\(M/PH/1\) queue with deterministic impatience time (Q2842359)

The paper under review studies an M/PH/1 queueing system with deterministic impatience time \(\tau\), in which customers arrive according to a Poisson process with rate \(\lambda\). The service has a phase-type distribution with representation \((\alpha, T)\) of order \(m\) (for a more detailed explanation of this notation, see page 386 of the paper) and mean \(\mu^{-1}\); \(\rho=\lambda/\mu\). The paper provides the exact analytical expressions for stationary characteristics such as the stationary distribution of the queue-length process, workload of the system, loss probability and waiting time distribution. The paper extends the earlier results by \textit{W. Xiong, D. Jagerman} and \textit{T. Altiok} [Performance Evaluation, 65, 308--316 (2008)].