26. Two typists have identical jobs. Each types letters dictated by a manager. Suppose that letters to be typed arrive at random (following Poisson distribution) at a rate of three per hour for each typist.

Suppose that each typist can type four letters on the average per hour (following exponential distribution).

(a) Assuming that each typist does her own work, what is the expected waiting time for a letter (time before work is started on a letter)?

(b) Suppose that the two typists are 'pooled'. That is, letters are sent to the two together and are done by whoever is free, in order of arrival. What is the expected waiting time for a letter under this arrangement? (MBA, Delhi, April, 1996)