Question

Given: Vehicles begin to arrive at a park entrance at 7:45 A.M. at a constant rate...

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?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Queuing at Amusement Park Vehicle Entrance: Vehicles begin arriving at an amusement park one hour before...
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 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...
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...
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?   
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...
Vehicles arrive in a single approach for two consecutive cycles at a signalized intersection. The signal...
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...
Autos arrive at a toll plaza located at the entrance to a bridge at a rate...
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...
Autos arrive at a toll plaza located at the entrance to a bridge at a rate...
Autos arrive at a toll plaza located at the entrance to a bridge at a rate of 20 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 1 second​(0.0167 minute)? c. What are the answers to​ (a) and​ (b) if the rate of...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT