Homework 8

Homework 8 - rate λ . Suppose that whether or not a newly...

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

View Full Document Right Arrow Icon
ORIE3510 Introduction to Engineering Stochastic Processes Spring 2010 Homework 8: Continuous Time Markov Chains Due 2:30pm, ( Friday! ) April 9, 2010 (drop box) In all questions, be sure to give the justification for your answers. There is one problem worth 100 points. This is a short assignment, and you have until April 9 to turn it in. However, on Wednesday April 7, we will post homework 9 which will be of the usual length. Make sure you budget your time accordingly! Problem 1 Consider a single-pump gas station to which customers arrive according to a Poisson process with
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: rate λ . Suppose that whether or not a newly arriving customer joins the queue is determined randomly, according to the following scheme: Pr[New customer joins queue | n customers already in system] = 1 n + 1 . Hence, a new customer will not join the system with probability n n +1 . If the pump service time is exponential with rate μ , show that the limiting distribution of the number of customers at the gas station is Poisson distributed with rate λ μ ....
View Full Document

This note was uploaded on 10/29/2011 for the course ORIE 3510 taught by Professor Resnik during the Spring '09 term at Cornell.

Ask a homework question - tutors are online