A single server queue with platooned arrivals and phase type services

A semi-Markovian point process which qualitatively models platooned arrivals is introduced. This process is used as the input to a single server queue in which the service times are independent and have a common distribution of phase type.It is shown that this queue has an embedded Markov chain of a particular block-partitioned type, whose invariant probability vector in the stable case is of matrix-geometric form. Detailed algorithms for the computation of the steady-state features of the queue are obtained and a representative numerical example is discussed.