Abstract
In this paper, the GIX/M/c queueing model is analyzed. An explicit expression of the generating function of equilibrium probabilities of customer numbers in the system for the model is derived. Based on the generating function, it is proved that the equilibrium probabilities are given by a linear combination of some geometric terms. Due to this result, other interesting measures are also considered without difficulty. Examples and numerical results are given.
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References
D.E. Baily and M.F. Neuts, Algorithmic methods for multi-server queues with group arrivals and exponential services, Eur. J. Oper. Res. 8 (1981) 184–196.
M.L. Chaudhry, M.V. Cromie and W.K. Grassmann, Further results for the queueing system MX/M/c, J. Oper. Res. Soc. 30 (1979) 755–763.
M.L. Chaudhry, D.G. Holman and W.K. Grassmann, Some results for the queueing system E Xk /M/c, Naval Res. Logist. Quart. 30 (1980) 217–222.
M.L. Chaudhry, J.G.C. Templeton and J. Medhi, Computational analysis of multiserver bulkarrival queues with constant service time MX/D/c, ORSA 40 (1992) 229–238 (Suppl. 2).
M.L. Chaudhry,QROOT Software Package (A&APubl, Kingston, Ontario, Canada, 1992).
M.L. Chaudhry, M. Agarwal and J.G.C. Templeton, Exact and approximate numerical solutions of steady-state distributions arising in the queue GI/G/1, Queueing Systems 10 (1992) 105–152.
M.L. Chaudhry and J.G.C. Templeton,A First Course in Bulk Queues (Wiley, New York, 1983).
D.R. Cox and D.V. Hinkley, Some properties of multiserver queues with appointments, Royal Stat. Soc. 133 (1970) 1–13.
W.K. Grassmann, The PHX/M/c queue, Selecta Stat. Canad. 7 (1986) 25–52.
M.F. Neuts,Matrix-Geometric Solutions in Stochastic Models (Johns Hopkins University Press, Baltimore, 1981).
A. Selvi and M. Rosenshine, Arrival point steady-state solutions for the DX/M/c queueing system,CORS, TIMS and ORSA Meeting, Toronto, Canada (1981).
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Zhao, Y. Analysis of the GIX/M/c model. Queueing Syst 15, 347–364 (1994). https://doi.org/10.1007/BF01189245
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DOI: https://doi.org/10.1007/BF01189245