Skip to main content

Monotone control of queueing networks

Abstract

This paper uses submodularity to obtain monotonicity results for a class of Markovian queueing network service rate control problems. Nonlinear costs of queueing and service are allowed. In contrast to Weber and Stidham [14], our monotonicity theorem considers arbitrary directions in the state space (not just control directions), arrival routing problems, and certain uncontrolled service rates. We also show that, without service costs, transition-monotone controls can be described by simple control regions and switching functions. The theory is applied to queueing networks that arise in a manufacturing system that produces to a forecast of customer demand, and also to assembly and disassembly networks.

This is a preview of subscription content, access via your institution.

References

  1. F. Beutler and D. Teneketzis, Routing in queueing networks under imperfect information: stochastic dominance and thresholds, Stoch. and Stoch. Reports 26 (1989) 81–100.

    Google Scholar 

  2. J. Buzacott, S. Price and J.G. Shanthikumar, Service levels in multistage MRP and base stock controlled production systems, Working paper, U. of California, Berkeley (1991).

    Google Scholar 

  3. H. Chen, P. Yang and D. Yao, Control and scheduling in a two-station queueing network: optimal policies, heuristics, and conjectures, Math. Oper. Res. (1991), submitted.

  4. H. Ghoneim and S. Stidham, Control of arrivals to two queues in series, Euro. J. Oper. Res. 21 (1985) 399–409.

    Google Scholar 

  5. P. Glasserman and D. Yao, Monotone optimal control of permutable GSMPs, Working paper, Columbia Univ., New York (1992).

    Google Scholar 

  6. B. Hajek, Optimal control of two interacting service stations, IEEE Trans. Auto. Control AC-29 (1984) 491–499.

    Google Scholar 

  7. B. Hajek, Extremal splittings of point processes, Math. Oper. Res. 10 (1985) 543–556.

    Google Scholar 

  8. J.M. Harrison,Brownian Motion and Stochastic Flow Systems (Wiley, New York, 1985).

    Google Scholar 

  9. S. Lippman, Applying a new device in the optimization of exponential queueing systems, Oper. Res. 23 (1975) 687–710.

    Google Scholar 

  10. Z. Rosberg, P. Varaiya and J. Walrand, Optimal control of service in tandem queues, IEEE Trans. Auto. Control AC-27 (1982) 600–610.

    Google Scholar 

  11. S. Stidham, Optimal control of admission to a queueing system, IEEE Trans. Auto. Control AC-30 (1985) 705–713.

    Google Scholar 

  12. S. Stidham, Scheduling, routing, and flow control in stochastic networks, in:Stochastic Control Theory and Applications, eds. W. Fleming and P.L. Lions, IMA vol. 10 (Springer, New York, 1988).

    Google Scholar 

  13. D. Topis, Minimizing a submodular function on a lattice, Oper. Res. 26 (1978) 305–321.

    Google Scholar 

  14. R. Weber and S. Stidham, Optimal control of service rates in networks of queues, Adv. Appl. Prob. 19 (1987) 202–218.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Veatch, M.H., Wein, L.M. Monotone control of queueing networks. Queueing Syst 12, 391–408 (1992). https://doi.org/10.1007/BF01158810

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158810

Keywords

  • Control of queues
  • dynamic programming
  • submodularity
  • monotone policies
  • make-to-stock queues