01quiz2 - Massachusetts Institute of Technology Logistical...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Massachusetts Institute of Technology Logistical and Transportation Planning Methods 1.203J/6.281J/13.665J/15.073J/16.76J/ESD.216J Quiz #2 OPEN BOOK December 5, 2001 Please do Problems 2 and 3 in a booklet separate from Problem 1. Remember to put your name on each booklet! And please explain all of your work! We like to give deserved partial credit. Good luck!
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Problem #1. Two Server Hypercube Problem (50 points) Consider a 1-mile-by-2-mile homogeneous service region served by two mobile patrolling servers as shown in Figure 1. Here are the assumptions of the model: 1. Customer locations are uniformly independently located over the entire rectangular service region. 2. Over time, customers arrive as a homogeneous Poisson process at aggregate rate =2 customers per hour. 3. While not busy serving customers, each server patrols its sector (sector 1 or 2, respectively). Under this circumstance, the server’s location at a random time is uniformly distributed over its sector. Each sector is a one-mile-by-one-mile square. 4. Travel distance is right-angle (“Manhattan metric”), with speed equal to 1000 mi./hr. 5. The on-scene time to serve a customer is a random variable having a negative exponential probability density function with mean equal to 30 minutes. Upon completion of service of a customer at the scene, the server resumes random patrol of his/her sector. 6. This is the dispatch strategy: For a customer from sector i ( i =1,2), dispatch server i if available. Else dispatch the other server if available; Else the customer is lost forever.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

01quiz2 - Massachusetts Institute of Technology Logistical...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online