Performance modelling of nonhomogeneous unreliable multiserver systems using MOSEL

In this paper, we introduce a nonhomogeneous unreliable multiserver system with Markovian arrival, service, breakdown, and repair processes. First, we consider the case with only one queue and different servers and the job is assigned 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 random strategy, the job is served by one of the free servers which is chosen randomly. In our problem, we consider a general queueing 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 to consider the possibility that a server might be up or down at some point in time. The performance modelling of this type of system is done using the programming language MOSEL (Modelling Specification and Evaluation Language), which contains several constructs to describe the system, the results (performance parameters), and the graphical representation.