Since this is a geometric series convergence

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: et from (11),  j j =  0 Now, e = 1 is j = 1 2 :::   +  2 + ::: = 1: 0 1 +   P For convergence in this case, we need the condition =j 1. Since this is a geometric series, convergence condition is satisfied by the requirement that = 1. We, thus, have " 0 = 1 ,  :  j  j = 1 ,    and hence, If we write j = 1 2 ::: = =, which is known as utilization or traffic intensity, then j = 1 ,  j : The convergence condition also has a simple physical interpretation. Since = = 1, this means the average arrival rate should be less than the average service rate; if it is other way around, the system will overflow. What has the M/M/1 queue anything to do with network design and analysis? We have mentioned earlier that to get a handle on network modeling and performance, we have to have some idea about traffic. The simplest network we can think of is just a network link. So, here  would refer to the arrival rate to a network link while  will refer to the average service rate of the link with the link being one server. Specifically,...
View Full Document

This document was uploaded on 03/19/2014 for the course CS 6030 at Western Michigan.

Ask a homework question - tutors are online