Omni Transforms: Applications to Renewal Theory.
Abstract
The theory of the renewal process has an important bearing on the single server queue, especially on the model M/G/1 (although some results are obtained for G/G/1 also). Since a renewal process can be viewed as a single-server saturated system (i.e., a system whose source keeps the server perpetually busy) this affinity is not surprising. Moreover, in deriving some results for the renewal process we gain insight into the use of the conservation method, based on the application of ergodic variables and of the so-called omni-transform, to the treatment of single-server queues. The renewal process adds insight into the theory of mixtures of random variables and of omni-forms (i.e., linear functions of omni-transforms). It allows to convert, when possible in principle, an omni-equation involving derivatives into an omni-equation without derivatives, an equation which is a statement about a mixture of distributions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1984
- Accession Number
- ADA146939
Entities
People
- Charles Thomas Harris
- M. Krakowski
Organizations
- University of Virginia