Vehicles arrive at a toll system at random at an average rate of 12 vehicles per minute. If there are 2 toll booths each at random at an average of 6 seconds after services are done for every vehicle at the toll system. Calculate the following: 1 Average length of queue of vehicles 2. Average waiting time in a queue 3. Average time spent in a queue
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- Vehicles arrive at a toll system at random at an average rate of 15 vehicles per minute. If there are 2 toll booths each at random at an average of 6 seconds after services are done for every vehicle at the toll system. Calculate the following:1.1 Average length of queue of vehicles1.2. Average waiting time in a queue1.3. Average time spent in a queue1.4. If one toll ticket booth is closed and service time is reduced by 4 seconds, what are the queuing characteristics of the system? And plot the arrival distribution curve for this traffic conditionVehicles arrive at a toll system at random at an average rate of 15 vehicles per minute. If there are 2 toll booths each at random at an average of 6 seconds after services are done for every vehicle at the toll system. Calculate the following: 5.1 Average length of queue of vehicles5.2. Average waiting time in a queue5.3. Average time spent in a queue5.4. If one toll ticket booth is closed and service time is reduced by 4 seconds, what are the system’s Q, W and T? And plot the arrival distribution curve for this traffic conditionA theme park has a single entrance gate where visitors must stop and pay for parking. The average arrival rate during the peak hour is 150 veh/h and is Poisson distributed. It takes, on average, 18 seconds per vehicle (exponentially distributed) to pay for parking. What is the average time in the system for this queuing system in minutes/veh? Answer in one-decimal place
- A toll bridge carries 10,000 veh/day. The current toll is ₱150/vehicle. Studies shown that for eachincrease in toll of ₱25, the traffic volume will decrease by 1000 veh/day. It is desired to increasethe toll to a point where revenue will be maximized.a. Write the expression for travel demand on the bridge related to toll increase and currentvolume. b. Determine the toll charge to maximize revenues. c. Determine traffic in veh/day after toll increase. d. Determine the total revenue increase with new toll.At the exit of a toll gate with a single booth, vehicles arrive at random at a rate of 20 vehicles per minute. The service has an average rate of 22 vehicles per minute. However, due to variable toll fees, the service is also random with an average rate of 22 vehicles per minute.Estimate average time vehicles spent in the systemGroup of answer choices0.400.500.450.35A toll bridge carries 10,000 veh/day. The current toll is $3.00/vehicle. Studies have shown that for each increase in toll of 50 cents, the traffic volume will decrease by 1000 veh/day. It is desired to increase the toll to a point where revenue will be maximized. Let V be the Volume X be the increase in toll charge (a) Write the expression for travel demand on the bridge related to toll increase and current volume. (b) Determine the increase in toll charge (c) Determine the new toll charge to maximize revenues. (d) Determine traffic in veh/day after toll increase. (e) Determine total revenue increase with new toll.
- A theme park has a single entrance gate where visitors must stop and pay for parking. The average arrival rate during the peak hour is 150 veh/h and is Poisson distributed. It takes, on average, 20 seconds per vehicle (exponentially distributed) to pay for parking. What is the average waiting time for this queuing system in minute/vehicle? Answer in two-decimal placesA toll bridge carries 5000 veh/day. the current tol is 50 cents. When the toll is increased by P0. 25. Traffic volume decreases by 5000 veh/day. Det. the additional amount of toll that should be charged such that the revenue is maximized.Vehicles leave an airport parking facility (arrive at parking fee collection booths) at a rate of 500 veh/h (the time between arrivals is exponentially distributed). The parking facility has a policy that the average time a patron spends in a queue waiting to pay for parking isnot to exceed 5 seconds. If the time required to pay for parking is exponentially distributed with a mean of 15 seconds, what is the smallest number of paymentprocessing booths that must be open to keep the average time spent in a queue below 5 seconds?
- On a certain bus terminal, there are two terminals that can travels to the south. The number of passengers going to the south arriving in the terminal is 150 persons per minute, and the number of people can ride the bus is 100 per minute. Both arrival and departure rates can be assumed to be exponentially distributed. What is the probability having 0 ppassengers in the queue? a. 0.143b. 0.375c. 0.209d. 0.182Note: Read the question carefully and give me BOTH right solutions with clear calculations. Vehicles begin to arrive at a toll booth at 5 vehicles per minute from 7 AM to 8 AM. The booth opens at 7:15 AM and services at a rate of 3 vehicles per minute until 7:45 AM. From 7:45 AM until 8 AM the service rate is 6 vehicles per minute. Assuming D/D/1 queuing, (A) have all vehicles that arrived between 7AM and 8AM exited the queue? and (B) what is the total vehicle delay while the queue exists?At the exit of a toll gate with a single booth, vehicles arrive at random at a rate of 20 vehicles per minute. The service has an average rate of 22 vehicles per minute. However, due to variable toll fees, the service is also random with an average rate of 22 vehicles per minute. Estimate average length of queue formed at the toll gate Group of answer choices 7.09 8.09 9.09 6.09