# Etn 1np so if p 1 n x etn 1mp p1 m1 this implies

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ther examples: Example 4.3. M/M/s queue. Imagine a bank with s 1 tellers that serve customers who queue in a single line if all of the servers are busy. We imagine that customers arrive at times of a Poisson process with rate , and that each service time is an independent exponential with rate µ. As in Example 4.2, q (n, n + 1) = . To model the departures we let ( nµ 0 n s q (n, n 1) = sµ n s To explain this, we note that when there are n s individuals in the system then they are all being served and departures occur at rate nµ. When n > s, all s servers are busy and departures occur at sµ. Example 4.4. Branching proceess. In this system each individual dies at rate µ and gives birth to a new individual at rate so we have q (n, n + 1) = n q (n, n 1) = µn A very special case called the Yule process occurs when µ = 0. Having seen several examples, it is natural to ask: Given the rates, how do you construct the chain? P Let i = j 6=i q (i, j ) be the rate at which Xt leaves i. If i = 1, th...
View Full Document

## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

Ask a homework question - tutors are online