Question

Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank lobby has enough space for 10 customers. When the lobby is full, an arriving customers goes to another branch and is lost. The bank manager assigns one teller to customer service as long as the number of customers in the lobby is 3 or less. She assigns two tellers if the number is more than 3 but less than 8. Otherwise she assigns three tellers. The service times of the customers are i.i.d. exponential random variables with mean 4 minutes. Compute the expected amount of time in which three tellers are assigned to customer service during an 8-hour day, assuming the lobby is empty at the beginning of the day.

Answer 1

Holutfons uibmers antve a bank accovding "D poisson proceu In steady State for a Contnuou me markov chaïn the rate at ohlch fndividuals trans?mon n a patcular tate muut be equa the rate a uhich ndividuals transition ow of that Xtate. If λη t the birth ate -for State. n, μn the death rate rfor Ataten, and Po fs the probabilit y of betnq n State n în áteady - stare. Then w have he Ser of cquatonc uahon qives vs lo Po .Substthun the Secons 2.

Th?s Suq9 es tr har we might have Auuminq ths, le have unt An Po T,싸 ission rote 20, 3 tellen aue ausiqned Which ↑mple

f-o n-0 0 ITro 까기 μι n-f