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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 arrive according to a Poisson process B. First-come, last-served basis C. Trucks might renege D. Trucks might balk E. Trucks don't balk F. Trucks wait until being served b. Suppose an average of 240 trucks arrive each day, there are four wellhead pumps, and each pump can serve an average of 3 trucks per hour. • What is the probability that exactly 10 trucks will arrive between 2:00 p.m. and 4:00 p.m. on any given day? • 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 two decimal places.) %. (Enter your response rounded to

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 arrive according to a Poisson process B. First-come, last-served basis C. Trucks might renege D. Trucks might balk E. Trucks don't balk F. Trucks wait until being served b. Suppose an average of 240 trucks arrive each day, there are four wellhead pumps, and each pump can serve an average of 3 trucks per hour. • What is the probability that exactly 10 trucks will arrive between 2:00 p.m. and 4:00 p.m. on any given day? • 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 two decimal places.) %. (Enter your response rounded to

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.4: Important Queueing Relationships
Problem 6P
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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 arrive according to a Poisson process B. First-come, last-served basis C. Trucks might renege D. Trucks might balk E. Trucks don't balk F. Trucks wait until being served b. Suppose an average of 240 trucks arrive each day, there are four wellhead pumps, and each pump can serve an average of 3 trucks per hour. • What is the probability that exactly 10 trucks will arrive between 2:00 p.m. and 4:00 p.m. on any given day? • 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 two decimal places.) %. (Enter your response rounded to
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 arrive according to a Poisson process B. First-come, last-served basis C. Trucks might renege D. Trucks might balk E. Trucks don't balk F. Trucks wait until being served b. Suppose an average of 240 trucks arrive each day, there are four wellhead pumps, and each pump can serve an average of 3 trucks per hour. • What is the probability that exactly 10 trucks will arrive between 2:00 p.m. and 4:00 p.m. on any given day? • 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 two decimal places.) %. (Enter your response rounded to
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