput of a closed queueing network with exponential servers, finite buffer capacity and a blocking after service discipline. The problem is tackled by decomposing the network. The population constraint is enforced by requiring that the sum of the expected number of customers in the various subsystems is equal to the population size. Each subsystem is analyzed as an M/M/1/Ci+1 queue with state-dependent arrival and service rates. The rationale behind this last assumption is that the behavior of the system at a given time is affected by the history of blockings and starvations. The results obtained by applying the proposed algorithm to a set of test problems show a good agreement with those obtained with simulation, the difference on the maximum throughput of the network being of the order of 3%. The obtained results also compare favorably with those described in the literature.