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Markov Decision Process and Linear Programming Based Control of MAP/MAP/N Queues

  • András Mészáros
  • Miklós Telek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8721)

Abstract

We investigate the control problem of the optimal choice of idle server (if any) for arriving customer in order to minimize the mean system time (waiting time + service time). The considered MAP/MAP/N queue consists of a common infinite buffer and multiple identical servers with MAP service processes whose phases (internal states) are known. Customers arrive according to a MAP (whose phase is also known) and are served with work conserving policy. Idle servers preserve their phases.

We transform the obtained infinite state optimization problem to a finite state one and apply two optimization procedures, policy iteration of finite state MDP and linear programming.

Keywords

Markov arrival process Markov decision process MAP/ MAP/N queue 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • András Mészáros
    • 1
    • 3
  • Miklós Telek
    • 1
    • 2
  1. 1.Budapest University of Technology and EconomicsHungary
  2. 2.MTA-BME Information Systems Research GroupHungary
  3. 3.Inter-University Center for Telecommunications and Informatics DebrecenHungary

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