Zureb is a new taxi-hailing app that has recently started operating in Los Angeles. Every hour 1,000 taxis are on Zureb. Once a passenger requests a ride, the app assigns the closest available taxi to her. However, sometimes no taxi is available. Then the passengers will be assigned the next available taxi on first-come-first-serve basis (independent of location). Suppose every minute 100 passengers request a ride. Each taxi, after they are matched to a passenger, picks up the passenger on average in 2.5 minutes. Each ride, after pick up, takes 7 minutes on average. Assume all the distributions are exponential.

a. How many seconds on average each passenger waits before they are assigned to a taxi?

b. Suppose the answer to the previous part is 60 seconds (this is not the answer but let’s assume it is for now). How much on average does it take for passengers from the time they request a ride on the app till they are dropped off?

c. Suppose the taxi-drivers are paid $1 per minutes for a ride. However, they are not paid for the time spent on picking up. If a driver works 8 hours a day, how much does he make a day?

d. The drivers are complaining about the long pick up time. Arpita, the manager of Zureb’s data science group, suggest the following policy: “Before assigning a passenger to a driver, wait for 15 seconds, even if there are available drivers. Then, assign the passenger to the closes available driver, or to the next driver that become available. She observes that this way, they can assign drivers to the passengers that are closer to them and reduce the average pick up time from 2.5 to 1 minutes.”

e. If Arpita’s policy is implemented, do the drivers earn more or less? Why?

f. How much on average does it take for passengers from the time they request a ride on the app till they are dropped off?

g. Do you agree with Arpita’s suggestions? Why?