Stability Analysis of a MAP/M/s Cluster Model by Matrix-Analytic Method

摘要

In this paper, we study the stability conditions of the mul-tiserver system in which each customer requires a random number of servers simultaneously and a random service time, identical at all occupied servers. We call it cluster model since it describes the dynamics of the modern multicore high performance clusters (HPC). Stability criterion of an M/M/s cluster model has been proved by the authors earlier. In this work we, again using the matrix-analytic approach, prove that the stability criterion of a more general MAP/M/s cluster model (with Markov Arrival Process) has the same form as for M/M/s system. We verify by simulation that this criterion (in an appropriate form) allows to delimit stability region of a MAP/PH/s cluster model with phase-type (PH) service time distribution. Finally, we discuss asymptotic results related to accelerated stability verification, as well as to the new method of accelerated regenerative estimation of the performance metrics.