Skip to main content
SpringerLink
Log in

Stochastic analysis of versatile workcentres

  • Stochastic Models For Manufacturing Systems
  • Published:
Sadhana Aims and scope Submit manuscript

Abstract

We analyse the system consisting of a highly capable workcentre, which processes a variety of part types, using queueing models. The various part types produced by the system have distinct arrival and processing durations that are stochastic in nature. When an arriving workpiece finds the machine busy, it waits in a pre-process storage buffer (queue); this buffer may be common for all the part types, or may be dedicated for that part type. Further, this buffer may be capable of holding only a finite number of workpieces, or may be of infinite capacity. When the machine changes over from producing one type of part to another, a setup operation of stochastic duration is necessary to adjust the machine and load the necessary tools for production of the next part type. This model is representative of a typical machining centre in an Automated Manufacturing System. We focus ongi/g/1 models and multiqueue polling models, and their variants. The important performance measures of the system obtained by queueing analysis are the part-type-wise values of the mean lead time, mean inventory level, and the mean machine utilisation.

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

  • Albin S L 1986 Delays for customers from different arrival streams to a queue.Manage. Sci. 32: 329–340

    MATH  Google Scholar 

  • Ancker C Jr, Gafarian A V 1961 Queueing with multiple poisson inputs and exponential service times.Oper. Res. 9: 321–327

    MATH  MathSciNet  Google Scholar 

  • Basharin G 1965 A single server with a finite queue and items of several types.Theory Probab. Its Appl. (USSR) 10: 261–274

    Article  MATH  Google Scholar 

  • Baskett F, Chandy K M, Muntz R R, Palacios F G 1975 Open, closed and mixed networks of queues with different classes of customers.J. Assoc. Comput. Mach. 22: 248–260

    MATH  MathSciNet  Google Scholar 

  • Bitran G R, Tirupati D 1988 Multiproduct queueing networks with deterministic routing: Decomposition approach and the notion of interference.Manage. Sci. 34: 75–100

    MATH  MathSciNet  Google Scholar 

  • Bitran G R, Tirupati D 1989 Approximations for product departures from single-server station with batch processing in multi-product queues.Manage. Sci. 35: 851–878

    MATH  MathSciNet  Google Scholar 

  • Boxma O J, Meister B W 1987 Waiting-time approximations for cyclic-service systems with switchover times.Performance Eval. 7: 299–308

    Article  MathSciNet  Google Scholar 

  • Buzacott J A, Shanthikumar J G 1985 On approximate queueing models of dynamic job shops.Manage. Sci. 31: 870–887

    Google Scholar 

  • Dobson G, Karmarkar U S, Rummel J 1987 Batching to minimise flow times on one machine.Manage. Sci. 33: 784–799

    Article  MATH  Google Scholar 

  • Fuhrmann S W, Wang Y T 1988 Analysis of cyclic service systems with limited service: Bounds and approximations.Performance Eval. 9: 35–54

    Article  MathSciNet  MATH  Google Scholar 

  • Gershwin S B 1989 Hierarchical flow control: A framework for scheduling and planning discrete events in manufacturing systems.Proc. IEEE 77: 195–209

    Article  Google Scholar 

  • Ibe O C, Cheng X 1989a Approximate analysis of asymmetric single-service token-passing systems.IEEE Trans. Commun. 37: 572–577

    Article  Google Scholar 

  • Ibe O C, Cheng X 1989b Performance analysis of asymmetric single-buffer polling systems.Performance Eval. 10: 1–14

    Article  MathSciNet  Google Scholar 

  • Kelly F P 1979Reversibility and stochastic networks (Chichester: John Wiley and Sons)

    MATH  Google Scholar 

  • Kleinrock L, Levy H 1988 The analysis of random polling systems.Oper. Res. 36: 716–732

    MATH  MathSciNet  Google Scholar 

  • Kuehn P J 1979 Approximate analysis of general networks by decomposition.IEEE Trans. Commun. 27: 113–126

    Article  MATH  Google Scholar 

  • Kumar P R, Scidman T I 1990 Dynamic instabilities and stabilisation methods in distributed real-time scheduling of manufacturing systems.IEEE Trans. Autom. Control. 35: 289–298

    Article  MATH  Google Scholar 

  • Lavenberg S S 1975 The steady-state queueing time distribution for the M/G/1 finite capacity queue.Manage. Sci. 21: 501–506

    MATH  Google Scholar 

  • Leachman R C, Gascon A 1988 A heuristic scheduling policy for multi-item single-machine production systems with time-varying, stochastic demands.Manage. Sci. 34: 377–390

    Article  MATH  MathSciNet  Google Scholar 

  • Marie R A 1979 An approximate analytical method for general queueing networks.IEEE Trans. Software Eng. 5: 530–538

    Article  MathSciNet  Google Scholar 

  • Perkins J R, Kumar P R 1989 Stable, distributed, real-time scheduling of flexible manufacturing/assembly/disassembly systems.IEEE Trans. Autom. Control 34: 139–148

    Article  MATH  MathSciNet  Google Scholar 

  • Seidmann A, Schweitzer P J, Nof S Y 1985 Performance evaluation of a flexible manufacturing cell with random feedback flow.Int. J. Product. Res. 23: 1171–1184

    Article  MATH  Google Scholar 

  • Shanthikumar J G, Buzacott J A 1980 On the approximations to the single server queue.Int. J. Product. Res. 18: 761–773

    Article  Google Scholar 

  • Shanthikumar J G, Buzacott J A 1981 Open queueing network models of dynamic jobshops.Int. J. Product. Res. 19: 255–266

    Article  Google Scholar 

  • Shanthikumar J G, Gocmen M 1983 Heuristic analysis of closed queueing networks.Int. J. Product. Res. 21: 675–690

    Article  MATH  Google Scholar 

  • Srinivasan M M 1988 An approximation for mean waiting times in cyclic server systems with nonexhaustive service.Performance Eval. 9: 17–33

    Article  Google Scholar 

  • Takagi H 1988 Queueing analysis of polling models.ACM Comput. Surv. 20: 5–28

    Article  MATH  MathSciNet  Google Scholar 

  • Takagi H 1990 Analysis of polling systems: An update.Stochastic analysis of computer and communication systems (Amsterdam: North Holland)

    Google Scholar 

  • Takine T, Takahashi Y, Hasegawa T 1988 Exact analysis of asymmetric polling systems with single buffers.IEEE Trans. Commun. 36: 1119–1127

    Article  Google Scholar 

  • Tedijanto 1990 Exact results for the cyclic-service queue with a Bernoulli schedule.Performance Eval. 11: 107–115

    Article  MathSciNet  Google Scholar 

  • Tran-Gia P, Raith T 1988 Performance analysis of finite capacity polling systems with nonexhaustive service.Performance Eval. 8: 1–16

    Article  Google Scholar 

  • Whitt W 1983 The queueing network analyser.Bell Syst. Tech. J. 62: 2779–2815

    Google Scholar 

  • Whitt W 1988 A light-traffic approximation for single-class departure process from multi-class queues.Manage Sci. 34: 1333–1346

    MATH  MathSciNet  Google Scholar 

  • Wolff R W 1982 Poisson arrivals see time averages.Oper. Res. 30: 223–231

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Automation, Indian Institute of Science, 560012, Bangalore, India

    R Ram & N Viswanadham

Authors
  1. R Ram
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N Viswanadham
    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

Ram, R., Viswanadham, N. Stochastic analysis of versatile workcentres. Sadhana 15, 301–317 (1990). https://doi.org/10.1007/BF02811327

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02811327

Keywords

Search

Navigation