Toshihisa Ozawa
Stochastic Models, 20(4) (2004), 391-413
Markovian service process (MSP) is a model similar to the Markovian arrival process (MAP), where arrivals are replaced with service completions. The MSP can represent various queueing models such as vacation models, N-policy models and exceptional service models. We analyze MAP/MSP/1 queues and obtain a new sort of matrix-type factorization of the vector generating function for the stationary queue length. The MAP/MSP/1 queue is a very tractable model since its behavior is represented as a quasi-birth-and-death process.