Question

Vehicles arrive at a toll booth starting at 6 AM at the rate of λ(t) =...

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

Engineering   Civil-Engineering   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Vehicles arrive at a freeway on-ramp meter at a constant rate of six per minute starting...
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...
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...
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...
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...
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...
An approach to a signalized intersection has a saturation flow rate of 1800 veh/h. At the...
An approach to a signalized intersection has a saturation flow rate of 1800 veh/h. At the beginning of an effective red, there are 6 vehicles in queue and vehicles arrive at 900 veh/h. The signal has a 60-second cycle with 25 seconds of effective red. What is the total vehicle delay after one cycle? What is the maximum length of queuing within this cycle? (assumeD/D/1 queuing)
A four-lane freeway (two lanes in each direction) has the arrival flow rate of λ(t)=40-0.15t (with...
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 opened. The capacity of the highway is 2,200 vehicles per hour per lane if not impacted by an accident. (Assuming D/D/1 queuing). When did...
Vehicles arrive at a small bridge according to a Poisson process with arrival rate l =...
Vehicles arrive at a small bridge according to a Poisson process with arrival rate l = 900 veh/hr. a. What are the mean and the variance of the number of arrivals during a 30 minutes interval? b. 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, what is the probability that a...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT