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Queuing Models Based on Birth-and-Death Processes

The assumptions of the birth-and-death processes are the following :

 

(a)    Given N(t) = n, (n = 0, 1 , 2, .. . . ), the current probability distribution of the remaining time until the next arrival is exponential with parameter λn.

 

(b)   Given N(t) = n, (n = 1, 2, .... ), the current probability distribution of the remaining time until the next service completion is exponential with parameter µn.

 

(c)    Only one birth or death can occur at a time.

 

In the queueing models, arrival of a customer implies a birth and departed customer implies a death. In queueing system both arrivals and departures take place simultaneously. This makes difference from birth-and-death process. In the following queueing models mean arrival rate and mean service rate are constant.