Abstract
We propose a new approach that gives a one-step computational algorithm to directly obtain the queue length distribution of an N/G/1 queueing system. The new approach is based on the supplementary variable method and the matrix–analytic method. We shall show that this approach enables us to derive the joint distribution of the queue length and the elapsed service time.
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References
C. Blondia, The N/G/1 finite capacity queue, Stochastic Models 5 (1989) 273–294.
D.R. Cox, The analysis of non-Markovian stochastic process by inclusion of supplementary variables, Proc. Cambridge Philos. Soc. 51 (1955) 433–441.
D.M. Lucantoni and V. Ramaswami, Efficient algorithms for solving the non linear matrix equation arising in phase type queues, Comm. Statist. Stochastic Models 1 (1989) 29–52.
M.F. Neuts, A versatile Markovian point process, J. Appl. Probab. 16 (1979) 764–779.
M.F. Neuts, The c-server queue with constant service times and a versatile Markovian arrival process, in: Proc. of Conf. on Applied Probability–Computer Science: The Interface, Boca Raton, FL (January 1981) eds. R.L. Disney and T.J. Ott, Vol. I (1982) pp. 31–70.
V. Ramaswami, The N=G=1 queue and its detailed analysis, Adv. in Appl. Probab. 12 (1980) 222–261.
V. Ramaswami, The N=G=1 queue, Technical Report, Department of Mathematics, Drexel University, Philadelphia, PA (1978).
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Lee, G., Jeon, J. A new approach to an N/G/1 queue. Queueing Systems 35, 317–322 (2000). https://doi.org/10.1023/A:1019158514629
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DOI: https://doi.org/10.1023/A:1019158514629