M/G/1 with Exceptional Service and Arrival Rate
Abstract
The model M/G/1 is modified by 1) providing the pioneer customer, i. e. the customer who terminates an idle period (an initiates a busy period) with exceptional service; and 2) by allowing an exceptional arrival rate during the idle period. The regimen is FCFS and the server idles only when customers are absent. This document derives omni-equations for the delay, for the backlog, and for the queue size as found by real or virtual arrivals. The author relates these processes to the regular M/G/1 as convolutions of the delay in M/G/1 with modifying variables in the model treated. The queue size is derived from the delay by applying the Poisson operator. This paper extends the results of P.D. Welch (1964) who allowed exceptional service but not exceptional arrival rate, and who did not discuss composition relations. His solutions used Laplace transforms and generating functions. It is believed that the current treatment is simpler and more suitable for further generalizations. Introducing the exceptional arrival rate forces us to distinguish between the perception of the observer and of the customer source. Keywords: Stochastic models.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 31, 1988
- Accession Number
- ADA201369
Entities
People
- Martin Krakowski
Organizations
- George Mason University