Consider an M/G/1 queue such that over and above the first ‘essential service’ having a general service time distribution, a unit may need a second ‘optional service’ with another independent general service time. A unit may depart from the system either after the first essential service with probability (1 – r) or at the end of the first service may immediately go for a second service with probability r (0≤r≤1). This is a generalization of a recent paper considered by Madan.
