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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. “1minute customers” and “3minute customers”
arrive randomly intermingled. There is infinite queue capacity.
(a) (20 points) Suppose that “1minute customers” are assigned nonpreemptive priority over “3
minute customers”. Find the expected waiting time (i.e., not including time spent in service) for
(i) “1minute customers”, (ii) “3minute 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 FirstCome, FirstServed (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% “1minute
customers” and 50% “3minute customers”). Suppose, as well, that “1minute customers” are
assigned nonpreemptive priority over “3minute customers”. Compute the expected waiting time
for (i) “1minute customers” and (ii) “3minute 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 nonpreemptive priority over “1minute 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.
 Fall '06
 hansman

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