The Queue State for Multiprocessor System with Waiting Time Restriction

Abstract

The queue state in multiprocessor computing systems is an actual problem for their use in the process of tasks scheduling. In this paper, a system of differential equations is obtained describing the probabilities of the system state at time t, which can be solved using numerical methods. However, the probabilities sought-for the system M|M|m|n with a constraint on the residence time can be obtained in terms of the Laplace- Stieltjes transform.