Analysis and Optimization of Systems with Heterogeneous Servers and Jump Priorities

Abstract

Markov models of systems with heterogeneous servers, various types of requests, and jump priorities are proposed. It is assumed that there are high and low priority requests; the high priority requests are assigned to the server with the high service rate, and the low priority requests are assigned to the server with the low service rate. Models of two types are studied: with separate queues and the shared queue for requests of different types. Jump priorities determine the rules according to which the type of low priority requests changes depending on the state of the queue. Methods for calculating the distribution of the probability of the system states are developed, formulas for the calculation of the characteristics of the system are derived, and the problem of the optimization of these characteristics is solved. The results of numerical experiments are presented.