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Performance optimization of open zero-buffer multi-server queueing networks. (English) Zbl 1183.90109
Summary: Open zero-buffer multi-server general queueing networks occur throughout a number of physical systems in the semi-process and process industries. In this paper, we evaluate the performance of these systems in terms of throughput using the generalized expansion method (GEM) and compare our results with simulation. Secondly, we embed the performance evaluation in a multi-objective optimization setting. This multi-objective optimization approach results in the Pareto efficient curves showing the trade-off between the total number of servers used and the throughput. Experiments for a large number of settings and different network topologies are presented in detail.

MSC:
 90B22 Queues and service in operations research 90B10 Deterministic network models in operations research 90C29 Multi-objective and goal programming 90C59 Approximation methods and heuristics in mathematical programming
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 [1] Fransoo, J.C.; Rutten, W.G.M.M., A typology of production control situations in process industries, International journal of operations and production management, 14, 12, 47-57, (1994) [2] Hall, N.G.; Sriskandarajah, C., A survey of machine scheduling problems with blocking and no-wait in process, Operations research, 44, 510-525, (1996) · Zbl 0864.90060 [3] Fey J. Design of a fruit juice blending and packaging plant. PhD thesis, Eindhoven University of Technology; 2000. [4] Ramudhin, A.; Ratliff, H.D., Generating daily production schedules in process industries, IIE transactions, 27, 646-656, (1995) [5] Tsybakov, B., Optimum discarding in a bufferless system, Queueing systems, 41, 165-197, (2002) · Zbl 1009.90023 [6] Buzacott, J.; Shanthikumar, J.G., Stochastic models of manufacturing systems, (1993), Prentice-Hall Englewood Cliffs, NJ [7] Perros, H.G., Queueing networks with blocking, (1994), Oxford University Press Oxford · Zbl 0616.60093 [8] Jain, S.; Smith, J.M., Open finite queueing networks with $$M / M / C / K$$ parallel servers, Computers & operations research, 21, 3, 297-317, (1994) · Zbl 0789.90034 [9] Kerbache, L.; Smith, J.M., Asymptotic behavior of the expansion method for open finite queueing networks, Computers & operations research, 15, 2, 157-169, (1988) · Zbl 0662.60105 [10] Walrand, J., An introduction to queueing networks, (1988), Prentice-Hall Englewood Cliffs, NJ · Zbl 0854.60090 [11] Dallery, Y.; Gershwin, S.B., Manufacturing flow line systems: a review of models and analytical results, Queueing systems, 12, 3-94, (1992) · Zbl 0782.90048 [12] Hildebrand, D., On the capacity of tandem server, finite queue, service systems, Operations research, 16, 72-82, (1968) · Zbl 0157.25401 [13] Hillier, F.; Boling, R., Finite queues in series with exponential or Erlang service times: a numerical approach, Operations research, 16, 286-303, (1967) · Zbl 0171.16302 [14] Muth, E.; Alkaff, A., The throughput rate of three-station production lines: a unifying solution, International journal of production research, 25, 1405-1413, (1987) · Zbl 0623.90031 [15] Rao, N., A generalization of the bowl phenomenon in series production systems, International journal of production research, 14, 4, 437-443, (1976) [16] Rao, N., A viable alternative to the method of stages solution of series production systems with Erlang service times, International journal of production research, 14, 6, 699-702, (1976) [17] Cruz, F.R.B.; Duarte, A.R.; van Woensel, T., Buffer allocation in general single-server queueing network, Computers & operations research, 35, 11, 3581-3598, (2008) · Zbl 1170.90361 [18] Cheah, J.; Smith, J.M., Generalized $$M / G / C / C$$ state dependent queueing models and Pedestrian traffic flows, Queueing systems, 15, 365-386, (1994) · Zbl 0797.90028 [19] Jain, R.; Smith, J.M., Modeling vehicular traffic flow using $$M / G / C / C$$ state dependent queueing models, Transportation science, 31, 4, 324-336, (1997) · Zbl 0920.90064 [20] Cruz, F.R.B.; Smith, J.M.; Queiroz, D.C., Service and capacity allocation in $$M / G / C / C$$ state dependent queueing networks, Computers & operations research, 32, 6, 1545-1563, (2005) · Zbl 1071.90014 [21] Cruz, F.R.B.; Smith, J.M., Approximate analysis of $$M / G / c / c$$ state-dependent queueing networks, Computers & operations research, 34, 8, 2332-2344, (2007) · Zbl 1144.90345 [22] Kerbache, L.; Smith, J.M., The generalized expansion method for open finite queueing networks, European journal of operational research, 32, 448-461, (1987) · Zbl 0691.60088 [23] Kerbache, L.; Smith, J.M., Multi-objective routing within large scale facilities using open finite queueing networks, European journal of operational research, 121, 105-123, (2000) · Zbl 0971.90014 [24] Spinellis, D.; Papodopoulos, C.; Smith, J.M., Large production line optimisation using simulated annealing, International journal of production research, 38, 3, 509-541, (2000) · Zbl 0944.90518 [25] Smith, J.M.; Cruz, F.R.B., The buffer allocation problem for general finite buffer queueing networks, IIE transactions, 37, 4, 343-365, (2005) [26] Labetoulle, J.; Pujolle, G., Isolation method in a network of queues, IEEE transactions on software engineering, SE-6, 4, 373-381, (1980) [27] Kleinrock, L., Queueing systems. theory, vol. I, (1975), Wiley New York · Zbl 0334.60045 [28] Adelman, D., A simple algebraic approximation to the Erlang loss system, Operations research letters, 36, 4, 484-491, (2008) · Zbl 1158.60375 [29] Gross, D.; Harris, C.M., Fundamentals of queueing theory, (1998), Wiley Series in Probability and Statistics New York · Zbl 0949.60002 [30] Purshouse, R.C.; Fleming, P.J., On the evolutionary optimization of many conflicting objectives, IEEE transactions on evolutionary computation, 11, 6, 770-784, (2007) [31] Mathieu, R.; Pittard, L.; Anandalingam, G., Genetic algorithms based approach to bi-level linear programming, Recherche opérationnelle/operations research, 28, 1, 1-21, (1994) · Zbl 0857.90083 [32] Deb, K.; Agrawal, S.; Pratap, A.; Meyarivan, T., A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, IEEE transactions on evolutionary computation, 6, 182-197, (2002) [33] Robinson, S., A statistical process control approach to selecting a warm-up period for a discrete-event simulation, European journal of operational research, 176, 1, 332-346, (2007) · Zbl 1137.90470 [34] Kelton, D.; Sadowski, R.P.; Sadowski, D.A., Simulation with arena, (2001), McGraw Hill College Div. New York [35] Rudenko O, Schoenauer M. A steady performance stopping criterion for Pareto-based evolutionary algorithms. In: Proceedings of the 6th international multi-objective programming and goal programming conference, Hammamet, Tunisia; 2004. [36] Hopp, W.J.; Spearman, M.L., Factory physics, (2000), McGraw Hill International Editions New York [37] Choi, D.W.; Kim, N.K.; Chae, K.C., A two-moment approximation for the $$\mathit{GI} / G / c$$ queue with finite capacity, INFORMS journal on computing, 17, 1, 75-81, (2005) · Zbl 1239.90029 [38] Kim, N.K.; Chae, K.C., Transform-free analysis of the $$\mathit{GI} / G / 1 / K$$ queue through the decomposed Little’s formula, Computers & operations research, 30, 3, 353-365, (2003) · Zbl 1029.90022 [39] Hughes EJ. Multiple single objective Pareto sampling. In: I. Press, editor. Congress on evolutionary computation CEC’03. Piscataway, NJ; 2003. p. 2678-84. doi: 10.1109/CEC.2003.1299427.
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