Abstract
A two-phase queuing system with access control is studied whose first phase consists of an infinite number of servers, while the second one consists of a finite number of servers. To the first phase, a Markovian input flow of queries arrives. On completion of the first-phase service, the customer either leaves the system or is passed to the second phase. In addition, a Markovian input flow of queries that do not require any first-phase service arrives to the second phase. An algorithm for finding a steady-state distribution of the system’s state probabilities is given, and some problems of the system’s paramaters optimization are considered.
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References
Gnedenko, B.W. and Konig, D., Handbuch der Bedienungstheorie (Handbook of Queuing Theory), Berlin: Academie Verlag, 1983.
Balsamo, S., Persone, V.D.N. and Inverardi, P., A Review on Queuing Network Models with Finite Capacity Queues for Software Architectures Performance Prediction, Performance Evaluation, 2003, vol. 51, pp. 269–288.
Perros, H.G., A Bibliography of Papers on Queuing Networks with Finite Capacity Queues, Performance Evaluation, 1989, vol. 10, pp. 255–260.
Klimenok, V.I., Kim, C.S., Tsarenkov, G.V., Breuer, L. and Dudin, A.N., The BMAP/G/1 → ·/PH/1/M Tandem Queue with Feedback and Losses, Performance Evaluation, 2007, vol. 64, pp. 802–818.
Gomez-Corral, A., Sojourn Times in a Two-Stage Queuing Network with Blocking, Naval Research Logistics, 2004, vol. 51, pp. 1068–1089.
Breuer, L., Dudin, A.N., Klimenok, V.I. and Tsarenkov, G.V., A Two-Phase BMAP/G/1/N → PH/1/M-1 System with Blocking, Automation and Remote Control, 2004, vol. 65, pp. 117–130.
Klimenok, V.I. and Dudin, A.N., Multi-Dimensional Asymptotically Quasi-Toeplitz Markov Chains and their Application in Queuing Theory, Queuing Systems, 2006, vol. 54, pp. 245–259.
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Original Russian Text © S.A. Dudin, A.V. Babitskii, 2009, published in Avtomatika i Vychislitel’naya Tekhnika, 2009, No. 6, pp. 18–27.
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Dudin, S.A., Babitskii, A.V. A two-phase queuing system with access control and correlated arrival processes. Aut. Conrol Comp. Sci. 43, 295–302 (2009). https://doi.org/10.3103/S0146411609060029
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DOI: https://doi.org/10.3103/S0146411609060029