Vehicles begin to arrive at a border gate at 06h50 with a deterministic arrival rate of A (t) = 5.2 - 0.01t (λ is in vehicles per minute and t in minutes after 06h50). However, the gate opens at 07h00 and serves vehicles at a rate of µ(t) =3.3 + 2.4t (with t in minutes after 07h00 and μ in vehicles per minute). Once the service rate reaches 10 vehicles per minute, it stays at that level for the rest of the day. ● ● ● Illustrate the operational characteristics of the vehicle queue-delay on a (cumulative) vehicle-Time graph. When will the queue that forms be dissipated? What will be the maximum queue length? Determine the total delay.

Vehicles begin to arrive at a border gate at 06h50 with a deterministic arrival rate of A (t) = 5.2 - 0.01t (λ is in vehicles per minute and t in minutes after 06h50). However, the gate opens at 07h00 and serves vehicles at a rate of µ(t) =3.3 + 2.4t (with t in minutes after 07h00 and μ in vehicles per minute). Once the service rate reaches 10 vehicles per minute, it stays at that level for the rest of the day. ● ● ● Illustrate the operational characteristics of the vehicle queue-delay on a (cumulative) vehicle-Time graph. When will the queue that forms be dissipated? What will be the maximum queue length? Determine the total delay.

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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