03quiz2 - 1.203J/6.281J/15.073J/16.76J Logistical and Transportation Planning Methods Massachusetts Institute of Technology Quiz 2 December 3 2003

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______________________________________________________________________ 1.203J/6.281J/15.073J/16.76J Logistical and Transportation Planning Methods Massachusetts Institute of Technology Quiz 2 December 3, 2003 1. Total time allotted is 90 minutes. 2. Please print your name clearly on each page you turn in. 3. Please answer each problem on a separate page Problem 1 (32 points) At a facility with a single server, customers arrive in a Poisson manner at the rate of 24 per hour. Exactly 50% of the customers require a service that takes exactly 1 minute, while the other 50% require service that takes exactly 3 minutes. “1-minute customers” and “3-minute customers” arrive randomly intermingled. There is infinite queue capacity. (a) (20 points) Suppose that “1-minute customers” are assigned non-preemptive priority over “3- minute customers”. Find the expected waiting time (i.e., not including time spent in service) for (i) “1-minute customers”, (ii) “3-minute customers” and (iii) a randomly selected customer. Furthermore, (iv) compare your answer to (iii) with the expected waiting time of a random customer, if all customers were served in a First-Come, First-Served (FCFS) order at the facility, irrespective of the length of their service time. Finally, (v) explain in a couple of sentences why the relationship (greater than, less than, equal) between your answers to (iii) and (iv) is what it is. [NUMERICAL ANSWERS ARE EXPECTED FOR PARTS (i) – (iv).] (b) (9 points) Suppose now that the demand rate increases to 40 per hour (with 50% “1-minute customers” and 50% “3-minute customers”). Suppose, as well, that “1-minute customers” are assigned non-preemptive priority over “3-minute customers”. Compute the expected waiting time for (i) “1-minute customers” and (ii) “3-minute customers”. (c) (3 points) With the situation as in (b), i.e., a demand rate of 40 per hour, suppose now that “3- minute customers” are assigned non-preemptive priority over “1-minute customers”. In a few (at most) sentences, please explain what is going to happen at this facility. No math please! 1
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This note was uploaded on 11/08/2011 for the course AERO 16.72 taught by Professor Hansman during the Fall '06 term at MIT.

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03quiz2 - 1.203J/6.281J/15.073J/16.76J Logistical and Transportation Planning Methods Massachusetts Institute of Technology Quiz 2 December 3 2003

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