homework10

# homework10 - ORIE 361/523 Homework 9 Instructor Mark E...

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

ORIE 361/523 – Homework 9 Instructor: Mark E. Lewis due April 16, 2008 (drop box) 1. Potential customers arrive at a a single-server station (which works at rate μ ) in accordance with a Poisson process with rate λ . However, if a customer finds n people already in the station, then he will enter the system with probability 1 / ( n +1). Find the limiting distribution of the number of customers in the system. 2. Customers arrive at a two-server station according to a Poisson process with rate λ . Upon arriving, they join a single queue. Whenever a server completes a service, the person first in line enters service. The service times of server i are exponential with rate μ i , i = 1 , 2 , where μ 1 + μ 2 > λ. An arrival finding both servers free is equally likely to go to either one. Define an appropriate CTMC for this model and find the limiting probabilities. 3. A total of N customers move about among r servers in the following manner. When a customer is served by i, he then goes to server j, j 6 = i , with probability 1 r - 1 . If the server he goes to
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern