06quiz2

# 06quiz2 - Logistical and Transportation Planning Methods...

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1 Logistical and Transportation Planning Methods 1.203J/6.281J/15.073J/16.76J/ESD.216J Massachusetts Institute of Technology Cambridge, Massachusetts Quiz #2 December 11, 2006 OPEN BOOK TWO HOURS 5 PAGES, 3 PROBLEMS PLEASE SHOW ALL YOUR WORK! INSPIRATIONAL QUOTE: “It’s tough to make predictions, especially about the future.” Yogi Berra, once a baseball catcher for the New York Yankees

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2 Problem 1 (35 points) Consider a single-server queueing system which operates as follows: 1. There are two types of customers, Type 1 and Type 2, each type arriving at the system in a Poisson manner at rates ! " and ! \$ respectively. 2. Customers of type 1 have negative exponential service times with expected value of 1/ % " per service time. Similarly, customers of type 2 have negative exponential service times with expected value of 1/ % \$ per service time. Successive service times are mutually independent. 3. The queueing system has a total capacity of three customers, including the one receiving service. In other words, whenever there are three customers in the system (the one receiving service and two waiting) any additional arriving customers are rejected and go elsewhere. 4. The next customer to be processed by the server is selected in the following way: If, after the completion of a service, there is no other customer waiting, then the next customer to arrive at the system, no matter of what type, obtains access to the server. If, after the completion of a service, there is at least one customer waiting, then customers (if any) of the same type as the customer who just completed service receive priority over the other type. If no customers of the same type are waiting, then a customer of the other type, if any is/are waiting, is admitted for service. Customers of each type are served in a
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06quiz2 - Logistical and Transportation Planning Methods...

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