An M/G/∞ queueing system is cleaned at the fixed times T, 2T, 3T,.... All customers in service when a cleaning begins are forced to leave early and a cost C1 is incurred for each customer. Suppose that a cleaning takes time T /4, and that all customers who arrive while the system is being cleaned are lost, and a cost C2 is incurred for each one.

(a) Find the long-run average cost per unit time.

(b) Find the long-run proportion of time the system is being cleaned.