Abstract
The analytical solution of a queueing network is an appreciable first option in performance studies of service systems. Under the so-called product-form conditions, Mean Value Analysis (MVA) is the standard algorithm still adopted, but the user has to face the exponential computational complexity in the number of customer classes. In the last three decades, some (pseudo) polynomial approximated variants to MVA have been proposed in literature. These approximations are based on the transformation of the recursive MVA equations into a system of nonlinear equations to be solved iteratively. They are consolidated only with reference to (fixed-rate) single-server stations and are used in practice even though theoretical convergence remains an open problem. In this paper we exploit the possibility of aggregating customer classes in order to replace the exact multi-class MVA by new approximated procedures where MVA has to be run under at the most two customer classes. The resulting procedures are developed around a nested fixed-point iteration schema and are especially suitable for solving large size multi-class networks with multi-server stations under a first-come-first-served discipline. Convergence and accuracy of our procedures are numerically assessed through a very large set of experiments against the exact solution by the multi-class MVA.
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05 February 2020
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References
Akyildiz, I.F., Bolch, G.: Mean value analysis approximation for multiple server queueing networks. Perform. Eval. 8, 77–91 (1988)
Bard, J.: Some extensions to multi-class queueing network analysis. In: Arato, M., Butrimenko, A., Gelenbe, E. (eds.) Performance of Computer Systems, pp. 51–62. North Holland, Amsterdam (1979)
Baskett, F., Chandy, K.M., Muntz, R.R., Palacios, F.G.: Open, closed, and mixed networks of queues with different classes of customers. J. ACM 22(2), 248–260 (1975)
Casale, G., Pérez, J.F., Wang, W.: QD-AMVA: evaluating systems with queue-dependent service requirements. Perform. Eval. 91, 80–98 (2015)
Chandy, K.M., Neuse, D.: Linearizer: a heuristic algorithm for queueing network models of computing systems. Commun. ACM 25(2), 126–134 (1982)
Degirmenci, G., Kharoufeh, J.P., Baldwin, R.O.: On the performance evaluation of query-based wireless sensor networks. Perform. Eval. 70, 124–147 (2013)
Kleinrock, L.: Queueing Systems: Computer Applications, vol. 2, 1st edn. Wiley, New York (1976)
Lenin, R.B., Ramaswamy, S.: Performance analysis of wireless sensor networks using queueing networks. Ann. Oper. Res. 233, 237–261 (2015)
Menascé, D.A., Almeida, V.A.: Capacity Planning for Web Services: Metrics, Models, and Methods. Prentice Hall, Upper Saddle River (2002)
Neuse, D., Chandy, K.M.: SCAT: a heuristic algorithm for queueing network models of computing systems. ACM SIGMETRICS Perform. Eval. Rev. 10(3), 59–79 (1981)
Pattipati, K.R., Kostreva, M.M., Teele, J.L.: Approximate mean value analysis algorithms for queueing networks: existence, uniqueness, and convergence results. J. ACM 37, 643–673 (1990)
Raei, H., Yazdani, N., Shojaee, R.: Modeling and performance analysis of cloudlet in mobile cloud computing. Perform. Eval. 107, 34–53 (2017)
Reiser, M., Lavenberg, S.S.: Mean-value analysis of closed multichain queueing networks. J. ACM 27(2), 312–322 (1980)
Schweitzer, P.J.: Approximate analysis of multi-class closed networks of queues. In: Arato, M., Butrimenko, A., Gelenbe, E. (eds.) Proceedings of the International Conference on Stochastic Control and Optimization, pp. 25–29, Amsterdam, Netherlands (1979)
Suri, R., Sahu, S., Vernon, M.: Approximate mean value analysis for closed queueing networks with multiple-server stations. In: Bayraksan, G., Lin, W., Son, Y., Wysk, R. (eds.) Proceedings of the 2007 Industrial Engineering Research Conference, pp. 1–6. Tennessee, USA (2007)
Wang, H., Sevcik, K.C.: Experiments with improved approximate mean value analysis algorithms. Perform. Eval. 39, 189–206 (2000)
Wang, H., Sevcik, K.C., Serazzi, G., Wang, S.: The general form linearizer algorithms: a new family of approximate mean value analysis algorithms. Perform. Eval. 65, 129–151 (2008)
Zahorjan, J., Eager, J.D., Sweillam, H.M.: Accuracy, speed and convergence of approximate mean value analysis. Perform. Eval. 8, 255–270 (1988)
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Legato, P., Mazza, R.M. (2019). Class Aggregation for Multi-class Queueing Networks with FCFS Multi-server Stations. In: Phung-Duc, T., Kasahara, S., Wittevrongel, S. (eds) Queueing Theory and Network Applications. QTNA 2019. Lecture Notes in Computer Science(), vol 11688. Springer, Cham. https://doi.org/10.1007/978-3-030-27181-7_14
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