Pasquist Water Company (PWC) operates a 24-hour facil-ity designed to efficiently fill water-hauling tanker trucks.Trucks arrive randomly to the facility and wait in line to ac-cess a wellhead pump. Since trucks vary in size and the filling operation is manually performed by the truck driver, the timeto fill a truck is also random.a. If the manager of PWC uses the multiple-server modelto calculate the operating characteristics of the facility’swaiting line, list three assumptions she must make regard-ing the behavior of waiting trucks and the truck arrivalprocess.b. Suppose an average of 336 trucks arrive each day, thereare four wellhead pumps, and each pump can serve anaverage of four trucks per hour.▪ What is the probability that exactly 10 trucks will arrivebetween 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 well-head, the filling time will be less than 15 minutes?c. Contrast and comment on the performance differencesbetween:▪ One waiting line feeding all four stations.▪ One waiting line feeding two wellhead pumps and asecond waiting line feeding two other wellhead pumps.Assume that drivers cannot see each line and mustchoose randomly between them. Further, assume thatonce a choice is made, the driver cannot back out of theline.
Pasquist Water Company (PWC) operates a 24-hour facil-
ity designed to efficiently fill water-hauling tanker trucks.
Trucks arrive randomly to the facility and wait in line to ac-
cess 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 regard-
ing 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 well-
head, 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.
Step by step
Solved in 3 steps
