论文信息 - The Queue M|G|1 with Markov Modulated Arrivals and Services

The Queue M|G|1 with Markov Modulated Arrivals and Services

We study an M|G|1 queue in which both the arrival rate and the service time distribution depend on the state of an underlying finite-state Markov chain. The solution is obtained by a matrix factorization method. This leads to results for waiting times and queue lengths both at arrival epochs and in continuous time. A numerical algorithm for the calculation of several quantities of interest is described and some numerical examples are given.

G. J. K. Regterschot | J. H. A. de Smit | J. D. Smit | G. Regterschot

[1] V. Ramaswami. The N/G/1 queue and its detailed analysis , 1980, Advances in Applied Probability.

[2] V. Ramaswami. THE N/G/1 QUEUE AND ITS DETAILED ANALYSIS , 1980 .

[3] Donald R. Smith,et al. An Asymptotic Analysis of a Queueing System with Markov-Modulated Arrivals , 1986, Oper. Res..

[4] J. D. Smit. The queue GI/M/s with customers of different types or the queue GI/Hm/s , 1983 .

[5] M. H. van Hoorn,et al. The SPP/G/1 queue: A single server queue with a switched Poisson process as input process , 1983 .

[6] Elja Arjas,et al. On the use of a fundamental identity in the theory of semi-Markov queues , 1972, Advances in Applied Probability.