A Dubai based bank is experiencing increased customer traffic and is considering implementing a waiting line system to enhance customer service.

The current arrival rate of its customers follows a Poisson distribution with an average rate of $15$ customers per hour. Also, the service rate for the only cashier which the bank has currently, is Exponentially distributed with an average rate of $20$ customers per hour. Based on this information answer all the questions below:

a$.$ Is the service Single$-$channel or Multiple Chanel?

b$.$ What is the probability that no customer is in the Bank's system?

Why?

$(1$ Point$)$

$(1$ Point$)$

c$.$ What is the average number of customers in the Bank's system?

$(2$ Points$)$

d$.$ What is a customer's average waiting time in the Bank's system?