Abstract
Major performance measures of a queueing network are the mean time a unit (i.e. customer) spends in a sector of the network and the mean time for a unit to move from one sector to another. We give expressions for these and other mean passage times on routes in Jackson queueing networks and in more general queueing networks with congestion-dependent processing and routing. In these networks, the units may overtake one another as they move.
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References
Daduna, H. (1982). Passage Times for Overtake-Free Paths in Gordon-Newell Networks. Adv. Appl. Prob. 14, 672–686.
Daduna, H. (1986). Cycle Times in Two-Stage Closed Queueing Networks: Applications to Multiprogrammed Computer Systems with Virtual Memory. Operations Res. 34, 281–288.
Fayolle, G., Iasnogorodski, R. and Mitrani, I. (1983). The Distribution of the Sojourn Time in a Queueing Network with Overtaking: Reduction to a Boundary Value Problem. In Performance ‘83 (eds. Agrawala, A.K. and S.K. Tripathi), North Holland, Amsterdam.
Kelly, F.P. (1979). Reversibility and Stochastic Networks. John Wiley and Sons.
Kelly, F.P. and Pollett, P.K. (1983). Sojourn Times in Closed Queueing Networks. Adv. Appl. Prob. 15, 638–656.
Kook, K. (1989). Equilibrium Behavior of Markovian Network Processes. Ph.D. Thesis, Georgia Institute of Technology.
Kook, K. and R.F. Serfozo (1989). Mean Passage Times in Markovian Network Processes. Technical report Georgia Institute of Technology (in preparation).
Kuehn, P.J. (1979). Approximate Analysis of General Queueing Networks by Decomposition. IEEE Trans. Comm. COM-27, 113–126.
Lemoine, A.J. (1979). Total Sojourn Time in Networks of Queues. TR No. 79–020–1, Systems Control, Inc., Palo Alto, California.
Mckenna, J. (1989). A Generalization of Little’s Law to Moments of Queue Lengths and Waiting Times in Closed, Product-Form Queueing Networks, J. Appl. Prob. 26 121–133.
Melamed, B. (1982), Sojourn Times in Queueing Networks, Math. Oper. Res. 7, 223–244.
Reich, E. (1957). Waiting Times When Queues are in Tandem. Ann. Math. Statist. 28 768–773.
Serfozo, R.F. (1975). Functional Limit Theorems for Stochastic Processes Based on Embedded Processes. Adv. Appl. Prob. 1, 125–139.
Serfozo, R.F. (1989). Markovian Network Processes: Congestion-Dependent Routing and Processing. To appear in Queueing Systems.
Shassberger, R. and H. Daduna (1983). The Time for a Round Trip in a Cycle of Exponential Queues. J. ACM 30, 146–150.
Walrand, J. and Varaiya, P. (1980). Sojourn Times and Overtaking Condition in Jacksonian Networks. Adv. App. Prob. 12, 1000–1018.
Whittle, P. (1986). Systems in Stochastic Equilibrium, John Wiley and Sons.
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© 1989 Springer-Verlag Berlin Heidelberg
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Kook, K., Serfozo, R.F. (1989). Mean Passage Times in Queueing Networks. 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_1
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DOI: https://doi.org/10.1007/978-3-642-75079-3_1
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