Retrial Queueing System with Processor Sharing

Abstract

We consider a retrial queueing system with limited processor sharing which can be used for modeling the operation of a cell of fixed capacity in a wireless cellular network with two types of customers (handover and new customers). Customers of two types arrive at the system according to the Marked Markovian Arrival Process (MMAP). Arriving customers of each type follow a bandwidth sharing policy. In period when the number of customers of definite type in the system exceeds a threshold (different between new and handover customers) newly arriving customers of one type (handover customers) are considered to be lost while the customers of another type (new customers) go to orbit of infinite size. From the orbit, they try their attempts to reach a server in exponentially distributed time. We describe the system operation by multi-dimensional Markov chain, calculate the steady state distribution and main performance measures of the system. Illustrative numerical examples are presented.