A train station has a shuttle bus that connects the main sta

A train station has a shuttle bus that connects the main station to a nearby city. The shuttle operates with a 15 minute headway between dispatches from the terminal. Suppose that the passengers arrive at the shuttle stop following a Poisson process with rate 120 passengers/hr. (a) What is the average number of passengers that board each departing shuttle? (b) If the shuttle operator wants to ensure that passenger demand exceeds the shuttle capacity less than 5% of the time, what is the smallest capacity that the shuttles should be designed for?

Solution

(a)time bteween shuttle =15 min=15/60=1/4=0.25 hour

No of passenger per hour =120

therfore no of passenger for each shuttle=0.25*120=30

(b)let x be the capacity of shuttle

then x+5x/100=30

=> x+0.05x=30

=> 1.05x=30

=> x=30/1.05=28.57= 29