A PH/PH/1/r queueing model with the server requiring a search for customers

A single-server queueing system in which the server is required to search for customers in a ...nite buoer is considered. The interarrivals times, service times and search times are i.i.d, random variables with probability distribution functions of phase-type. For the stationary distribution of the underlying Markov process a matrix-geometric solution is obtained.