Rock Property Management (RPM) team win the contract of managing the parking building close to the new Mega Outlets shopping complex. Currently the parking

Rock Property Management (RPM) team win the contract of managing the parking building close to the new Mega RPM noticed that the number of customers increased and consequently the waiting times to validate parking

Rock Property Management (RPM) team win the contract of managing the parking building close to the new Mega Outlets shopping complex. Currently the parking building is operating with one lane and one parking validation window, where one parking staff operated on a first-come first served basis. There are variety of stores in this shopping complex and the area surrounded by the office buildings. Due to shortage of the parking spaces in the surrounding areas, the customer population is fairly large. The parking staff can validate the parking passes/tickets and issue receipts at a rate of fifty seconds per car on average following a negative exponential distribution. Following a Poisson distribution, sixty six cars will arrive at the entrance every hour on average during business hour. (a) What is the average number of cars waiting in line? (b) What is the average time in minutes that a car has to spend waiting in line at the parking entrance? (c) What is the probability that there will be more than two cars at the parking entrance? RPM noticed that the number of customers increased and consequently the waiting times to validate parking passes/tickets started to increase. RPM want to manage the system in a faster way they decided that the average waiting time in the line should not be more than three minutes, and hence opened two additional parking validation windows, increasing the number of windows to serve customers to three. Customers arrive following a Poisson distribution, 202 cars will arrive at the entrance every hour on average during business hour. They wait in a single waiting line to validate the parking passes and get a receipt where the queue discipline is FCFS. Service times at each attendant are identical and distributed exponentially; each attendant spends an average of fifty seconds per customer. (d) What is the average length of the waiting line with three validation windows? Is RPM achieving their goal of having the average waiting time in the line less than three minutes? (A simple Yes/No answer will not get any mark/s.)

Step by Step Solution

There are 3 Steps involved in it

Step: 1

a Average Number of Cars Waiting in Line The average number of cars waiting in line can be calculated using the formula for the average number of customers in a Poisson arrival system with exponential service L X W Where L is the average number of cars in the system waiting in line A is the arrival rate cars per hour W is the average time a car spends in the system Given A 66 cars per hour W 1 50 seconds per car 50 50 3600 L 66 cars 0917 cars b Average Time a Car Spends Waiting in Line The average time a car spends waiting in line W can be calculated using Littles Law W W 0917 hours 60 minuteshour 083 minutes 66 c Probability of More Than Two Cars at the Entrance Using the Poisson distribution we can find the probability of more than two cars arriving in one hour PX 2 1 PX 2 Using the Poisson formula calculate ... blur-text-image