Overload control in a finite message storage buffer

An approach to the analysis of overload control in a finite buffer is introduced in which the original queuing process is modeled by a birth-and-death (BD) or quasi-birth-and-death (QBD) process. Overload control means to adapt the input process or the service process during the time period when the buffer content exceeds a certain level until it drops to another level. Such a control is necessary to reduce the occurrence of system shutdown periods and to protect high-priority messages against low-priority ones. Since the controlled process two be computed in terms of the will no longer be BD or QBD, the methodology commonly used for analyzing BD or QBD process cannot be applied. This makes direct analysis and computation of the controlled performance more complicated. The analytical methods consists in dividing the controlled process into two altering transient BD or QBD subprocesses, by observing only some selected transitions. Such a division enables the equilibrium probabilities of the controlled process to be computed in terms of the sojourn times of the two transient processes. It is shown that this is equivalent to the analysis and computation of equilibrium probabilities of the underlying stationary BD or QBD process