Invariance of the Stationary Distribution of States of Networks with Multimode Service, Different Types of Requests, and Discriminatory Processor Sharing

Abstract

—Open and closed queuing networks with multimode strategies and several types of requests are studied. Singleline nodes can operate in several modes. The time spent in each mode has an expo nential distribution. The queuing discipline of the server is the discriminatory processor sharing (DPS). The number of requests is a random variable with an arbitrary distribution function. The invariance is established of the stationary distribution of the probabilities of the network states with respect to the functional form of the distributions of the work required to service the requests.