The state operates a weigh station for trucks traveling on the highway. Every truck must pull off the highway, enter the weigh station, and undergo state inspection procedures before counting on. Trucks arrive at this station at a poisson rate of seven per hour. The time to inspect/weigh a truck varies, having an exponential probability density with a mean of 7 minutes. A. How many trucks are detained at the station on the average? B. How long can a truck expect to be detained? C. How many trucks are lined up in front of the station on the average? D. How long on the average does a truck driver have to wait in line for the truck to beinspected?
The state operates a weigh station for trucks traveling on the highway. Every truck must pull off the highway, enter the weigh station, and undergo state inspection procedures before counting on. Trucks arrive at this station at a poisson rate of seven per hour. The time to inspect/weigh a truck varies, having an exponential probability density with a mean of 7 minutes. A. How many trucks are detained at the station on the average? B. How long can a truck expect to be detained? C. How many trucks are lined up in front of the station on the average? D. How long on the average does a truck driver have to wait in line for the truck to beinspected?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 9P
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The state operates a weigh station for trucks traveling on the highway. Every truck must pull off the highway, enter the weigh station, and undergo state inspection procedures before counting on. Trucks arrive at this station at a poisson rate of seven per hour. The time to inspect/weigh a truck varies, having an exponential probability density with a mean of 7 minutes.
A. How many trucks are detained at the station on the average?
B. How long can a truck expect to be detained?
C. How many trucks are lined up in front of the station on the average?
D. How long on the average does a truck driver have to wait in line for the truck to beinspected?
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