Vehicles leave an airport parking facility (arrive at parking fee collection booths) at a rate of 400 veh/h (the time between arrivals is exponentially distributed). The parking facility has a policy that the average time a patron spends in a queue waiting to pay for parking is not to exceed 3 seconds. If the time required to pay for parking is exponentially distributed with a mean of 12 seconds, what is the smallest number of payment processing booths that must be open to keep the average time spent in a queue below 3 seconds?

Vehicles leave an airport parking facility (arrive at parking fee collection booths) at a rate of 400 veh/h (the time between arrivals is exponentially distributed). The parking facility has a policy that the average time a patron spends in a queue waiting to pay for parking is not to exceed 3 seconds. If the time required to pay for parking is exponentially distributed with a mean of 12 seconds, what is the smallest number of payment processing booths that must be open to keep the average time spent in a queue below 3 seconds?

Traffic and Highway Engineering

5th Edition

ISBN:9781305156241

Author:Garber, Nicholas J.

Publisher:Garber, Nicholas J.

Chapter6: Fundamental Principles Of Traffic Flow

Section: Chapter Questions

Problem 26P: The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to bePoisson...

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Quantity takeoff

Quantity takeoffs (QTO) are precise estimates of the materials and labor costs required to finish a construction project. During the pre-construction phase, an estimator prepares them, breaking down the project into smaller, more manageable parts that are easier to evaluate. These measurements are used to prepare a construction scope bid. Estimators examine the drawings, specifications, and models to figure out different quantities and their costs. Since, the components, their quantity, and price are all included in the model, quantity take-off can be done automatically using Building Information Modelling (BIM). The time taken for completing a construction project can be reduced by the use of quantity takeoff. These takeoffs are also called material takeoffs and construction takeoffs.

Question

Vehicles leave an airport parking facility (arrive at parking fee collection booths) at a rate of 400 veh/h (the time between arrivals is
exponentially distributed). The parking facility has a policy that the average time a patron spends in a queue waiting to pay for parking is not
to exceed 3 seconds. If the time required to pay for parking is exponentially distributed with a mean of 12 seconds, what is the smallest
number of payment processing booths that must be open to keep the average time spent in a queue below 3 seconds?

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