A Study of Monotone Optimal Operating Policy for Some Tandem Queueing System
Whang, Kyu-Seung
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Permalink
https://hdl.handle.net/2142/67321
Description
Title
A Study of Monotone Optimal Operating Policy for Some Tandem Queueing System
Author(s)
Whang, Kyu-Seung
Issue Date
1980
Department of Study
Business Administration
Discipline
Business Administration
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Business Administration, General
Language
eng
Abstract
This paper examines a monotone policy as an optimal control rule for a tandem queueing service system with an ordered sequence of N job stages. Each job can be viewed as a single service station. A finite queue is allowed to accumulate before each station.
It is assumed that the system is observed only at discrete points in time, namely, those corresponding to arrivals, service completions, and certain no change events. Customers arrive according to a Poisson process with rate (lamda). A customer who arrives and finds a full queue for station 1 will leave the system. A manager can choose from s(,k) alternative service types or stop the service for each station k whenever he observes the system. Let "a" be a certain action which is chosen by a manager. At each station k, an exponential server possesses a customer at a rate (mu)(,k)(a) if this station is not blocked.
The cost structure includes an operating cost for running each stage, where the rate of operating cost depends on the type of service. A fixed revenue is collected when all stages have been completed.
To determine the optimal control rule, we formulate the system as a discrete-time Markov decision process. The optimality criterion is the total discounted expected cost. We characterize the form of optimal value functions inductively. Applying the characteristics of optimal value functions, we present several monotonic properties of the optimal value policies. We eliminate the inefficient facilities in the optimal policies. In a set of optimal actions, the operating cost rate at each stage is an increasing convex function of the service rate. We show that an optimal action is an antitone function of a discount factor. We present the equivalent results between discrete- and continuous-time Markov decision processes over an infinite time horizon.
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