01quiz2 - Massachusetts Institute of Technology Logistical...

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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!
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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.
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01quiz2 - Massachusetts Institute of Technology Logistical...

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