A single-server queue with vacations and gated time-limited service

An analysis is conducted of an M/G/1 queue with server vacations and gated time-limited service. The authors derive a functional equation which characterizes the amount of work, U_p, at the server´s return from a vacation. To solve the equation, they use a numerical technique in which the complementary cumulative function for U_p is closely approximated by a weighted sum of Laguerre functions with unknown coefficients. The functional equation is transformed into a set of linear equations from which the coefficients can be computed. Using the work-decomposition and PASTA (Poisson Arrivals Sec Time Averages) properties, the average customer waiting time can be readily obtained. Several numerical examples are included to demonstrate the validity of the technique. The model studied is applicable to analyzing a specific recently proposed communication channel that alternately serves voice and data traffic, token-passing networks with token-holding timers, and other communication and computer systems where times are used to allocate service among multiple types of customers