Carrefour Hypermarket employs four cashiers in a certain store to serve its customers. Suppose that Cashier 1 has an average service time of 6 minutes, Cashier 2 has an average service time of 4 minutes, Cashier 3 has an average service time of 2 minutes, and Cashier 4 has an average service time of 3 minutes, respectively. Suppose also that the service times are exponentially distributed and independent from each
other.
Let T1 be the service time of Cashier 1, T2 be the service time of Cashier 2, T3 be the
service time of Cashier 3, and T4 be the service time of Cashier 4 (please use this notation
in your solutions).
Suppose on a given day Cashier 4 is on leave, and Cashier 1, Cashier 2, and Cashier 3 are serving their customers. A customer arriving at the cashier area finds all cashiers serving other customers and no one else is waiting. What is the expected service time for the customer?
A small company has a call center with two phone lines only.
Carrefour Hypermarket employs four cashiers in a certain store to serve its
customers. Suppose that Cashier 1 has an average service time of 6 minutes, Cashier 2 has an average service time of 4 minutes, Cashier 3 has an average service time of 2 minutes, and Cashier 4 has an average service time of 3 minutes, respectively. Suppose also that the service times are exponentially distributed and independent from each other.
Let T1 be the service time of Cashier 1, T2 be the service time of Cashier 2, T3 be the
service time of Cashier 3, and T4 be the service time of Cashier 4 (
-A customer arriving at the cashier area sees all cashiers serving other
customers and no one else is waiting. Let Tw be the time the customer waits before
getting served. Express Tw in terms of T1, T2, T3, and T4. How long the waiting time will
be on average?
A small company has a call center with two phone lines only. An average of 40 people per hour calls in for orders, and it takes an average of 2 minutes to handle a call. Interarrival time between call arrivals and time to serve calling customers is on phone are exponentially distributed. If there are more than two customers waiting to be served, a caller gets a busy signal and hangs up.
b)What is the average time that the phone lines stay idle?
c) Calculate the fraction of the time that the line will be busy?
d) Calculate the average number of customers on hold waiting to be answered