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.b. Suppose an average of 336 trucks arrive each day, there are four wellhead pumps, and each pump can serve an average of four trucks per hour.▪ What is the probability that exactly 10 trucks will arrive between 1:00 p.m. and 2:00 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?c. Contrast and comment on the performance differences between:▪ One waiting line feeding all four stations.▪ One waiting line feeding two wellhead pumps and a second waiting line feeding two other wellhead pumps.Assume that drivers cannot see each line and must choose randomly between them. Further, assume that once a choice is made, the driver cannot back out of the line.
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.
b. Suppose an average of 336 trucks arrive each day, there are four wellhead pumps, and each pump can serve an average of four trucks per hour.
▪ What is the probability that exactly 10 trucks will arrive between 1:00 p.m. and 2:00 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?
c. Contrast and comment on the performance differences between:
▪ One waiting line feeding all four stations.
▪ One waiting line feeding two wellhead pumps and a second waiting line feeding two other wellhead pumps.
Assume that drivers cannot see each line and must choose randomly between them. Further, assume that once a choice is made, the driver cannot back out of the line.
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