On a Slow Server Problem

Part of the Lecture Notes in Statistics book series (LNS, volume 208)


The slow server problem is generalized for the case of additional cost structure. With the help of special partial ordering of the system state space it is shown that the optimal policy for the problem has a monotone property consisting in the following: an additional server should be switched on only in the case if the queue length exceeds some level depending on the system state, and in this case the server with minimal service cost should be used.


Optimal Policy Queue Length Sojourn Time Monotonicity Property Qualitative Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [143]
    Efrosinin, D.: Controlled queueing systems with heterogeneous servers: Dynamic optimization and monotonicity properties. Saarbrücken: VDM Verlag (2008)Google Scholar
  2. [144]
    Efrosinin, D. and Breuer, L.: Threshold policies for controlled retrial queues with heterogeneous servers. Annals of Operations Research, 141, 139–162 (2006)MathSciNetCrossRefGoogle Scholar
  3. [187]
    Hajek, B.: Optimal control of two interacting service stations. IEEE Transactions on Automatic Control, 29, 491–499 (1984)MATHCrossRefGoogle Scholar
  4. [239]
    Kitaev, M. Y. and Rykov, V. V.: Controlled queueing systems. CRC Press, New York (1995)MATHGoogle Scholar
  5. [265]
    Koole, G.: A simple proof of the optimality of a threshold policy in two-server queueing system. Systems & Control Letters, 26, 301–303 (1995)MathSciNetMATHCrossRefGoogle Scholar
  6. [268]
    Krishnamoorthy, B.: On Poisson queue with two heterogeneous servers. Operational Research, 11, 321–330 (1963)CrossRefGoogle Scholar
  7. [271]
    Langrock, P. and Rykov V. V.: Methoden und Modelle zur Steurung von Bedienungssystemen. Handbuch der Bedienungs theorie. Berlin, Akademie-Verlag, B. 2, 422–486 (1984)Google Scholar
  8. [282]
    Lin, W. and Kumar, P. R.: Optimal control of a queueing system with two heterogeneous servers. IEEE Transactions on Automatic Control, 29, 696–703 (1984)MathSciNetMATHCrossRefGoogle Scholar
  9. [369]
    Pedro, T.: One size does not fit all: a case for heterogeneous multiprocessor systems. IADIS International Conference Applied Computing, 15–22 (2005)Google Scholar
  10. [402]
    Rykov, V. V.: On monotonicity conditions of optimal control policies for controllable Queueing Systems. Automation and Remote Control, 9, 92–106 (1999)MathSciNetGoogle Scholar
  11. [403]
    Rykov, V. V.: Monotone Control of Queueing System with heterogeneous servers. Queueing Systems, 37, 391–403 (2001)MathSciNetMATHCrossRefGoogle Scholar
  12. [404]
    Rykov, V. V. and Efrosinin, D. V.: Numerical study of optimal control of queueing system with heterogeneous servers. Automation and Remote Control, 64(2), 302–309 (2003)MathSciNetMATHCrossRefGoogle Scholar
  13. [405]
    Rykov, V. V. and Efrosinin, D. V.: On slow Server Problem. Automation and Remote Control, 70(12), 2013–2023 (2009)MathSciNetMATHCrossRefGoogle Scholar
  14. [416]
    Sennott, L. I.: Stochastic Dynamic Programming and the Control of Queueing Systems. Wiley, New York (1999)MATHGoogle Scholar
  15. [462]
    Vericourt, F. and Zhou, Y. P.: On the incomplete results for the heterogeneous server problem. Queueing Systems, 52, 189–191 (2006)MathSciNetMATHCrossRefGoogle Scholar
  16. [463]
    Vishnevsky, V. M. and Semenova, O. V.: Polling systems: theory and applications in bandwidth wireless networks (in Russian). M.: Tekhnosppere (2007)Google Scholar
  17. [471]
    Weber, R.: On a conjecture about assigning jobs to processors of different speeds. IEEE Transactions on Automatic Control, 38, no. 1, 166–170 (1993)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computational ModelingGubkin Russian State University of Oil and GasMoscowRussia

Personalised recommendations