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.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 4
Vehicles begin to arrive at a border gate at 06h50 with a deterministic arrival
rate of λ (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 μµ(t)
=3.3 + 2.4t (with t in minutes after 07h00 and u 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.
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