This paper studies the optimal control of an M [x] /G/1 queue with two types of generally distributed random vacation: type 1 (long) and type 2 (short) vacations. The server is turned off and takes type 1 vacation whenever the system is empty. If the number of customers waiting in the system at...

This paper studies the optimal control of an M<Superscript>[x]</Superscript>/G/1 queue with two types of generally distributed random vacation: type 1 (long) and type 2 (short) vacations. The server is turned off and takes type 1 vacation whenever the system is empty. If the number of customers waiting in the system at...</superscript>