Note—Note on a Control Problem of Balachandran and Tijms

In this note a conjecture of Balachandran and Tijms [Balachandran, K. R., H. C. Tijms. 1975. On the D-policy for the M/G/1 queue. Management Sci.21 1073–1076.] concerning the optimality of the D-policy over the N-policy in an M/G/1 queueing system is proved, using an inequality for renewal functions. This inequality seems to have some importance of its own.