Talk:Birth-death process

From Wikipedia, the free encyclopedia

[edit] Infinite Calling Population Assumption

The article says "In queueing theory the birth-death process is the most fundamental example of a queueing model, the M/M/C/K/\infty/FIF0". Why is it that the calling population must be infinite? It seems that a finite calling population would be easy to model with a birth-death process since the μ,λ parameters can depend on the number of customers in the queue, which is easily related to the number of customers not in the queue when the population is finite. A5 15:24, 1 June 2007 (UTC)

If you have a finite calling population, rather than infinite one, you can have constant parameters μ,λ for all levels of the queue, but the blocking probability changes. Have a look at Erlang unit, there is a parameter A = λ / μ which is constant reguardless of the number of queueing customers, however the blocking probability changes for the infinite population (Erlang C formula) in the finite case (Engset formula), this make it computationally simpler then having to place a weight on λ as the queue increases. Aiden Fisher 06:12, 5 June 2007 (UTC)