SCHEDULING IN A QUEUING SYSTEM WITH ASYNCHRONOUSLY VARYING SERVICE RATES

  • Authors:
  • Matthew Andrews;Krishnan Kumaran;Kavita Ramanan;Alexander Stolyar;Rajiv Vijayakumar;Phil Whiting

  • Affiliations:
  • Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974, E-mail: andrews@research.bell-labs.com;Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974, E-mail: kumaran@research.bell-labs.com;Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974, E-mail: kavita@research.bell-labs.com;Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974, E-mail: stolyar@research.bell-labs.com;University of Michigan, Ann Arbor, Michigan, E-mail: rvijayak@engin.umich.edu;Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974, E-mail: pwhiting@research.bell-labs.com

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2004

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Abstract

We consider the following queuing system which arises as a model of a wireless link shared by multiple users. There is a finite number N of input flows served by a server. The system operates in discrete time t = 0,1,2,…. Each input flow can be described as an irreducible countable Markov chain; waiting customers of each flow are placed in a queue. The sequence of server states m(t), t = 0,1,2,…, is a Markov chain with finite number of states M. When the server is in state m, it can serve &mgr;im customers of flow i (in one time slot).The scheduling discipline is a rule that in each time slot chooses the flow to serve based on the server state and the state of the queues. Our main result is that a simple online scheduling discipline, Modified Largest Weighted Delay First, along with its generalizations, is throughput optimal; namely, it ensures that the queues are stable as long as the vector of average arrival rates is within the system maximum stability region.