. M/G/1 queue under T-policy with zero start-up time.

Here the facility is controlled in a different manner. Every time the server becomes idle after exhaustive service, the service facility is utilized for other work for fixed length of time T, and then the facility is reactivated only when there is at least one unit (i.e ., multiple-server vacation with fixed vacation time T). Suppose that K is the fixed setup cost, h is the holding cost per unit time per unit present, and start-up time is zero.

(a) Defining a cycle C as the interval between two consecutive epochs at which a vaction period starts, show that T

E(C) =-

1 - p

(b) Show that with probability 1, the long-run average cost per unit time is given by K(1-P) +hp+

22bz AT|

2(1 -0) + 2)

and that the average cost per unit time is mimimal for 2(1-p)K T =

hr

(Tijms, 1986)