Optimal Control for an MX/G/1/N + 1 Queue with Two Service Modes

  • Rein D. Nobel
  • Adriaan A. N. Ridder
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 246)


A finite-buffer queueing model is considered with batch Poisson input and controllable service rate. A batch that upon arrival does not fit in the unoccupied places of the buffer is partially rejected. A decision to change the service mode can be made at service completion epochs only, and vacation (switch-over) times are involved in preparing the new mode. During a switch-over time, service is disabled. For the control of this model, three optimization criteria are considered: the average number of jobs in the buffer, the fraction of lost jobs, and the fraction of batches not fully accepted. Using Markov decision theory, the optimal switching policy can be determined for any of these criteria by the value-iteration algorithm. In the calculation of the expected one-step costs and the transition probabilities, an essential role is played by the discrete fast Fourier transform.


Finite-buffer model Value iteration Fast Fourier transform 


  1. 1.
    J.H. Dshalalow (1997). Queueing systems with state dependent parameters. In Frontiers in Queueing, edited by J.H. Dshalalow. CRC Press, New York.Google Scholar
  2. 2.
    S. Nishimura and Y. Jiang (1994). An M/G/1 vacation model with two service modes. Probability in the Engineering and Informational Sciences, 9, 355–374.Google Scholar
  3. 3.
    R.D. Nobel and H.C. Tijms (1999). Optimal control for a M X /G/1 queue with two service modes. In European Journal of Operational Research, 113, 610–619.Google Scholar
  4. 4.
    R.D. Nobel (1998). A regenerative approach for an M X /G/1 queue with two service modes. Automatic Control and Computer Science, 1, 3–14 (in Russian).Google Scholar
  5. 5.
    G.M. Koole (1998). Structural results for the control of queueing systems using event-based dynamic programming. In Queueing Systems and its Applications, 30, 332–339.Google Scholar
  6. 6.
    S. Stidham and R.R. Weber (1993). A survey of Markov decision models for control of networks of queues. Queueing Systems and its Applications, 13, 291–314.Google Scholar
  7. 7.
    M.Y. Kitaev and V.V. Rykov (1995). Controlled queueing systems. CRC Press, New York.Google Scholar
  8. 8.
    L.I. Sennot (1998). Stochastic dynamic programming and the control of queueing systems. Wiley, New York.Google Scholar
  9. 9.
    R. Cavazos-Cadena and L.I. Sennot (1992). Comparing recent assumptions for the existence of average cost optimal stationary policies. Operations Research Letters, 11, 33–37.Google Scholar
  10. 10.
    R.D. Nobel and M. van der Heeden (2000). A lost-sales production/inventory model with two discrete production modes. Stochastic Models, 16, 453–478Google Scholar
  11. 11.
    M.L. Puterman (1994). Markov decision processes. Wiley, New York.Google Scholar
  12. 12.
    H.C. Tijms (1994). Stochastic models: an algorithmic approach, Wiley, New York.Google Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Department of EconometricsVrije UniversiteitAmsterdamThe Netherlands

Personalised recommendations