The epochs in which successive increases-or decreases-in the levels of a quasi birth-and-death process QBD process occur are of special interest. In queueing models they usually correspond to the times of successive increments or decrements. We derive general formulas for the variances of the times between successive increments or decrements in a stationary QBD process. In the case of the decrements we also obtain the variance of the time between an arbitrary decrement and the n-th subsequent decrement. These variances provide tractable descriptors of the relative variability of the input and output processes of queues that can be modeled as QBD processes.
|Journal||Methodology and Computing in Applied Probability|
|Publication status||Published - 2000|