An experimental analysis of steady state convergence in simple queueing systems: Implications for flexible manufacturing system models

Abstract Queueing models are widely used for performance analysis of Flexible Manufacturing Systems (FMS). Most studies are done under steady state assumptions. The inherent flexibility of FMS in terms of input, volume, and mix makes such an assumption hard to justify. In this paper, we investigate the convergence rate to steady state in simple queueing models that constitute the basic building blocks of more complex FMS models. The study reveals that steady-state conditions are not achieved during the execution of batches of moderate size. We therefore conclude that although equilibrium models are appropriate for studying long-term planning problems, for the operational control of FMSs, it is highly desirable to study the transient behaviour of the system. On a broader scope, our investigation also shows that steady-state assumptions used in the analysis of any inherently transient system should be carefully validated.

[1]  Amedeo R. Odoni,et al.  An Empirical Investigation of the Transient Behavior of Stationary Queueing Systems , 1983, Oper. Res..

[2]  Erhan Çinlar,et al.  Introduction to stochastic processes , 1974 .

[3]  Nico M. van Dijk,et al.  Transient Error Bound Analysis for Continuous-Time Markov Reward Structures , 1991, Perform. Evaluation.

[4]  Ward Whitt,et al.  Untold Horrors of the Waiting Room: What the Equilibrium Distribution Will Never Tell About the Queue-Length Process , 1983 .

[5]  P. Glynn,et al.  Conditions Under Which a Markov Chain Converges to its Steady State in Finite Time , 1988, Probability in the Engineering and Informational Sciences.

[6]  J. A. Buzacott,et al.  Models for Understanding Flexible Manufacturing Systems , 1980 .

[7]  Rajan Suri,et al.  Single run optimization of a SIMAN model for closed loop flexible assembly systems , 1987, WSC '87.

[8]  J. Kleijnen.  Statistical tools for simulation practitioners , 1986 .

[9]  J. A. Buzacott,et al.  Queueing models for a flexible machining station Part I: The diffusion approximation , 1985 .

[10]  J. A. Buzacott,et al.  Impact of flexible machines on automated manufacturing systems , 1988 .

[11]  Enver Yücesan,et al.  Randomization tests for initialization bias in simulation output , 1993 .

[12]  Didier Dubois,et al.  Heuristic methods based on mean-value analysis for flexible manufacturing systems performance evaluation , 1982, 1982 21st IEEE Conference on Decision and Control.

[13]  Averill M. Law,et al.  Simulation Modeling & Analysis , 1991 .

[14]  Ludo Gelders,et al.  A review of FMS planning models , 1986 .

[15]  Xi-Ren Cao,et al.  Perturbation analysis and optimization of queueing networks , 1983 .

[16]  Ward Whitt,et al.  Transient behavior of regulated Brownian motion, II: Non-zero initial conditions , 1987 .

[17]  Frank D. Chance.  Conjectured upper bounds on transient mean total waiting times in queuing networks , 1993, WSC '93.

[18]  J. A. Buzacott,et al.  Queueing models for a flexible machining station Part II: The method of Coxian phases , 1985 .

[19]  J. A. Buzacott,et al.  Flexible manufacturing systems: a review of analytical models , 1986 .

[20]  George S. Fishman,et al.  Solution of Large Networks by Matrix Methods , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  Harry G. Perros,et al.  Open Networks of Queues with Blocking: Split and Merge Configurations: , 1986 .

[22]  W. David Kelton,et al.  Transient exponential-Erlang queues and steady-state simulation , 1985, CACM.

[23]  Averill M. Law,et al.  The Transient Behavior of the M/M/s Queue, with Implications for Steady-State Simulation , 1985, Oper. Res..

[24]  Ward Whitt,et al.  Transient behavior of the M/M/l queue: Starting at the origin , 1987, Queueing Syst. Theory Appl..

[25]  A. Alan B. Pritsker,et al.  Introduction to simulation and SLAM II , 1979 .

[26]  Kathryn E. Stecke,et al.  The Optimality of Unbalancing Both Workloads and Machine Group Sizes in Closed Queueing Networks of Multiserver Queues , 1985, Oper. Res..

[27]  C. J. Ancker,et al.  Evaluation of commonly used rules for detecting “steady state” in computer simulation , 1978 .

[28]  Amedeo R. Odoni,et al.  On Finding the Maximal Gain for Markov Decision Processes , 1969, Oper. Res..

[29]  Lee W. Schruben,et al.  Optimal Tests for Initialization Bias in Simulation Output , 1983, Oper. Res..