Question

Vehicles arrive at an entrance to a stadium. There is a single gate (at which all vehicles must stop), where a stadium attendant collects a parking fee. There are 20 vehicles waiting in a queue at the stadium gate when it opens at 7:00 PM, at which time vehicles arrive at a rate of 240 veh/h. If the time required to collect a parking fee is 12 seconds and assuming D/D/1 queuing, (1) What time does the queue dissipate and (2) what is the total delay from 7:00 PM to the time queue dissipates

Answer #1

Queuing at Amusement Park Vehicle Entrance: Vehicles begin
arriving at an amusement park one hour before the park opens, at a
rate of 3 vehicles per min (assume D/D/1). The gate to the parking
lot opens 30 minutes before the park opens. If the total delay to
vehicles entering the parking lot is 4,056 vehicle-minutes,
A. How long after the first vehicle arrival will the queue
dissipate?
B. What is the average service rate at the parking lot gate?

Given: Vehicles begin
to arrive at a park entrance at 7:45 A.M. at a constant rate of six
per minute and at a constant rate of four vehicles per minute from
8:00 A.M. on. The park opens at 8:00 A.M. and the manager wants to
set the departure rate so that the average delay per vehicle is no
greater than 9 minutes (measured from the time of the first arrival
until the queue clears).
Find: Assuming D/D/1 queuing, what is...

At the signalized intersection, the vehicles began to arrive
from 7:00 am (beginning of the traffic study) at the rate of 6
veh/min for 20 minutes, and declined to 1 veh/min. The traffic
signal is assumed to have an effective red and green only starting
from red at 7:00 am. The length of the effective green is 4 minutes
and effective red time is 3 minutes per cycle. The discharge rate
of the vehicles on effective green is 6 veh/minute....

Trucks begin to arrive at a weigh station (with a single scale)
at 6:00 AM at a rate of λ(t) = 4.0 – 0.25t (t in minutes and λ(t)
in vehicles per minute). The time to weigh each truck is constant
30 seconds. Draw the queuing diagram and determine the
following.
a) The time when the queue that formed will be cleared
b) Maximum queue
c) The average delay per truck

Vehicles arrive at a toll booth starting at 6 AM at the rate of
λ(t) = 5 - 0.05t with λ(t) in veh/min and t in minutes after 6 AM.
The first operator processes cars at a rate of 3.5 veh/min from 6
AM until 6:15 AM when the person leaves because of illness. From
6:15 AM to 6:30 AM, no one is at the toll booth but a new operator
arrives at 6:30 AM and processes at the rate...

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