MULTI-QUEUES WITH CHANGEOVER TIMES.
Abstract
The problem of a queuing system with changeover times is studied to determine the effect of the queue discipline. Several specific disciplines for the two-line case are investigated and compared. The alternating priority and strict priority disciplines are investigated for the general two-line system. A class of disciplines are analyzed for the two-line system with zero changeover times. For alternating priority, the mean waiting times are obtained and it is shown how higher moments may be derived. For each of the other disciplines, explicit expressions for the Laplace-Steiltjes transforms of the waiting time distributions are obtained and the means of these distributions are computed. The non-saturation condition and several other measures of performance are found in each case. The technique used throughout is the application of generating functions to the 'imbedded' process formed at the instants of service-completion. In an appendix the mean waiting time of an arbitrary customer is obtained for a specialized K-line system. The mean waiting times for various disciplines are compared for a specific system. It is observed that disciplines which increase the idle time do not necessarily decrease the waiting time, and in fact, might cause the waiting time to increase. It is shown that disciplines which are potentially optimum can be classified in a general way. The specific disciplines studied are found to fall into this classification. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1968
- Accession Number
- AD0669628
Entities
People
- Martin Eisenberg
Organizations
- Massachusetts Institute of Technology