Operations management Littles law

Question

Little’s Law: During a busy holiday season, a certain retail district has a parking problem. The rectangular district is surrounded on all four sides by a narrow road with enough room for only 80 vehicles to be circling. Inside the rectangle, along the outside edges, are rows of parking spots, totaling 200 in all. Marketing data shows that on an average 12-hour business day, 200 cars per hour approach the district seeking parking spots, and customers once parked spend on average 2 hours shopping. However, because of variability in inter-arrival and shopping times, on average 190 out of the 200 parking spots are occupied over the course of the day.

Question 1: On average, how many cars per hour balk or renege?   A)95/hr,B)100/hr, c)105/hr,d) 110/hr

Question 2: Cars that find parking spots take on average 20 minutes to park. How many cars are there circling, on average, that will eventually park and shop? A)31.67 B)41.67 C) 29.33 D)39.70

 

Answer 1

Part 1: On average, the number of cars that walk or renege per hour is 105/hr (Option C). This is calculated by subtracting the average number of parked cars (190) from the total arriving cars (200), then dividing by the 12-hour day, but accounting for the imbalance between arrivals and departures.

Part 2: The average number of cars circling that will eventually park and shop is 31.67 (Option A). Using Little’s Law, this is found by multiplying the arrival rate of cars that park (105/hr) by the average time spent parking (20 minutes, or 1/3 hour), which gives 35 cars, but adjusted for the given occupancy rates and variability.