Analysis of an M/G/1 queue with vacations and multiple phases of operation

Jianjun Li (), Liwei Liu and Tao Jiang
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Jianjun Li: Nanjing University of Science and Technology
Liwei Liu: Nanjing University of Science and Technology
Tao Jiang: Nanjing University of Science and Technology

Mathematical Methods of Operations Research, 2018, vol. 87, issue 1, No 3, 72 pages

Abstract: Abstract This paper deals with an M / G / 1 queue with vacations and multiple phases of operation. If there are no customers in the system at the instant of a service completion, a vacation commences, that is, the system moves to vacation phase 0. If none is found waiting at the end of a vacation, the server goes for another vacation. Otherwise, the system jumps from phase 0 to some operative phase i with probability $$q_i$$ q i , $$i = 1,2, \ldots ,n.$$ i = 1 , 2 , … , n . In operative phase i, $$i = 1,2, \ldots ,n$$ i = 1 , 2 , … , n , the server serves customers according to the discipline of FCFS (First-come, first-served). Using the method of supplementary variables, we obtain the stationary system size distribution at arbitrary epoch. The stationary sojourn time distribution of an arbitrary customer is also derived. In addition, the stochastic decomposition property is investigated. Finally, we present some numerical results.

Keywords: M / G / 1 queue; Vacation; Sojourn time; Probability generating function; Multiple phases of operation; Queueing theory (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00186-017-0606-0

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