4.1 Model of a taxi station Consider a taxi station where taxis looking for passengers and passengers looking for taxis arrive according to Poisson processes, with mean rates per minute of 1 and 1.25. A taxi will wait no matter how many other taxis are in line, but an arriving passenger waits only if the number of passengers already waiting for taxis is two or less. Assuming steady-state conditions, find:

a. The mean number of taxis waiting for passengers.

b. The mean number of passengers waiting for taxis.

c. The mean number of passengers who in the course of an hour do not join the waiting line because at least three passengers were already waiting.