Pasquist Water Company (PWC) operates a 24-hour facility designed to efficiently fill water-hauling tanker trucks. Trucks arrive randomly to the facility and wait in line to access a wellhead pump. Since trucks vary in size and the filling operation is manually performed by the truck driver, the time to fill a truck is also random. a. If the manager of PWC uses the "multiple-server model" to calculate the operating characteristics of the facility's waiting line, list three assumptions she must make regarding the behavior of waiting trucks and the truck arrival process. (Check all assumptions that apply.) A. Trucks don't balk B. Trucks arrive according to a Poisson process C. Trucks wait until being served D. Trucks might renege O E. Trucks might balk O F. First-come, last-served basis b. Suppose an average of 288 trucks arrive each day, there are four wellhead pumps, and each pump can serve an average of 4 trucks per hour. o What is the probability that exactly 10 trucks will arrive between 2:00 p.m. and 4:00 p.m. on any given day? o How likely is it that once a truck is in position at a wellhead, the filling time will be less than 15 minutes? The probablity that 10 trucks will arrive between 2:00 p.m. and 4:00 p.m. is %. (Enter your response rounded to two decimal places.)
Pasquist Water Company (PWC) operates a 24-hour facility designed to efficiently fill water-hauling tanker trucks. Trucks arrive randomly to the facility and wait in line to access a wellhead pump. Since trucks vary in size and the filling operation is manually performed by the truck driver, the time to fill a truck is also random. a. If the manager of PWC uses the "multiple-server model" to calculate the operating characteristics of the facility's waiting line, list three assumptions she must make regarding the behavior of waiting trucks and the truck arrival process. (Check all assumptions that apply.) A. Trucks don't balk B. Trucks arrive according to a Poisson process C. Trucks wait until being served D. Trucks might renege O E. Trucks might balk O F. First-come, last-served basis b. Suppose an average of 288 trucks arrive each day, there are four wellhead pumps, and each pump can serve an average of 4 trucks per hour. o What is the probability that exactly 10 trucks will arrive between 2:00 p.m. and 4:00 p.m. on any given day? o How likely is it that once a truck is in position at a wellhead, the filling time will be less than 15 minutes? The probablity that 10 trucks will arrive between 2:00 p.m. and 4:00 p.m. is %. (Enter your response rounded to two decimal places.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Pasquist Water Company (PWC) operates a 24-hour facility designed to efficiently fill water-hauling tanker trucks.
Trucks arrive randomly to the facility and wait in line to access a wellhead pump. Since trucks vary in size and the
filling operation is manually performed by the truck driver, the time to fill a truck is also random.
a. If the manager of PWC uses the "multiple-server model" to calculate the operating characteristics of the facility's
waiting line, list three assumptions she must make regarding the behavior of waiting trucks and the truck arrival
process. (Check all assumptions that apply.)
A. Trucks don't balk
B. Trucks arrive according to a Poisson process
C. Trucks wait until being served
D. Trucks might renege
E. Trucks might balk
F. First-come, last-served basis
b. Suppose an average of 288 trucks arrive each day, there are four wellhead pumps, and each pump can serve an
average of 4 trucks per hour.
o What is the probability that exactly 10 trucks will arrive between 2:00 p.m. and 4:00 p.m. on any given day?
o How likely is it that once a truck is in position at a wellhead, the filling time will be less than 15 minutes?
The probablity that 10 trucks will arrive between 2:00 p.m. and 4:00 p.m. is %. (Enter your response rounded to
two decimal places.)
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