Vehiclesfor CoVid-19arriving atthe multi-level parking space started collecting parking fees at 07:003.starttheentrance of The Galeónat06:3 amvaccination; however,am. The deterministic arrival rate of vehicles is given as a function of time,a(t) = 18 – 0.3tOn the other hand, the service rate - which includes receiving the fee and giving back thechange - was deterministically modeled as a function of time,u(t) = 3 + 0.74t= time, minutesarrival rate, vph= departure rate, vphWhereA(t)u(t)Considering only one park attendant, determine:The time the queue will dissipate,Assuming a vehicle entered the system (started to queue up) at 07:02 am, how long did ittake this to be served?a.b.C.The average delay in the system in vehicles per minute.

procedure: first, find the departure rate Make a table column and find the arrivals and departures…

Answered: Vehicles start arriving at the entrance…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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The arrival rate at a parking lot is 6 veh/ min. Vehicles start arriving at 6:00 P. M., and when the queue reaches 36 vehicles, service begins. If company policy is that total vehicle delay should be equal to 540 veh-min, what is the service rate? (Assume D/ D/ 1 queuing and a constant service rate.)
At 10 am, vehicles arrive at a toll booth facility at the rate of 480vehicles/hour. Initially, the toll booth is closed from 10:00 am until 10:15 am. Then it opens from 10:15with a service rate of 6 seconds per vehicle. Assuming D/D/1 queuing, determine:(1) At what time queue disappears? (2) What is the total delay? (3) What is the maximum Queuelength? (4) What is the queue length at 10:00 am? (5) What is maximum delay? (6) What is thedelay for the 140th and 170th vehicle?
The average queue length at the intersection of the two roads with a stop sign is 4 vehicles. If the arrival rate of vehicles at the stop sign is 300 veh/hr, determine the service rate of the road in veh/hr. Assume both arrival and departure rates are exponentially distributed.
7. The following table shows traffic flow data collected at the main road in an urban area, in two successive days during the peak period Day one Flow (veh) Day two Time Flow (veh) 7:30 – 7:45 7:45 – 8:00 900 950 960 8:00 – 8:15 1010 1015 8:15 – 8:30 990 980 (a) Determine the peak hour factor (PHF) (b) Estimate the missing traffic flow count (x) on day two.
At exactly 8:00 AM, vehicles start to enter a single toll gate at a rate of 8 veh/min following a deterministic distribution. Due to the teller being late, the toll booth opened at 8:10 AM having a service rate of 10 veh/min following a deterministic distribution. What is the Maximum Queue Length in the system? What is the longest waiting time in the system?
Question 5 A shopping centre has two types of checkouts, traditional checkouts which are staffed by cashiers, and which are usually preferred by older customers, and self- serve checkouts which are preferred by younger customers. One day, it was recorded that an average of 20 older people an hour left the staffed checkouts and approximately 1 young person every two minutes began queuing for the self- checkout machines. If both checkout methods have an average wait time of 5 minutes per person, what is the arrival rate for the traditional checkouts and the departure rate for the self-checkouts? O A 20 people/hr; µ = 19 people/hr A 19 people/hr; μ = 20 people/hr λ = 13 people/hr; μ = 39 people/hr λ = 39 people/hr; μ 13 people/hr
Question 4 Vehicles begin to arrive at a border gate at 06h50 with a deterministic arrival rate of λ (t) = 5.2 - 0.01t (λ is in vehicles per minute and t in minutes after 06h50). However, the gate opens at 07h00 and serves vehicles at a rate of μµ(t) =3.3 + 2.4t (with t in minutes after 07h00 and u in vehicles per minute). Once the service rate reaches 10 vehicles per minute, it stays at that level for the rest of the day. ● ● Illustrate the operational characteristics of the vehicle queue-delay on a (cumulative) vehicle-Time graph. When will the queue that forms be dissipated? What will be the maximum queue length? Determine the total delay.
A toll booth on a temple is open from 8:00 AM to 12 midnight. Vehicles start arriving at 7:45 AM at a uniform deterministic rate of six per minute until 8:15 AM and from then on at two per minute. If vehicles are processed at a uniform deterministic rate of six per minute, determine the (a) time of queue dissipation in minutes (b) total number of vehicles in queue and (c) total vehicle delay
Vehicles arrive at a recreational park booth at a uniform deterministic rate of 4 veh/min. If uniform deterministic processing of vehicles (collecting fees) begins 30 minutes after the first arrival and the total delay is 3600 veh-min, how long after the arrival of the first vehicle will it take the queue to dissipate?
Drivers arrive at a toll booth at a rate of 5 per minute during peak traffic periods. The time between consecutive driver arrivals follows an exponential distribution. What is the probability that it will take a) more one minute between consecutive drivers? b) between 30 seconds and 90 seconds between consecutive drivers?
13. An incident that occurs on a particular highway results in traffic incurring an average delay of one hour per vehicle. An estimated 2,000 vehicles are impacted by the incident. If the distribution of traffic is comprised of 5% five-axle trucks, 2% three-axle trucks, 4% six-tire trucks, 2% four-tire trucks, 4% medium auto for business purposes, 3% small auto for business purposes, and the remainder are automobiles for personal purposes, what is the value of the total delay incurred by the traffic.

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