02q2sol

# 02q2sol - Massachusetts Institute of Technology

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1 Massachusetts Institute of Technology 1.203J/6.281J/13.665J/15.073J/16.76J/ESD.216J Logistical and Transportation Planning Methods Fall 2002 Quiz 2 Solutions (Larson 2002) (a) With probability 0.3, the emergency occurs on one of the two links incident to the garage location of ambulance 2. In this case, the travel distance is U(0 , 1). With probability 0.7, the emergency occurs on one of the two links not incident to the garage location of ambulance 2. In this case, the travel distance is U(1 , 2). Accordingly, as shown in Figure 1, the conditional pdf of the travel distance for ambulance 2 to travel to the scene of the emergency incident is f D ( d )= 0 . 3 ,d [0 , 1) 0 . 7 [1 , 2] f D (d) 0.7 0.3 2 1 0 d Figure 1: Conditional pdf of Travel Distance (b) The state transition diagram for this system is shown in Figure 2, where ﬁrst component of the state indicates whether ambulance 2 is busy and the second component indicates whether ambulance 1 is busy. We can thus write the following balance equations. Page 1 of 6

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Massachusetts Institute of Technology 1.203J/6.281J/13.665J/15.073J/16.76J/ESD.216J Logistical and Transportation Planning Methods Fall 2002 1 0.7 1 1 1 0,1 0,0 1,1 1,0 1 0.3 1 Figure 2: State Transition Diagram P 0 , 0 (0 .
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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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02q2sol - Massachusetts Institute of Technology

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