Adaptive Policies for a System of Competing Queues I: Convergene Results for the Long-Run Average Cost
Abstract
This paper considers a system of discrete-time queues competing for the attention of a single geometric server. The problem of implementing a given Markov stationary service allocation policy g through an adaptive allocation policy a is posed and convergence of the long-run average cost under such adaptive policy a to the long-run average cost under the policy g is investigated. Such question typically arises in the context of Markov decision problems associated with this queueing system, say when some of the model parameters are not available [1, 20], or when the optimality criterion incorporates constraints [14. 21, 20]. Conditions are given so that the long-run average cost under the policy alpha converges to the corresponding cost under the policy g , provided a natural condition on the relative asymptotic behavior of the policies g and alpha holds. Applications of the results developed here are discussed in a companion paper [20]. However, the ideas of this paper are of independent interest and should prove useful in studying implementation and adaptive control issues for broad classes of Markov decision problems [12).
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1986
- Accession Number
- ADA444428
Entities
People
- Adam Shwartz
- Armand M. Makowski
Organizations
- University of Maryland