Summary
We investigate under equilibrium conditions the duration of times where in a prescribed subnetwork of a product-form network at each node of the subnetwork at least a fixed number of customers is present. For the open network case we obtain closed formulas, for the closed network case recursion formulas and computational algorithms to compute mean values for such times intervals.
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Akyildiz, I.F.; Bolch, G. : Erweiterung der Mittelwertanalyse zur Berechnung der Zustandswahrscheinlichkeiten für geschlossene und gemischte Netze, in: Kühn, P.J.; Schulz, K. M. (eds.): Messung, Modellierung und Bewertung von Rechensystemen, Proc. 2. GI/NTG-Fachtagung, Stuttgart 1983, Informatik-Fachberichte 61, 267–276, 1983.
Bacelli, F.; Massey, W.A. : A transient analysis of the two-node series Jackson network, Report INRIA, 1988.
Bacelli, F.; Massey, W.A.; Wright, P.E. : Determining the exit time distribution for a closed cyclic network, Report INRIA, 1988.
Balsamo, S.; Iazeolla, G. : Aggregation and Disaggregation in Queueing Networks: The Principle of Product-Form-Synthesis, in: Iazeolla, G.; Courtois, P.J.; Hordijk, A.(eds.): Mathematical Computer Performance and Reliability 95–109, North-Holland, Amsterdam, 1984.
Baskett, F.; Chandy, K.M.; Muntz, R.R.; Palacios, F.G. : Open, closed, and mixed networks of queues with different classes of customers, J. Assoc. Comput. Mach. 22, 248–260, 1975.
Bruell, S.C.; Balbo, G. : Computational algorithms for closed queueing networks, North-Holland, New York 1980.
Buzen, J.P. : Computational algorithms for closed queueing networks with exponential servers. Communications ACM 16, 527–531, 1973.
Conway, A.E.; Georganas, N.D. [86]: A new method for computing the normalization constant of multiple chain queueing networks, INFOR 24(3), 1986.
Daduna, H. : The busy period distribution in a closed tandem of queues, Optimization 16, 755–766, 1985.
Daduna, H. : Busy periods for subnetworks in stochastic networks: Mean value analysis, J. Ass. Comput. Mach. 35, 668–674, 1988.
Daduna, H. : Simultaneous busy periods for nodes in a stochastic network, Performance Evaluation 9, 103–109, 1989.
Keilson, J. : Markov chain models — Rarity and exponentiality, Springer-Verlag, Heidelberg, 1979.
Kelly, F.P. : Reversibility and stochastic networks, Wiley, Chichester, 1979.
Kelly, F.P.; Pollett, P.K. : Sojourn times in closed queueing networks, Adv. Appl. Prob. 15, 638–656, 1983.
Kühn, P.J. : Analysis of busy periods and response times in queueing networks by the method of first passage times, in: Agrawala, A.K.; Tripathi, S.K. (eds.): Performance ‘83, 437–455, North-Holland, Amsterdam, 1983.
Kühn, P.J. : Analysis of busy period and response time distributions in queueing networks, in Kühn, P.J.; Schulz, K.M.(eds.): Messung, Modellierung und Bewertung von Rechensystemen, Inform. Fachber. 61, Springer-Verlag, Heidelberg, 135–149, 1983.
Lavenberg, S. (ed.) : Computer performance modelling handbook, Academic Press, New York, 1983.
Massey, W.A. : Calculating exit times for series Jackson networks, J. Appl. Prob. 24, 226–234, 1987.
Reiser, M. : Performance evaluation of data communication systems, Proc. of the IEEE 70, 171–196, 1982.
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© 1989 Springer-Verlag Berlin Heidelberg
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Daduna, H. (1989). Mean Value Analysis for the Duration of Heavy Traffic Periods in Subnetworks of a Queueing Network. In: Stiege, G., Lie, J.S. (eds) Messung, Modellierung und Bewertung von Rechensystemen und Netzen. Informatik-Fachberichte, vol 218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75079-3_2
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DOI: https://doi.org/10.1007/978-3-642-75079-3_2
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