Communications of the
Korean Mathematical Society CKMS

We consider an $M/PH/1$ queue with deterministic impatience time. An exact analytical expression for the stationary distribution of the workload is derived. By modifying the workload process and using Markovian structure of the phase-type distribution for service times, we are able to construct a new Markov process. The stationary distribution of the new Markov process allows us to find the stationary distribution of the workload. By using the stationary distribution of the workload, we obtain performance measures such as the loss probability, the waiting time distribution and the queue size distribution.

Keywords: $M/PH/1$ queue, impatience time, workload, loss probability, waiting time distribution, queue size distribution