Abstract
In this paper, we present a capacity analysis of an automated transportation system in a flexible assembly factory. The transportation system, together with the workstations, is modeled as a network of queues with multiple job classes. Due to its complex nature, the steady‐state behavior of this network is not described by a product‐form solution. Therefore, we present an approximate method to determine the capacity of the network. We first study a number of key elements of the system separately and subsequently combine the results of this analysis in an Approximate Mean Value Analysis (AMVA) algorithm. The key elements are a buffer/transfer system (the bottleneck of the system), modeled as a preemptive‐repeat priority queue with identical deterministic service times for the different job classes, a set of elevators, modeled as vacation servers, a number of work cells, modeled as multi‐server queues, and several non‐accumulating conveyor belts, modeled as ample servers. The AMVA algorithm exploits the property that the initial multi‐class queueing network can be decomposed into a sequence of single‐class queueing networks and hence is very efficient. Comparison of numerical results of the AMVA algorithm for the throughputs for the different job classes to simulation results shows that the AMVA algorithm is also accurate. For several series of instances, the maximum relative error that we found was only 4.0%.
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I.J.B.F. Adan, W.A. van de Waarsenburg and J. Wessels, Analyzing EkjErjc queues, European Journal of Operational Research 92 (1996) 112–124.
I.J.B.F. Adan, G.J. van Houtum and J. Van der Wal, Upper and lower bounds for the waiting time in the symmetric shortest queue system, Annals of Operations Research 48 (1994) 197–217.
I.J.B.F. Adan, J. Wessels and W.H.M. Zijm, Analysis of the symmetric shortest queue problem, Stochastic Models 6 (1990) 691–713.
F. Baskett, K.M. Chandy, R.R. Muntz and F.G. Palacios, Open, closed and mixed networks of queues with different classes of customers, Journal of the Association of Computing Machinery 22 (1975) 248–260.
D. Bertsimas, An exact FCFS waiting time analysis for a class of GjGjs queueing systems, Queueing Systems 3 (1988) 305–320.
D. Bertsimas, An analytic approach to a general class of GjGjs queueing systems, Operations Research 38 (1990) 139–155.
D. Bertsimas and X.A. Papaconstantinou, Analysis of the EkjC2js queueing system, European Journal of Operational Research 37 (1988) 272–287.
A.B. Bondi and Y.M. Chuang, A new MVA-based approximation for closed queueing networks with a pre-emptive priority server, Performance Evaluation 8 (1988) 195–221.
R.M. Bryant, A.E. Krzesinski and P. Teunissen, The MVA preempt resume priority approximation, Performance Evaluation Review 5 (1983) 12–27.
R.M. Bryant, A.E. Krzesinski, M.S. Lakshmi and K.M. Chandy, The MVA priority approximation, ACM Trans. Comput. Sys. 4 (1984) 335–359.
R. Buitenhek, Performance evaluation of dual resource manufacturing systems, Ph.D. thesis, University of Twente, Enschede (1998).
E.G. Coffman, E. Gelenbe and E.N. Gilbert, Analysis of a conveyor queue in a flexible manufacturing system, European Journal of Operational Research 35 (1988) 382–392.
R.B. Cooper, Introduction to Queueing Theory (Edward Arnold, New York, 1981).
B.T. Doshi, Queueing systems with vacations-A survey, Queueing Systems 1 (1986) 29–66.
D.L. Eager and J.N. Lipscomb, The AMVA priority approximation, Performance Evaluation 8 (1988) 173–193.
N.K. Jaiswall, Priority Queues (Academic Press, New York, 1968).
L. Kleinrock, Queueing Systems 1: Theory (Wiley, New York, 1975).
J.S. Kaufman, Approximation methods for networks of queues with priorities, Performance Evaluation 4 (1984) 183–198.
M. Reiser and S.S. Lavenberg, Mean value analysis of closed multichain queueing networks, Journal of the Association of Computing Machinery 22 (1980) 313–322.
S.M. Ross, Introduction to Probability Models, 6th ed. (Academic Press, London, 1997).
H.C. Tijms, Stochastic Modelling and Analysis: A Computational Approach (Wiley, Chichester, 1986).
G.J. Van Houtum, I.J.B.F. Adan, J. Wessels and W.H.M. Zijm, Performance analysis of parallel machines with a generalized shortest queue arrival mechanism, Working paper LPOM–97–08, University of Twente (1997).
R.W. Wolff, Poisson arrivals see time averages, Operations Research 30 (1982) 223–231.
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Zijm, W., Adan, I., Buitenhek, R. et al. Capacity analysis of an automated kit transportation system. Annals of Operations Research 93, 423–446 (2000). https://doi.org/10.1023/A:1018936209774
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DOI: https://doi.org/10.1023/A:1018936209774