A monotonic property of the optimal admission control to an M/M/1 queue under periodic observations with average cost criterion

Jianhua Cao, Christian Nyberg

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

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Abstract

We consider the problem of admission control to an M/M/1 queue under periodic
observations with average cost criterion. The admission controller receives
the system state information every ø :th second and can accordingly adjust the
acceptance probability for customers who arrive before the next state information
update instance. For a period of ø seconds, the cost is a linear function of the
time average of customer populations and the total number of served customers
in that period. The objective is to Ønd a stationary deterministic control policy
that minimizes the long run average cost. The problem is formulated as a discrete
time Markov decision process whose states are fully observable. By taking the
control period ø to 0 or to 1, the model in question generalizes two classical
queueing control problems: the open and the closed loop admission control to an
M/M/1 queue. We show that the optimal policy is to admit customers with a
non-increasing probability with respect to the observed number of customers in
the system. Numerical examples are also given.
Original languageEnglish
Title of host publicationSeventeenth Nordic Teletraffic Seminar, NTS 17, Fornebu, Norway, 25-27 August 2004
PublisherFornebu : Telenor
ISBN (Print)82-423-0595-1
Publication statusPublished - 2004

Subject classification (UKÄ)

  • Communication Systems
  • Electrical Engineering, Electronic Engineering, Information Engineering

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