Performance optimization of open zero-buffer multi-server queueing networks

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.

[1]  Peter J. Fleming,et al.  On the Evolutionary Optimization of Many Conflicting Objectives , 2007, IEEE Transactions on Evolutionary Computation.

[2]  Frederico R. B. Cruz,et al.  Approximate analysis of M/G/c/c state-dependent queueing networks , 2007, Comput. Oper. Res..

[3]  James MacGregor Smith,et al.  Generalized M/G/C/C state dependent queueing models and pedestrian traffic flows , 1994, Queueing Syst. Theory Appl..

[4]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[5]  H. D. Ratliff,et al.  Generating daily production schedules in process industries , 1995 .

[6]  Chelliah Sriskandarajah,et al.  A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process , 1996, Oper. Res..

[7]  Stewart Robinson,et al.  A statistical process control approach to selecting a warm-up period for a discrete-event simulation , 2007, Eur. J. Oper. Res..

[8]  Carl M. Harris,et al.  Fundamentals of queueing theory , 1975 .

[9]  J. MacGregor Smith,et al.  The generalized expansion method for open finite queueing networks , 1987 .

[10]  Guy Pujolle,et al.  Isolation Method in a Network of Queues , 1980, IEEE Transactions on Software Engineering.

[11]  Nori Prakasa Rao,et al.  A generalization of the ‘bowl phenomenon’ in series production systems , 1976 .

[12]  Jean C. Walrand,et al.  An introduction to queueing networks , 1989, Prentice Hall International editions.

[13]  F. Cruz,et al.  The buffer allocation problem for general finite buffer queueing networks , 2005 .

[14]  Jc Jan Fransoo,et al.  A Typology of Production Control Situations in Process Industries , 1994 .

[15]  James MacGregor Smith,et al.  Modeling Vehicular Traffic Flow using M/G/C/C State Dependent Queueing Models , 1997, Transp. Sci..

[16]  Boris Tsybakov Optimum Discarding in a Bufferless System , 2002, Queueing Syst. Theory Appl..

[17]  Kyung C. Chae,et al.  A Two-Moment Approximation for the GI/G/c Queue with Finite Capacity , 2005, INFORMS J. Comput..

[18]  David K. Hildebrand,et al.  On the Capacity of Tandem Server, Finite Queue, Service Systems , 1968, Oper. Res..

[19]  Tom Van Woensel,et al.  Buffer allocation in general single-server queueing networks , 2008, Comput. Oper. Res..

[20]  N. P. Rao,et al.  A viable alternative to the ‘method of stages’ solution of series production systems with Erlang service times , 1976 .

[21]  Sushant Jain,et al.  Open finite queueing networks with M/M/C/K parallel servers , 1994, Comput. Oper. Res..

[22]  Eginhard J. MUTHf,et al.  The throughput rate of three-station production lines: a unifying solution , 1987 .

[23]  Yves Dallery,et al.  Manufacturing flow line systems: a review of models and analytical results , 1992, Queueing Syst. Theory Appl..

[24]  Leonard Kleinrock,et al.  Queueing Systems - Vol. 1: Theory , 1975 .

[25]  G. Anandalingam,et al.  Genetic algorithm based approach to bi-level linear programming , 1994 .

[26]  Mehrdad Tamiz Multi-Objective Programming and Goal Programming , 1996 .

[27]  Daniel Adelman A simple algebraic approximation to the Erlang loss system , 2008, Oper. Res. Lett..

[28]  John A. Buzacott,et al.  Stochastic models of manufacturing systems , 1993 .

[29]  Diomidis Spinellis,et al.  Large production line optimization using simulated annealing , 2000 .

[30]  Carl M. Harris,et al.  Fundamentals of queueing theory (2nd ed.). , 1985 .

[31]  Frederico R. B. Cruz,et al.  Service and capacity allocation in M/G/c/c state-dependent queueing networks , 2005, Comput. Oper. Res..

[32]  Harry G. Perros Queueing networks with blocking , 1994 .

[33]  Randall P. Sadowski,et al.  Simulation with Arena , 1998 .

[34]  F. Cruz,et al.  Buffer allocation in general single-server queueing networks , 2008, Comput. Oper. Res..

[35]  James MacGregor Smith,et al.  Asymptotic behavior of the expansion method for open finite queueing networks , 1988, Comput. Oper. Res..

[36]  J. Ben Atkinson,et al.  An Introduction to Queueing Networks , 1988 .

[37]  E. Hughes Multiple single objective Pareto sampling , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[38]  Frederick S. Hillier,et al.  Finite Queues in Series with Exponential or Erlang Service Times - A Numerical Approach , 1966, Oper. Res..

[39]  James MacGregor Smith,et al.  Multi-objective routing within large scale facilities using open finite queueing networks , 2000, Eur. J. Oper. Res..

[40]  J.J.H. Fey,et al.  Design of a fruit juice blending and packaging plant , 2000 .

[41]  Kyung C. Chae,et al.  Transform-free analysis of the GI/G/1/K queue through the decomposed Little's formula , 2003, Comput. Oper. Res..