Question

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 of µ(t) = 7 + 0.2t (with µ(t) in veh/min and t in min after 6:30 AM). Assuming D/D/1 queuing, determine the following queue characteristics,

1. Time of queue dissipation

2. Average delay

Answer #1

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?

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...

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
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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
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Toll processing rate (vehicle departure...

At the signalized intersection, the vehicles began to arrive
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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....

An approach to a signalized intersection has a saturation flow
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6 vehicles in queue and vehicles arrive at 900 veh/h. The signal
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A four-lane freeway (two lanes in each direction) has the
arrival flow rate of λ(t)=40-0.15t (with t in minutes and λ(t) in
vehicles per minute). At 7 am, an accident occurred in the
northbound and blocked both lanes. Twenty minutes later, one lane
was opened. At 7:40 am the accident was cleared and both lanes were
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When did...

Vehicles arrive at a small bridge according to a Poisson process
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What is the probability of 0 cars arriving during a 4 second
interval? c. A pedestrian arrives at a crossing point just after a
car passed by. If the pedestrian needs 4 sec to cross the street,
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