×

zbMATH — the first resource for mathematics

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

MSC:
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
[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
[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
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.