Stalling for solving slow server problem

Abstract

The model of stalling in queueing system (QS) with two heterogeneous severs is considered, the probabilities of steady states by means of Tchebyshev polynomials of second order are derived. The obtained expressions are stable numerically, their complexity does not depend on the number of states, and they enable us to study QS characteristics analytically. Optimization of a stalling buffer is considered as well and it was shown that stalling helps us to solve the slow server problems under an appropriate choice of stalling buffer size, making a slow server usable under various values of system load. Asymptotic conditions of optimal query distribution in servers are established, when the ratio of capacities of fast and slow channels is increasing. Application of the model developed in computer networks is discussed as well.