Abstract
A birth-death queueing system with two identical servers, first-come first-served discipline, and Poisson arrivals is considered. Only one of the servers is active when the number of customers in the system does not exceed a prescribed threshold, whereas both are active above the threshold. The problem of determining the equilibrium density of the waiting time is formulated. A generating function is given for the Laplace transform of the density of the waiting time, and it is pointed out that it leads to an explicit expression for this quantity. Explicit expressions are obtained for the first and second moments of the waiting and sojourn times, and they are compared with the corresponding quantities for a single-server system with the same state-dependent mean service rates.
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References
D.P. Gaver, Jr., Diffusion approximations and models for certain congestion problems, J. Appl. Probab. 5 (1968) 607–623.
D. Gross and C.M. Harris,Fundamentals of Queueing Theory, 2nd ed. (Wiley, New York, 1985) p. 91.
J. Keilson,Markov Chain Models — Rarity and Exponentiality, Applied Mathematical Sciences, vol. 28 (Springer, New York, 1979) p. 58.
L. Kleinrock,Queueing Systems, vol. I: Theory (Wiley, New York, 1975).
J.A. Morrison, Sojourn and waiting times in a single-server system with state-dependent mean service rate, Queueing Systems 4 (1989) 213–235.
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Morrison, J.A. Two-server queue with one server idle below a threshold. Queueing Syst 7, 325–336 (1990). https://doi.org/10.1007/BF01154549
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DOI: https://doi.org/10.1007/BF01154549