Abstract
Simple lower and upper bounds on service cycle times in stochastic acyclic fork-join queueing networks are derived using a (max, +)-algebra based representation of network dynamics. The behaviour of the bounds under various assumptions concerning the service times in the networks is discussed, and related numerical examples are presented.
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References
Baccelli, F., Cohen, G., Olsder, G. J. and Quadrat, J.-P. (1992). Synchronization and Linearity, Chichester: John Wiley & Sons.
Baccelli, F. and Konstantopoulos, P. (1991). Estimates of cycle times in stochastic Petri nets, Applied Stochastic Analysis, pp. 1–20, New York: Springer-Verlag, Lecture Notes in Control and Information Sciences, 177.
Baccelli, F. and Makowski, A. M. (1989). Queueing models for systems with synchronization constraints, Proceedings of the IEEE, 77 138–160.
Baccelli, F., Massey, W. A. and Towsley, D. (1989). Acyclic fork-join queueing networks, Journal of the ACM, 36 615–642.
Cohen, G., Dubois, D., Quadrat, J.-P. and Viot, M. (1985). A linearsystem-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing, IEEE Transactions on Automatic Control, 30 210–220.
Cuninghame-Green, R. A. (1979). Minimax Algebra, Berlin: Springer-Verlag, Lecture Notes in Economics and Mathematical Systems, 166.
Gumbel, E. J. (1954). The maxima of the mean largest value and of the range, Annals of Mathematical Statistics, 25 76–84.
Hartly, H. O. and David, H. A. (1954). Universal bounds for mean range and extreme observations, Annals of Mathematical Statistics, 25 85–99.
Kingman, J. F. C. (1973). Subadditive ergodic theory, Annals of Probability, 1 883–909.
Krivulin, N. K. (1994). Using max-algebra linear models in the representation of queueing systems, Proceedings of the 5th SIAM Conference on Applied Linear Algebra, Snowbird, UT, June 15–18 (Ed., J. G. Lewis), pp. 155–160.
Krivulin, N. K. (1995). A max-algebra approach to modeling and simulation of tandem queueing systems, Mathematical and Computer Modelling, 22 25–37.
Krivulin, N. K. (1996). The max-plus algebra approach in modelling of queueing networks, Proceedings of the 1996 SCS Summer Computer Simulation Conference, Portland, OR,July 21–25, pp. 485–490, San Diego: SCS.
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Krivulin, N.K. (2000). Algebraic Modelling and Performance Evaluation of Acyclic Fork-Join Queueing Networks. In: Balakrishnan, N., Melas, V.B., Ermakov, S. (eds) Advances in Stochastic Simulation Methods. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1318-5_5
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DOI: https://doi.org/10.1007/978-1-4612-1318-5_5
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7091-1
Online ISBN: 978-1-4612-1318-5
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