Question

**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 the
minimum departure rate needed to achieve this?

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?

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...

At 8:00 A.M. there are no vehicles in queue at a toll booth and
vehicles start arriving at a rate of ?(?) = ?. ? − ?. ?? ?. From
8:00 to 8:05 A.M. no vehicles are serviced, ?(?) = ? for ? ≤ ? <
?, and beginning at 8:05 A.M. vehicles are serviced at a rate ?(?)
= ?. ? ? − ? for ? ≥ ? min (?(?) and ?(?) are in vehicles/minute
and ? is in...

Vehicles arrive at a freeway on-ramp meter at a constant rate of
six per minute starting at 6.00 A.M. Service begins at 6.00 AM such
that µ(t) = 2 + 0.4, where µ(t) is in veh/min and t is in minutes
after 6:00 A.M. What is the total delay and the maximum queue
length in vehicles?

Vehicles arrive at a freeway on-ramp meter at a constant rate of
six per minute starting at 6.00 A.M. Service begins at 6.00 AM such
that µ(t) = 2 + 0.4, where µ(t) is in veh/min and t is in minutes
after 6:00 A.M. What is the total delay and the maximum queue
length in vehicles?

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

A vehicle queue is formed at an entrance to the toll plaza due
to a malfunction of one of the toll booths. The malfunction is
corrected after 30 minutes, at which time all the toll booths are
fully operational. The following is known about the traffic and
service rate at the toll plaza:
Demand (vehicle arrival rate), constant during the entire time
= 29 veh/min
Normal toll processing rate (vehicle departure rate) = 34
veh/min
Toll processing rate (vehicle departure...

Vehicles arrive in a single approach for two consecutive cycles
at a signalized intersection. The signal has a 60 second cycle time
which consists of a 30 second green interval and a 30 second red
interval (ignore yellow interval). The arrival rates are assumed to
be constant in both cycles. The arrival rate was 1,080
vehicles/hour in the first cycle and it decreased to 720
vehicles/hour in the second cycle. Assume that all vehicles in the
queue formed on red...

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....

Autos arrive at a toll plaza located at the entrance to a bridge
at a rate of 50 per minute during the 5:00-to-6:00 P.M. hour.
Determine the following probabilities assuming that an auto has
just arrived.
a. What is the probability that the next auto will arrive within
6 seconds (0.1 minute)?
b. What is the probability that the next auto will arrive within
1second (0.0167 minute)?
c. What are the answers to (a) and (b) if the rate of...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 24 minutes ago

asked 25 minutes ago

asked 34 minutes ago

asked 34 minutes ago

asked 40 minutes ago

asked 40 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago