Mr Chips manufactures an automated vending machine that can

. Mr. Chips manufactures an automated vending machine that can prepare a single order of french fries in an average of 40 seconds. The company has placed one of its machines in the USM Student Center, where it believes customers will arrive according to a Poisson process with a mean rate of 1 per minute.

(i) Mr. Chips is considering placing a second french-fry vending machine in the Student Center. Given the current vending machine service level, would it be worthwhile for Mr. Chips to do this? Justify your answer quantitatively.

(ii) If an arriving customer found two people ahead of him/her at the vending machine (one getting fries and the other waiting), how long would you expect him/her to wait before being able to use the machine?

Solution

(i) No, it is not worthwhile for Mr.Chips to place a second machine because the rate at which the machine is giving out order is only 40seconds on aversge while the rate of customers arriving is 1 per minute. So, on an average the machine is doing work faster than the average number of person arriving at the machine. So, its not needed.

(ii) Since there are two persons ahead:

For 1st person: the time taken should be half of the average time machine takes to give product because this person may be standing there for unknown time till then. So it is safe to assume the half of average time.

For 2nd person the time taken will be the average time taken by machine.

So overall average time needed will be 20+40 = 60 seconds = 1 minute