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Approximate analysis of discrete-time tandem queueing networks with bursty and correlated input traffic and customer loss. (English) Zbl 0824.60098

The paper begins by providing an approximation to the output process of 2-\(MMBP/GEO/1/K\) queue using another 2-\(MMBP\) (two-state Markov modulated Bernoulli process). The burstiness and the correlation of the output process are shown to be well approximated by the 2-\(MMBP\). The output approximation is achieved by matching the average output rate, its squared coefficient of variation, the autocorrelation coefficients of the interdeparture times and the number of departures per slot. A tandem configuration of five notes is analysed using the approximation in a decomposition algorithm and the result compared to simulation, with good agreement.

MSC:

60K25 Queueing theory (aspects of probability theory)
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
90B22 Queues and service in operations research
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References:

[1] Pujolle, G.; Perros, H. G., Queueing systems for modelling ATM networks, (Proc. of the Int’l. Conf. on the Performance of Distributed Systems and Integrated Comm. Networks. Proc. of the Int’l. Conf. on the Performance of Distributed Systems and Integrated Comm. Networks, Kyoto, Japan (1991)), 10-12
[2] Park, D.; Perros, H. G., Approximate analysis of discrete-time tandem queueing networks with customer loss, (IEEE GLOBECOM’ 92. IEEE GLOBECOM’ 92, Olando, FL (1992)), 1503-1507
[3] Starvrakakis, I., Efficient modeling of merging and splitting processes in large networking structure, IEEE J. Select. Areas Commun., 8 (1991)
[4] Meier-Hellstern, K., A fitting algorithm for Markov-modulated Poisson process having two arrival rates, E.J.O.R., 29, 370-377 (1987) · Zbl 0615.62122
[5] Tran-Gia, P., Discrete time analysis for the interdeparture distribution of GI/G/1 queue, (Boxma, O. J.; Cohen, J. W.; Tijms, H. C., Teletraffic Analysis and Computer Performance Evaluation (1986), North-Holland: Elsevier Science), 341-357
[6] Ohba, Y.; Murata, M.; Miyahara, H., Analysis of interdeparture process for bursty traffic in ATM networks, IEEE J. Select. Areas Commun., 3, 468-476 (1991)
[7] Morrison, J., Two discrete-time queues in tandem, IEEE Trans. Commun., 3, 563-573 (1979) · Zbl 0394.60097
[8] Hsu, J.; Burke, P., Behavior of tandem buffers with geometric input and Markovian output, IEEE Trans. Commun., 358-361 (1976) · Zbl 0349.60101
[9] Pujolle, G., Multiclass discrete-time queueing systems with a product from solution, (Int’l. Seminar on the Performance of Distributed and Parallel Systems (1991)), 261-270
[10] Bhargava, A.; Kurose, J.; Towsley, D.; Vanleemput, G., Performance comparison of error control schemes in high-speed computer communication network, IEEE J. Select. Areas Commun., 9, 1565-1575 (1988)
[11] Bocharov, P. P.; Albores, F. K., On two-stage exponential queueing system with internal losses or blocking, Prob. Control Inform. Theory, 365-379 (1980) · Zbl 0436.60073
[12] Morris, T. D.; Perros, H. G., Performance analysis of a multi-buffered Banyan ATM switch under bursty traffic, (INFOCOM ’92. INFOCOM ’92, Florence, Italy (1992)), 436-445
[13] A. Nilsson, Private Communication North Carolina State University, Raleigh, NC; A. Nilsson, Private Communication North Carolina State University, Raleigh, NC
[14] Hashida, O.; Takahashi, Y.; Shimogawa, S., Switched Batch Bernoulli Process (SBBP) and the discrete-time SBBP/G/1 queue with application to statistical multiplexer performance, IEEE J. Select. Areas Commun., 3 (1991)
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