A convenience store has four available parking spaces. The owner predicts that the duration of customer shopping (the time the customer's vehicle will occupy a parking space) is exponentially distributed with a mean of 6 minutes. The owner knows that in the busiest hour customer arrivals are exponentially distributed with a mean arrival rate of 30 customers per hour. What is the probability that a customer will not have an open parking space available when arriving at the store? Round off answer in four decimal places.
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- A ferry boat queuing lane holds 30 vehicles. If the service rate is a uniform deterministic 4 vehicles per minute and service begins when the lane reaches capacity, what is the uniform deterministic arrival rate if the queue dissipates 30 min. after vehicles begin to arrive?Vehicles are known to arrive according to a Poisson process at a specific spot on a highway. Vehicles are tallied at 20-second intervals, with 150 of these intervals being 20-second intervals. In 20 of the 150 periods, no automobiles have arrived. Estimate the number of these 150 intervals in which four automobiles arrive at the same time. Please do 3 decimal places. AsaapVehicle arrivals in an event are assumed Poisson distributed with an average arrival rate of (15.4) vehicles in every 2 minutes. What is the probability of the following: a. Exactly 14 vehicles arrive in a 2.5-minute interval. b. Less than 14 vehicles arrive in a 2.5-minute interval. c. More than 14 vehicles arrive in a 2.5-minute interval.
- 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?Vehicles arrive at the parking booth of SM City Tarlac at a rate of 250 vehicles per hour. If the attendant can process a vehicle in 12 seconds, determine the average length of the queue if both the arrivals and departures are exponentially distributed. Note: Answer must be whole number. No need to include the unit. (i.e. 2)At a specified point on a highway, vehicles are known to arrive according to a Poisson process. Vehicles are counted in 20-second intervals, and vehicle counts are taken in 120 of these time intervals. It is noted that no cars arrive in 18 of these 120 intervals. Approximate the number of these 120 intervals in which exactly three cars arrive. Wrong answers will be downvoted read question carefully
- Consider the following plot of cumulative arriving and departing vehicles at a freeway bottleneck location: Vehicles 20,000 15,000 10,000 5,000 0 0 30 60 90 120 150 180 210 240 270 300 330 360 Time (mins) Arrivals (vehs) Departures (vehs) From this plot, determine the following: A. What is the capacity of the bottleneck location? 9000 whole number, i.e. X000.) B. What is the maximum size of the queue that develops? 3250 whole number, i.e. X000.) C. What is the longest wait time that any vehicle experiences during the breakdown? to the nearest whole number, i.e. XX.) (Hint: Provide the answer as a numerical number only in units of vehicles per hour and rounded to the nearest thousand (Hint: Provide the answer as a numerical number only in units of vehicles and rounded to the nearest thousand (Hint: Provide the answer as a numerical number only in units of minutes and roundedA simple work-mode-choice model is estimated from data in a small urban area to determine the probabilities of individual travelers selecting various modes. The mode choices include automobile drive-alone (DL), automobile shared-ride (SR), and bus (B), and the utility functions are estimated as: UDL = 2.2-0.2(costp)-0.03(travel timepz) USR 0.8 – 0.2(costsR) – 0.03(travel timesR) Us = -0.2(costa)- 0.01(travel time,) where cost is in dollars and time is in minutes. Between a residential area and an industrial complex, 4000 workers (generating vehicle-based trips) depart for work during the peak hour. For all workers, the cost of driving an automobile is $6.00 with a travel time of 20 minutes, and the bus fare is $1.00 with a travel time of 25 minutes. If the shared-ride option always consists of two travelers sharing costs equally, how many workers will take each mode?The following 3 Travel Demand Forecasting models were created to estimate the number of peak-hour trips in the suburb of Croydon: T1 = 1.0 + 0.3(household size) + 0.01(household income in thousands of $) T2 = 1.5 + 0.2(household size) + 0.01(household income in thousands of $) T3 = 0.5 + 0.5(household size) + 0.01(household income in thousands of $) The suburb has a total of 3500 households with an average of 4 people per household, an average household income of $90,000 and survey data shows that it generates a total of 11,550 trips in the peak-hour. Which of the above models is the most accurate? A. T1 B. T2 C. T3 D. Can't say as 2 or more models are equally accurate.
- At a specified point on a highway, vehicles are known to arrive according to a Poissonprocess. Vehicles are counted in 30-second intervals, and vehicle counts are taken in 120 ofthese time intervals. It is noted that no cars arrive in 18 of these 120 intervals. a) Approximate the number of these 120 intervals in which exactly three cars arrive. b) Estimate the Percentage of time headways that will be 10 seconds or greater andthose that will be less than 6 seconds.At an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 1200 veh/h, and at the booth, drivers take an average of 10 seconds to pay their tolls. Both the arrival and departure rates can be assumed to be exponentially distributed. How would the average queue length, time in the system change if a fifth toll booth were opened? Queue Analysis - Numerical M/M/N - Average length of queue Ō - Average time waiting in queue - Average time spent in system A = arrival rate = 11 W= Pop-1 1 NIN (1-p/NY P/N<1.0 p+Ō_1 2 i=P+Q 2 μl = departure rate M/M/N - More Stuff 1 - Probability of having no vehicles 1 P₁ P₁ = N-10²² pN Σ + n = n! N!(1-p/N) - Probability of having n vehicles p"Po for n ≤N n! www P = P₁ = n - Probability of being in a queue PAN Pop NIN(1-p/N) A = arrival rate p"Po NT-NN! p: P/NPARKING STUDIES PROB 1. Data collected at a parking lot indicate that a total of 300 cars park between 8 a.m. and 6 p.m. 10% of these cars are parked for an average of 2 hr, 30% for an average of 4 hr, and the remaining cars are parked for an average of 10 hr. Determine the space-hours of demand at the lot PROB 2. If 10% of the parking bays are vacant on average (between 8 a.m. and 6 p.m.) at the parking lot of PROB1, determine the number of parking bays in the parking lot. Assume an efficiency factor of 0.85SEE MORE QUESTIONS