Skip to main content
SpringerLink
Log in

On the optimality of a full-service policy for a queueing system with discounted costs

  • Original Article
  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

We provide weak sufficient conditions for a full-service policy to be optimal in a queueing control problem in which the service rate is a dynamic decision variable. In our model there are service costs and holding costs and the objective is to minimize the expected total discounted cost over an infinite horizon. We begin with a semi-Markov decision model for a single-server queue with exponentially distributed inter-arrival and service times. Then we present a general model with weak probabilistic assumptions and demonstrate that the full-service policy minimizes both finite-horizon and infinite-horizon total discounted cost on each sample path.

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

  • Bell C (1971) Characterization and computation of optimal policies for operating an M/G/1 queuing system with removable server. Oper Res 19:208–218

    MATH  Google Scholar 

  • Lippman S (1975) Applying a new device in the optimization of exponential queuing systems. Oper Res 23:687–710

    Article  MATH  MathSciNet  Google Scholar 

  • Puterman M (1994) Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York

    MATH  Google Scholar 

  • Sobel M (1982) The optimality of full service policies. Oper Res 30:636–649

    MATH  Google Scholar 

  • Stidham S (1972) L=λ W: a discounted analogue and a new proof. Oper Res 20:1115–1126

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Operations Research, University of North Carolina, CB 3180, Smith Building, Chapel Hill, NC, 27599-3180, USA

    Shaler Stidham Jr.

Authors
  1. Shaler Stidham Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shaler Stidham Jr..

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stidham, S. On the optimality of a full-service policy for a queueing system with discounted costs. Math Meth Oper Res 62, 485–497 (2005). https://doi.org/10.1007/s00186-005-0040-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00186-005-0040-6

Keywords

Search

Navigation