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Analysis of a $$GI/M/1$$ queue with multiple working vacations. (English) Zbl 1099.90013
Summary: Consider a $$GI/M/1$$ queue with vacations such that the server works with different rates rather than completely stops during a vacation period. We derive the steady-state distributions for the number of customers in the system both at arrival and arbitrary epochs, and for the sojourn time for an arbitrary customer.

##### MSC:
 90B22 Queues and service in operations research 60K25 Queueing theory (aspects of probability theory)
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##### References:
 [1] Doshi, B.T., Queueing systems with vacations—a survey, Queueing systems, 1, 29-66, (1986) · Zbl 0655.60089 [2] Doshi, B.T., Single server queues with vacations, (), 217-264 [3] Gross, D.; Harris, C.M., Fundamentals of queueing theory, (1998), Wiley New York · Zbl 0949.60002 [4] Neuts, M.F., Matrix-geometric solutions in stochastic models, (1981), Johns Hopkins University Press Baltimore · Zbl 0469.60002 [5] Servi, L.D.; Finn, S.G., M/M/1 queues with working vacations (M/M/1/WV), Performance evaluation, 50, 41-52, (2002) [6] H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation, Vol 1: Vacation and Priority Systems, Part 1, Elsevier, Amsterdam, 1991. · Zbl 0744.60114 [7] Tian, N.; Zhang, D.; Cao, C., The GI/M/1 queue with exponential vacations, Queueing systems, 5, 331-344, (1989) · Zbl 0684.60072 [8] D.A. Wu, H. Takagi, M/G/1 queues with multiple working vacations, Proceedings of the Queueing Symposium, Stochastic Models and their Applications, Kakegawa, 2003, pp. 51-60.
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