Accession Number:

ADA371628

Title:

Difference Equations and the Optimal Control of Single Server Queueing Systems

Descriptive Note:

Research rept.

Corporate Author:

NAVAL WEAPONS CENTER CHINA LAKE CA

Personal Author(s):

Report Date:

1974-06-01

Pagination or Media Count:

105.0

Abstract:

This report demonstrates the use of difference equations in solving optimal control problems in single server queueing systems. One obtains the discounted or relative cost function associated with a specific stationary policy by solving an appropriate system of difference equations. The policy improvement algorithm is applied parametrically leading to a characterization of the cost function satisfying the functional equation of optimality. If this cost function satisfies an appropriate sufficient condition, the associated stationary policy is optimal. The method of solution is illustrated by solving three queueing optimization problems. These problems include optimal control of the MG1 queue with intermittent service, a bulk queueing version of this same problem, and control of the MM1 queue with selection of running speed. All of these problems have been investigated by other authors. Results in this report believed to be new include a complete characterization of optimal policies for the optimal control of the MG1 queue in the discounted case, the extension of the optimal control of the bulk queueing problem from instantaneous to general service, and the determination of an optimal speed selection policy for the MM1 queue without solving a sequence of truncated problems.

Subject Categories:

  • Computer Systems

Distribution Statement:

APPROVED FOR PUBLIC RELEASE