My Math Forum

My Math Forum (
-   Advanced Statistics (
-   -   A quick help needed in Markov chain (

power3173 March 11th, 2015 06:37 AM

A quick help needed in Markov chain
I found the Q matrix, and I know that I will solve pi*Q=0. But I have difficulty for the second part, to find the probability Poo

The question is below:

A mail order company receives orders via an automated telephone answering service. The orders arrive according to a Poisson process with intensity λ>0. The answering machine is emptied at time points that form another Poisson process, which is independent of the arrivals and has intensity µ > 0, after which all received orders on the
answering machine are immediately treated. It is assumed that new calls can arrive immediately upon emptying the answering machine and that there are no orders waiting for service at time t = 0.

a) Find the unique stationary distribution for the number of customer orders on the answering machine.
b) Show that the probability that the answering machine is empty at time t ≥ 0 is given by (P_zero_zero_t)
Poo(t)=(µ / (λ+µ)) + (λ / (λ+µ))*e^-(λ+µ)t

All times are GMT -8. The time now is 12:54 PM.

Copyright © 2019 My Math Forum. All rights reserved.