Abstract
For finite-capacity queuing systems of the type M θ/G/1, convenient formulas for the ergodic distribution of the queue length are found, an estimate for the rate of convergence of the distribution of the queue length in the transient mode to the ergodic distribution is obtained, and computational algorithms for finding the rate of convergence are presented.
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References
H. Takagi, Queueing Analysis, Vol. 2, North Holland (1993).
V. S. Korolyuk, Boundary-Value Problems for Compound Poisson Processes [in Russian], Naukova Dumka, Kiev (1975).
M. S. Bratiichuk, “Exact formulas for E θ/G/1/N-type queuing systems,” Ukr. Mat. Zh., 52, No. 8, 1034–1044 (2000).
N. P. Kartashov, “Power estimates for the rate of convergence in the renewal theorem,” Teor. Ver. Primen., 25, 600–607 (1979).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1169–1178, September, 2007.
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Bratiichuk, A.M. Rate of convergence to ergodic distribution for queue length in systems of the type M θ/G/1/N . Ukr Math J 59, 1300–1312 (2007). https://doi.org/10.1007/s11253-007-0089-x
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DOI: https://doi.org/10.1007/s11253-007-0089-x