论文信息 - Simpler proofs of some properties of the fundamental period of the MAP/G/1 queue

Simpler proofs of some properties of the fundamental period of the MAP/G/1 queue

By an argument which involves matching sample paths, some useful equations for the probability distribution of the fundamental period in the MAP/G/1 queue are derived with less calculational effort than in earlier proofs. It is further shown that analogous equations hold for the MAP/SM/1 queueing model. These results are then used to derive explicit formulas for the mean vectors of the number served during and the duration of the fundamental period.

M. Neuts | D. Lucantoni

[1] Marcel F. Neuts,et al. Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1989 .

[2] G. F. Newell,et al. Introduction to the Theory of Queues. , 1963 .

[3] David M. Lucantoni,et al. New results for the single server queue with a batch Markovian arrival process , 1991 .

[4] David M. Lucantoni,et al. The BMAP/G/1 QUEUE: A Tutorial , 1993, Performance/SIGMETRICS Tutorials.

[5] M. Neuts,et al. A single-server queue with server vacations and a class of non-renewal arrival processes , 1990, Advances in Applied Probability.

[6] Marcel F. Neuts. The Fundamental Period of the Queue with Markov-Modulated Arrivals , 1989 .

[7] Vaidyanathan Ramaswami. From the matrix-geometric to the matrix-exponential , 1990, Queueing Syst. Theory Appl..