Skip to main content
SpringerLink
Log in

A review of open queueing network models of manufacturing systems

  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

In this paper we review open queueing network models of manufacturing systems. The paper consists of two parts. In the first part we discuss design and planning problems arising in manufacturing. In doing so we focus on those problems that are best addressed by queueing network models. In the second part of the paper we describe developments in queueing network methodology. We are primarily concerned with features such as general service times, deterministic product routings, and machine failures — features that are prevalent in manufacturing settings. Since these features have eluded exact analysis, approximation procedures have been proposed. In the second part of this paper we review the developments in approximation procedures and highlight the assumptions that underlie these approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S.L. Albin, Approximating queues with superposition arrival processes, PhD dissertation, Dept. of IE and OR, Columbia University, New York (1981).

    Google Scholar 

  2. S.L. Albin, Approximating a point process by a renewal process. II. Superposition arrival processes to queues, Oper. Res., 32 (1984) 1133–1162.

    Google Scholar 

  3. R.N. Anthony, Planning and control systems: A framework for analysis, Graduate School of Business Administration, Harvard University, Boston (1965).

    Google Scholar 

  4. M. Avriel,Nonlinear Programming. Analyses and Methods (Prentice-Hall, Englewood Cliffs, NJ, 1976).

    Google Scholar 

  5. F. Baskett, K.M. Chandy, R.R. Muntz and F.G. Palacios, Open, closed and mixed networks of queues with different classes of customers, J. ACM 22 (1975) 248–260.

    Google Scholar 

  6. M. Berman and M. Westcott, On queueing systems with renewal departure processes, Adv. Appl. Prob. 15 (1983) 657–673.

    Google Scholar 

  7. D.P. Bertsekas,Constrained Optimization and Lagrange Multiplier Methods (Academic Press, New York, 1982).

    Google Scholar 

  8. D. Bertsimas and D. Nakazato, The departure process from aGI/G/1 queue and its application to the analysis of tandem queues, Working Paper, Sloan School of Management, M.I.T. (1990).

  9. G.R. Bitran and S. Dasu, Approximating non-renewal processes by Markov chains, to appear in Oper. Res. (1990).

  10. G.R. Bitran and S. Dasu, Analysis of∑Ph i /Ph/1 queues, to appear in Oper. Res. (1990).

  11. G.R. Bitran and D. Sarkar, Throughput analysis in manufacturing networks, Working paper, Sloan School of Management, M.I.T. (1990).

  12. G.R. Bitran and D. Tirupati, Multiproduct queueing networks with deterministic routing: Decomposition approach and the notion of interference, Manag. Sci. 35 (1988) 851–878.

    Google Scholar 

  13. G.R. Bitran and D. Tirupati, Capacity planning with discrete options in manufacturing networks, Ann. Oper. Res. 17 (1989) 119–136.

    Google Scholar 

  14. G.R. Bitran and D. Tirupati, Trade-off curves, targeting and balancing in manufacturing networks, Oper. Res. 37 (1989) 547–564.

    Google Scholar 

  15. G.R. Bitran and D. Tirupati, Approximations for product departures from a single server station with batch processing in multi-product queues, Manag. Sci. 35 (1989) 851–878.

    Google Scholar 

  16. G.R. Bitran and D. Tirupati, Approximations for network of queues with overtime, Manag. Sci. 37 (1991) 282–300.

    Google Scholar 

  17. O.J. Boxma, J.W. Cohen and N. Huffels, Approximations of the mean waiting time in anM/G/s queueing system, Oper. Res. 27 (1979) 1115–1127.

    Google Scholar 

  18. O.J. Boxma, A.H.G. Rinnooy Kan and M. van Vliet, Machine allocation algorithms for job shop manufacturing, Econometric Institute Report 9014/A, Erasmus University, Rotterdam, The Netherlands (1990), to appear in J. Intelligent Manufacturing.

    Google Scholar 

  19. A. Brandwajn and Y.L. Jow, An approximation method for tandem queues with blocking, Oper. Res. 36 (1988) 73–83.

    Google Scholar 

  20. E.S. Buffa and R.K. Sarin,Modern Production / Operations Management, 8th ed. (Wiley, New York, 1987).

    Google Scholar 

  21. A.A. Bugalak and J.L. Sanders, Modelling and design optimization of asynchronous flexible assembly systems with statistical process control and repair, Technical report, University of Wisconsin — Madison (1989).

    Google Scholar 

  22. J.A. Buzacott and J.G. Shanthikumar, Models for understanding flexible manufacturing systems, AIIE Trans. 14 (1980) 339–350.

    Google Scholar 

  23. J.A. Buzacott and J.G. Shanthikumar, Approximate queueing models of dynamic job shops, Manag. Sci. 31 (1985) 870–887.

    Google Scholar 

  24. J.A. Buzacott and D.D. Yao, On queueing network models of flexible manufacturing systems, Queueing Systems 1 (1986) 5–27.

    Google Scholar 

  25. J.A. Buzacott and D.D. Yao, Flexible manufacturing systems: A review of analytic models, Manag. Sci. 32 (1986) 890–905.

    Google Scholar 

  26. K.M. Chandy, J. Hogarth and C.H. Sauer, Selecting capacities in computer communication systems, IEEE Trans. Software Eng. SE-3 (1977) 290–295.

    Google Scholar 

  27. K.M. Chandy and C.H. Sauer, Approximate method for analyzing queueing network models of computer systems, ACM Comput. Survey 10 (1978) 281–317.

    Google Scholar 

  28. R.B. Chase and N.J. Aquilano,Production and Operations Management — a Life Cycle Approach (Richard D. Irwin, Homewood, 1989).

    Google Scholar 

  29. H. Chen, J.M. Harrison, A. Mandelbaum, A.A. Ackere and L.M. Wein, Empirical evaluation of a queueing network model for semiconductor wafer fabrication, Oper. Res. 36 (1988) 202–215.

    Google Scholar 

  30. T.C.E. Cheng, Analysis of job flow-time in a job shop, J. Oper. Res. Soc. 36 (1967) 225–230.

    Google Scholar 

  31. G.P. Cosmetatos, Approximate explicit formulae for the average queueing time in the process (M/D/r) and (D/M/r), INFOR 13 (1975) 328–331.

    Google Scholar 

  32. E.V. Denardo and C.S. Tang, Linear control of Markov production systems, Oper. Res. 40 (1992) 259–278.

    Google Scholar 

  33. P.J. Denning and J.P. Buzen, The operational analysis of queueing network models, Comput. Surveys 10 (1978) 225–261.

    Google Scholar 

  34. R.L. Disney and D. Konig, Queueing networks: A survey of their random processes, SIAM Rev. 27 (1985) 335–403.

    Google Scholar 

  35. M.E. Dyer and L.G. Proll, On the validity of marginal analysis for allocating servers inM/M/c queues, Manag. Sci. 23 (1977) 1019–1022.

    Google Scholar 

  36. A.K. Erlang, Solution of some problems in the theory of probabilities of some significance in automatic telephone exchanges, Post Office Electrical Engineer's Journal 10 (1917) 189–197.

    Google Scholar 

  37. A. Federgruen and H. Groenevelt,M/G/c queueing systems with multiple customer classes: characterization and control of achievable performance under nonpreemptive priority rules, Manag. Sci. 34 (1988) 1121–1138.

    Google Scholar 

  38. H.D. Friedman, Reduction methods for tandem queueing systems, Oper. Res. 13 (1965) 121–131.

    Google Scholar 

  39. M.R. Garey, D.S. Johnson and R. Sethi, Complexity of flow shop and job shop scheduling algorithms, Oper. Res. 24 (1976) 117–129.

    Google Scholar 

  40. S.B. Gershwin and I.C. Schick, Modelling and analysis of three stage transfer lines, with unreliable machines and finite buffers, Oper. Res. 31 (1983) 354–380.

    Google Scholar 

  41. S.C. Graves, A review of production scheduling, Oper. Res. 29 (1981) 646–675.

    Google Scholar 

  42. S.C. Graves, A tactical planning model for a job shop, Oper. Res. 34 (1986) 522–533.

    Google Scholar 

  43. R.W. Hall,Zero Inventories (Dow-Jones Irwin, Homewood, 1983).

    Google Scholar 

  44. A. Harel and P.H. Zipkin, Strong convexity results for queueing systems, Oper. Res. 35 (1987) 405–418.

    Google Scholar 

  45. J.M. Harrison, Brownian models of queueing networks with heterogeneous customer populations, in:Stochastic Differential Systems, Stochastic Control Theory and Applications, eds. W. Fleming and P.L. Lions, IMA vol. 10 (Springer, New York, 1988) pp. 147–186.

    Google Scholar 

  46. J.M. Harrison and R.J. Williams, Brownian models of open queueing networks with homogeneous customer populations, to appear in Stochastics (1987).

  47. J.M. Harrison and L.M. Wein, Scheduling networks of queues: Heavy traffic analysis of a simple open network, Queueing Systems 5 (1990) 265–280.

    Google Scholar 

  48. J.M. Harrison and L.M. Wein, Scheduling networks of queues: Heavy traffic analysis of a two-station closed network, Oper. Res. 38 (1990) 1052–1064.

    Google Scholar 

  49. A.C. Hax and D. Candea,Production and Inventory Management (Prentice-Hall, New Jersey, 1984).

    Google Scholar 

  50. R.H. Hayes and S.C. Wheelwright,Restoring Our Competitive Edge; Competing Through Manufacturing (Wiley, New York, 1984).

    Google Scholar 

  51. J.R. Jackson, Networks of waiting lines, Oper. Res. 5 (1957) 518–521.

    Google Scholar 

  52. J.R. Jackson, Jobshop-like queueing systems, Manag. Sci. 10 (1963) 131–142.

    Google Scholar 

  53. A.S. Kapadia and B.P. Hsi, Steady state waiting time in a multicenter job shop, Naval Res. Log. Quarterly 25 (1978) 149–154.

    Google Scholar 

  54. U. Karmarkar, Lot sizes, lead times and in-process inventories, Manag. Sci. 33 (1987) 409–418.

    Google Scholar 

  55. U. Karmarkar, S. Kekre and S. Kekre, Lotsizing in multi-item, multi-machine job shops, IIE Trans. 17 (1985) 290–298.

    Google Scholar 

  56. F.P. Kelly, Networks of queues with customers of different types, J. Appl. Prob. 12 (1975) 542–554.

    Google Scholar 

  57. F.P. Kelly,Reversibility and Stochastic Networks (Wiley, New York, 1979).

    Google Scholar 

  58. L. Kleinrock,Communication Nets: Stochastic Message Flow and Delay (Dover Publ., New York, 1964).

    Google Scholar 

  59. L. Kleinrock,Queueing Systems, vol. 2: Computer Applications (Wiley, New York, 1976).

    Google Scholar 

  60. W. Kraemer and M. Langenbach-Belz, Approximate formulae for the delay in the queueing systemGI/G/1,Congressbook, 8th Int. Teletraffic Congress, Melbourne (1976) p.235–1/8.

  61. P.J. Kuehn, Approximate analysis of general networks by decomposition, IEEE Trans. Commun. COM-27 (1979) 113–126.

    Google Scholar 

  62. C.N. Laws and G.M. Louth, Dynamic scheduling of four station network, Prob. Eng. Inf. Sci. (1989).

  63. A.J. Lemoine, Network of queues — A survey of equilibrium analysis, Manag. Sci. 24 (1977) 464–481.

    Google Scholar 

  64. J.K. Lenstra, A.H.G. Rinnooy Kan and P. Brucker, Complexity of machine scheduling problems, Ann. Discr. Math. 1 (1977) 343–362.

    Google Scholar 

  65. D.V. Lindley, The theory of queues with a single server, Proc. Camb. Phil. Soc. Math. Phys. Sci. 48 (1952) 277–295.

    Google Scholar 

  66. D.M. Lucantoni, New results on the single server queue with a batch Markovian arrival process, Stochastic Models 7 (1991) 1–46.

    Google Scholar 

  67. W.G. Marchal, An approximate formula for waiting time in single server queues, AIIE Trans. 8 (1976) 473–486.

    Google Scholar 

  68. K.T. Marshall, Some inequalities in queueing, Oper. Res. 16 (1968) 651–665.

    Google Scholar 

  69. H. Matsuo and L. Gong, Smoothing production and stabilizing WIP in a production system with yield loss, Working paper, University of Texas, Austin (1990).

    Google Scholar 

  70. G.L. Nemhauser and L.A. Wolsey,Integer and Combinatorial Optimization (Wiley, New York, 1988).

    Google Scholar 

  71. M.F. Nuets, A versatile Markovian point process, J. Appl. Prob. 16 (1979) 764–779.

    Google Scholar 

  72. Neuts, M.F.,Matrix Geometric Solutions in Stochastic Models (Johns Hopkins Univ. Press, Baltimore, 1981).

    Google Scholar 

  73. E. Page,Queueing Theory in O.R., Operational Research Series, ed. K.B. Haley (1972).

  74. S.S. Panwalker and W. Iskander, A survey of scheduling rules, Oper. Res. 25 (1977) 45–61.

    Google Scholar 

  75. H.G. Perros and T. Altiok (eds.),Queueing Networks with Blocking (Elsevier Science, New York, 1989).

    Google Scholar 

  76. V. Ramaswami, TheN/G/1 queue and its detailed analysis, Adv. Appl. Prob. 12 (1980) 222–261.

    Google Scholar 

  77. E. Reich, Waiting times when queues are in tandem, Ann. Math. Statist. 28 (1957) 768–773.

    Google Scholar 

  78. M. Reiser and H. Kobayashi, Accuracy of diffusion approximations for some queueing systems, IBM J. Res. Dev. 18 (1974) 110–124.

    Google Scholar 

  79. M. Reiser and S.S. Lavenberg, Mean value analysis of closed multichain queueing networks, J. ACM 27 (1980) 313–322.

    Google Scholar 

  80. A.H.G. Rinnooy Kan,Machine Scheduling Problems: Classification, Complexity and Computations (Nijhoff, The Hague, The Netherlands, 1976).

    Google Scholar 

  81. M. Rudemo, Point processes generated by transitions of Markov chains, Adv. Appl. Prob. 5 (1973) 262–286.

    Google Scholar 

  82. M. Segal and W. Whitt, A queueing network analyzer for manufacturing,Proc. 12th. Int. Tektraffic Congress, Torino, Italy (1988).

  83. A. Seidman, P.J. Schweitzer and S. Shalev-Oren, Computerized closed queueing network models of flexible manufacturing systems: A comparative evaluation, Large Scale Syst. 12 (1987) 91–107.

    Google Scholar 

  84. K.C. Sevick and I. Mitrani, The distribution of queueing network states at input and output instants, J. ACM 28 (1981) 358–471.

    Google Scholar 

  85. K.C. Sevick, A.I. Levy, S.K. Tripathi and J.L. Zahorjan, Improving approximations of aggregated queueing network systems,Proc. Computer Performance, Modeling, Measurement and Evaluation (1977).

  86. J.G. Shanthikumar, Stochastic majorization of random variables with proportional equilibrium rates, Adv. App. Prob. 19 (1987) 854–872.

    Google Scholar 

  87. J.G. Shanthikumar and J.A. Buzacott, On the approximations to the single server queue, Int. J. Prod. Res. 18 (1980) 761–773.

    Google Scholar 

  88. J.G. Shanthikumar and J.A. Buzacott, Open queueing network models of dynamic job shops, Int. J. Prod. Res. 19 (1981) 255–266.

    Google Scholar 

  89. J.G. Shanthikumar and J.A. Buzacott, The time spent in a dynamic job shop, Europ. J. Oper. Res. 17 (1984) 215–226.

    Google Scholar 

  90. J.G. Shanthikumar and K.E. Stecke, Reducing work-in-process inventory in certain classes of flexible manufacturing systems, Europ. J. Oper. Res. 26 (1986) 266–271.

    Google Scholar 

  91. J.G. Shanthikumar and U. Sumita, Approximations for the time spent in a dynamic job shop with applications to due-date assignment, Int. J. Prod. Res. 26 (1988) 1329–1352.

    Google Scholar 

  92. B. Simon and R. Foley, Some results on sojourn times in acyclic Jackson networks, Manag. Sci. 25 (1979) 1027–1034.

    Google Scholar 

  93. W. Skinner, The focussed factory, Harvard Bus. Rev. (May-June, 1974) 113–121.

  94. M.J. Sobel, Optimal operation of queues, in:Mathematical Models in Queueing Theory, Lecture Notes in Economical and Mathematical Systems, vol. 98 (Springer, 1979).

  95. A.N. Tantawi and D. Towsley, Optimal static load balancing in distributed computer systems, J. ACM 32 (1985) 445–465.

    Google Scholar 

  96. L.M. Wein, Capacity allocation in generalized Jackson networks, Oper. Res. Lett. 8 (1990) 143–146.

    Google Scholar 

  97. L.M. Wein, Optimal control of a two-station Brownian network, Math. Oper. Res. 15 (1990) 215–242.

    Google Scholar 

  98. L.M. Wein, Scheduling networks of queues: Heavy traffic analysis of a multistation network with controllable input, Oper. Res. 40 (1992) S312-S334.

    Google Scholar 

  99. L.M. Wein, Scheduling networks of queues: Heavy traffic analysis of a two-station network with controllable inputs, to appear in Oper. Res. (1990).

  100. W. Whitt, Approximating a point process by a renewal process: A general framework, Bell Laboratories (1979).

  101. W. Whitt, Approximating a point process by a renewal process: Two basic methods, Oper. Res. 30 (1982) 125–147.

    Google Scholar 

  102. W. Whitt, The queueing network analyzer, Bell Syst. Techn. J. 62 (1983) 2779–2843.

    Google Scholar 

  103. W. Whitt, Performance of the queueing network analyzer, Bell Syst. Techn. J. 63 (1983) 1911–1979.

    Google Scholar 

  104. W. Whitt, Approximations for departure processes and queues in series, Naval Res. Log. Quarterly 31 (1984) 499–521.

    Google Scholar 

  105. W. Whitt, Approximations for theGI/G/m queue, to appear in Adv. Appl. Prob. (1985).

  106. W. Whitt, Best order for queues in series, Manag. Sci. 31 (1985) 745–487.

    Google Scholar 

  107. W. Whitt, A light traffic approximation for single-class departures from multi-class queues, Manag. Sci. 34 (1988) 1333–1346.

    Google Scholar 

  108. D.D. Yao and S.C. Kim, Reducing congestion in class of job shops, Manag. Sci. 33 (1987) 1165–1172.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sloan School of Management, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    Gabriel R. Bitran

  2. Anderson Graduate School of Management, University of California at Los Angeles, 90024, Los Angeles, CA, USA

    Sriram Dasu

Authors
  1. Gabriel R. Bitran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sriram Dasu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bitran, G.R., Dasu, S. A review of open queueing network models of manufacturing systems. Queueing Syst 12, 95–133 (1992). https://doi.org/10.1007/BF01158637

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158637

Keywords

Search

Navigation