Performance Modeling of Non-homogeneous Unreliable Multi-Server Systems using MOSEL1

In this paper, we introduce a non-homogeneous unreliable multi-server system with Markovian arrival, service, breakdown and repair processes. First we consider the case with only one queue and different servers and the job assigns to one server. Then we extend this model to more than one queue in which the jobs are assigned to different queues. We assume that our system has different servers with different service times and a job is assigned to a server using the following strategies: FFS (Fastest Free Server) or random selection. FFS strategy means that the job is served by the fastest available server, and if this server is busy then the job goes to the next available server and so on. In the ran1Acknowledgment: Research is partially supported by GermanHungarian Bilateral Intergovernmental Scientific Cooperation, OMFBDLR No. HUN97/015, OMFKFP grant 0004/99 and Hungarian Scientific Research Fund OTKA-T30685/99. dom strategy, the job served by one of the free servers which is choosen randomly. In our problem, we consider a general queuing system (M/M/n) with a finite number of jobs K in the whole system. Our system is unreliable; this means that we need to specify the parameters, mtbf and mttr (mean time between failures and mean time to repair), and we need to consider the possibility that a server might be up or down at some point of time. The performance modeling of this type of system is done using the programming language MOSEL (MOdeling Specification and Evaluation Language), which contains several constructs to describe the system, the results (performance parameters) and the graphical representation. 1. Problem Description The calculation of the performance measure is fairly simple if there is only one server (M/M/1), or several servers with identical service time arranged in parallel, and the inter-arrival