Analysis of a discrete-time queueing system with time-limited service

The authors analyze a discrete-time, single-server queueing system in which the length of each service period is limited. The server takes a vacation when the limit expires or the queue empties, whichever occurs first. In the former case, the preempted service is resumed after the vacation without loss or creation of any work. This system models the transmission of message frames from a station on timed-token local-area networks (for example, FDDI and IEEE 802.4 token bus). The authors study the process of the unfinished work and the joint process of the queue size and the remaining service time. By using the technique of discrete Fourier transforms to determine some unknown functions in the governing equations, they numerically obtain exact mean waiting times.