Markov-modulated finite-source queueing models in evaluation of computer and communication systems

Abstract

The present paper deals with a first-come, first-served (FCFS) queueing model to analyze the behaviour of a heterogeneous finite-source system with a single server. The sources and the server are assumed to operate in independent Markovian environments, respectively. Each request is characterized by its own exponentially distributed source and service time with parameter depending on the state of the corresponding environment; that is, the arrival 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 number of requests staying at the server, mean queue lengths, average waiting, and sojourn times. In the case of fast arrivals or fast service, asymptotic methods can be applied. In the intermediate situations, stochastic simulation is used. As applications of this model, some problems in the field of telecommunications and reliability theory are treated.