The queueing system that takes advantage of the idle period to adjust or maintain the service facilities, or the attendants go on vacation during the idle period, or engage in auxiliary work, is called the vacation queueing system. Since the middle of the 20th century, because of the important role in computer systems, communication systems, management engineering and other fields, this kind of queueing system has been widely concerned. Takagi (1991) (1991) and Tian and Zhang (2006)(2006) have made in-depth and extensive studies on the vacation queueing system, and have achieved rich results in both theoretical and practical applications.