Optimal Control of a Single-Server Queue with Balking and Reneging.
Abstract
Models are developed for intermittent operation of the service facility in a single-server queue with Poisson arrivals and general service-time distribution. When the server is inoperative for periods of time, customer losses from the queue by halting and reneging can be significant. To account for this effect, provisions for balking and reneging are included in the models. Balking is handled by a simple modification of the arrival rate parameters. Reneging, which is allowed only when the server is shut down, is characterized by a Poisson process whose rate is dependent on the number of customers in the queue. Two models are considered for the reneging process: the occurrence of the reneging event results in the loss of either all the customers in the queue (model I) or a single customer (model II). A number of applications for these models are discussed. A reward structure is specified and stationary optimal policies are found which maximize the expected discounted reward over an infinite horizon. The optimal policies have a simple critical-number characterization in terms of the number of customers in the queue. Algorithms for computing the critical numbers are described. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 16, 1970
- Accession Number
- AD0714802
Entities
People
- Joseph D. Blackburn
Organizations
- Stanford University