Overload control in a finite message storage buffer

An approach is presented to the analysis of overload control in a finite buffer. The author considers that the original queuing process is modeled by a birth-death (BD) or quasi-birth-death (QBD) process. By overload control, the author means to adapt the input process or the service process during the time period when the buffer content exceeds a certain level. Such control is necessary to reduce the number of system shutdown periods and to protect high-priority messages. The controlled process is no longer to be BD or QBD, which makes direct analysis and computation of the controlled performance more complicated. The analytical method is based on dividing the controlled process into two alternating transient BD or QBD subprocesses, by only observing some selected transitions. Using this method, the author finds closed-form solutions for the queue length distribution when the control is placed on any type of BD process or the M/PH/1/K and PH/M/1/K queues. As an example, this model is applied to the overload control of packet voice transmission on a TDM (time-division-multiplexed) link