Stationary Characteristics of an Unreliable Multi-Server Queueing System with Losses and Time Redundancy

Abstract

This paper considers an unreliable restorable multi-server queueing system with losses in which failures may occur during requests service; in case of such failures, requests are served using a random time redundancy. The incoming flow is assumed to be elementary and all other random variables in the system’s description are assumed to obey a generalform distribution. A semi-Markov model of system’s evolution over time is developed and a stationary distribution of the embedded Markov chain is found. Explicit-form expressions for determining the stationary probabilities and mean stationary sojourn times in different physical states of the system are obtained, which can be used to estimate the time redundancy effect for the stationary characteristics of the system.