Performance Analysis of Unreliable Queue with Back-Up Server

Abstract

We consider an unreliable single-server queueing system with a reserve (back-up) server which is appropriate for modeling, e.g., the hybrid communication systems having the atmospheric optic channel (FSO-Free Space Optics) and standby radio channel IEEE 802.11n. We assume that the main server of the system (optic channel, server 1) is unreliable while the reserve server (radio channel, server 2) is absolutely reliable. It is assumed that the service time on the server 1 is essentially smaller than the service time on the server 2. If the server 1 fails during the service of a customer, the customer immediately occupies the reserve server. After failure occurence, the server 1 immediately goes to repair. When the repair period of the server 1 ends and the customer is served by the server 2, the customer immediately moves to the server 1. We consider exponential distributions of all random variables describing the operation of the system. This assumption allows to minimize the use of matrix-geometric technique and provide more or less simple analytical analysis of the system. We derive ergodicity condition and determine the stationary distribution of the Markov chain describing the process of the system states using the generating functions and roots methods, calculate some key performance measures and derive an expression for the Laplace-Stieltjes transform of the sojourn time distribution of an arbitrary customer. Illustrative numerical results are presented.