Analyzing Markov-Modulated Finite Source Queueing Systems

This paper deals with a First-Come, First-Served (FCFS) queueing model to analyze the steady-state behaviour of heterogeneous finite-source queueing system with a single server. The request sources and the server are supposed to operate in random environments, thus allowing the arrival and service processes to be Markov-modulated ones. Each request of the sources is characterized by its own exponentially distributed source and service time with parameter depending on the state of the corresponding environment, that is, the request generation and service rates are subject to random fluctuations. Our aim is to get the usual stationary performance measures of the system, such as utilizations, mean queue lengths, average response times. In this paper we describe the mathematical model and introduce a software tool to produce analytical computational results for the investigated model. The MARKMOD software package was built on MOSEL and SPNP (see [6], [9]) and gives an easy way to use Markov-modulated queueing systems for modeling real life computer and communication systems. Finally, we show some numerical examples to illustrate the efficiency of the software tool.