On a given day, 425 veh/h arrive at a tollbooth located at the end of an off-ramp of a rural expressway. If the vehicles can be serviced by only a single channel at the service rate of 625 veh/h, determine (a) the percentage of time the operator of the tollbooth will be free, (b) the average number of vehicles in the system, and (c) the average waiting time for the vehicles that wait. (Assume Poisson arrival and negative exponential service time.)

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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On a given day, 425 veh/h arrive at a tollbooth located at the end of an off-ramp of a rural expressway. If
the vehicles can be serviced by only a single channel at the service rate of 625 veh/h, determine (a) the
percentage of time the operator of the tollbooth will be free, (b) the average number of vehicles in the
system, and (c) the average waiting time for the vehicles that wait. (Assume Poisson arrival and negative
exponential service time.)

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