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Asymptotic behavior of the stationary distributions in the GI/PH/c queue with heterogeneous servers. (English) Zbl 0451.60085

60K25Queueing theory
90B22Queues and service (optimization)
Full Text: DOI
[1] Bellman, R.: Introduction to Matrix Analysis. New York: McGraw Hill 1960 · Zbl 0124.01001
[2] Gantmacher, F.R.: The Theory of Matrices. New York: Chelsea 1959 · Zbl 0085.01001
[3] Lavenberg, S.S.: Stability and Maximum Departure Rate of Certain Open Queueing Networks having Finite Capacity Constraints. R.A.I.R.O. Informatique/Computer Science12, 353-370 (1978) · Zbl 0387.68032
[4] Neuts, M.F.: Probability Distributions of Phase Type. Liber Amicorum Prof. Emeritus H. Florin. Dept. Math., Univ. Louvain, Belgium, 173-206 (1975)
[5] Neuts, M.F.: Renewal Processes of Phase Type. Naval. Res. Logist. Quart.25, 445-454 (1978) · Zbl 0393.90096 · doi:10.1002/nav.3800250307
[6] Neuts, M.F.: Markov Chains with Applications in Queueing Theory, which have a Matrix-geometric Invariant Probability Vector. Advances in Appl. Probability10, 185-212 (1978) · Zbl 0382.60097 · doi:10.2307/1426725
[7] Neuts, M.F.: The Probabilistic Significance of the Rate Matrix in Matrix-geometric Invariant Vectors. J. Appl. Probability17, 291-296 (1980) · Zbl 0424.60091 · doi:10.2307/3212949
[8] Neuts, M.F.: Matrix-geometric Solutions in Stochastic Models. An Algorithmic Approach. Baltimore, MD.: Johns Hopkins University Press 1981 · Zbl 0469.60002
[9] Neuts, M.F.: Stationary Waiting Time Distributions in the GI/PH/1 Queue. J. Appl. Probability18 (1981) · Zbl 0475.60086
[10] Takahashi, Y., Takami, Y.: A Numerical Method for the Steady-state Probabilities of a GI/G/c Queueing System in a General Class. J. Operations Res. Soc. Japan19, 147-157 (1976) · Zbl 0348.60127
[11] Takahashi, Y.: Asymptotic Exponentiality of the Tail of the Waiting Time Distribution in a PH/PH/c Queue. Advances in Appl. Probability13 (1981) · Zbl 0463.60083