Search for customers in a finite capacity queueing system with phase-type distributions of interarrival and service times

With the rapid spread of new technologies many efforts have been addressed towards the modelling of telecommunications systems. Since actual statistics shows that queueing systems characterized by Poisson flows of customers with exponentially distributed service times are not good models for multimedia flows, queueing systems with distributions different from traditional ones have to be investigated. In this paper we deal with a single-server queueing system in which the server requires a search for customers allocated in a finite buffer. Queueing systems with the server searching for customers can be used to evaluate performance of telecommunication systems in which the processor must spend a random time to choose the next item to be processed. We assume PH-distributions for the probability distribution functions of interarrival times, service times and search times. The solution of the equilibrium equations of the underlying Markov process is obtained in a matrix-geometric form. Numerical examples are presented and some system performance indices are computed.