Stalling in Queuing Systems with Heterogeneous Channels

Abstract

The present paper considers a model of stalling in a queueing system (QS) with any number of different capacities of heterogeneous servers. The state graph and the corresponding linear system for steady-state probabilities are derived using the standard Markov chain technique. The obtained solution of the steady-state probabilities model is numerically stable; the complexity of the corresponding expressions does not depend on the number of QS states; thus, they enable us to analytically study the QS characteristics. Optimization of a stalling buffer is considered as well, and it is shown that stalling helps us to solve the slow server problem under an appropriate choice of stalling buffer size, making the slow servers usable under various values of system load. The asymptotic conditions of optimal query distribution in channels, when the ratio of the capacities of the fast and slow servers is increasing, are also established. Moreover, some applications of the developed model in heterogeneous server clusters and in work productivity modelling for forest harvesting applications are discussed.