Since this is a geometric series convergence

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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,...
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