Note—Note on a Control Problem of Balachandran and Tijms

Abstract

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.