Skip to main content
SpringerLink
Log in

Stabilizing an uncertain production system

  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

Consider a production system that consists ofm machines each of which can produce parts ofn types. When machinek is used, it produces a part of typei with probabilityp ki . Requests arrive for parts, one at a time. With probability λ i an arriving request is for a part of typei. The requests must be served without waiting. Thus, if a requested part is not available, it must be produced. We find necessary and sufficient conditions for the existence of a strategy (a choice of the machines to be used) which makes the inventory of parts stable and we provide such a strategy.

Two variations of this model are also considered: the case of batch arrivals of requests, and that of a system where the requests can be queued.

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. Asmussen,Applied Probability and Queues (J. Wiley, 1987).

  2. C. Courcoubetis and R. Weber, Necessary and sufficient conditions for stability of a bin-packing system, J. Appl. Prob. 23 (1986) 989–999.

    Google Scholar 

  3. B. Hajek, Hitting-time and occupation-time bounds implied by drift analysis with applications, Adv. Appl. Prob. 14 (1986) 502–525.

    Google Scholar 

  4. R. Tweedie, Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space, Stoch. Proc. and Appl. 3 (1975) 385–403.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA

    Costas Courcoubetis

  2. EECS, Univ. of California at Berkeley, 94720, Berkeley, CA, USA

    Panagiotis Konstantopoulos & Jean Walrand

  3. Queens' College, University of Cambridge, Cambridge, UK

    Richard R. Weber

Authors
  1. Costas Courcoubetis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Panagiotis Konstantopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jean Walrand
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Richard R. Weber
    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

Courcoubetis, C., Konstantopoulos, P., Walrand, J. et al. Stabilizing an uncertain production system. Queueing Syst 5, 37–54 (1989). https://doi.org/10.1007/BF01149185

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01149185

Keywords

Search

Navigation