M/G/1 Subject to an Initial Quorum of Customers.
Abstract
The model M/G/1 is modified in the following manner. The server is idled when he runs out of customers and resumes serving when the (m+1)st customers arrives, where m > or = 0; m+1 is referred to as the 'initial quorum' and m is the maximal queue size (and system size) while the server idles or vacations. The modified model is designated as M/G/A(m). When m=0 we have the regular M/G/1. In Section 1 we derive the omni-equations for the backlog process B (equation (1.17) and for the delay process w (equation (1.24)) by exploiting the simple relation between B and w in M/G/1(m), a relation which results in equation (1.12). In Section 2 we derive several composition properties for the backlog and for the delay. In particular, equation (2.8) says that the backlog is distributed like the sum of the backlog in M/G/1 and of a random variable which depends on the service time; and equation (2.9) says that the delay is distributed like the sum of the delay in M/G/1 and of a random variable which depends on the service time and on the interarrival time. Keywords: Computer networks; Local area networks; Queueing models. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1986
- Accession Number
- ADA175125
Entities
People
- Martin Krakowski
Organizations
- George Mason University