Recurrence times of buffer overflows in Jackson networks

The estimation of the statistics of buffer overflows in networks of queues by means of simulation is inherently costly, simply because of the rarity of these events. An alternative analytic approach is presented, with very low computational cost, for calculating the recurrence time of buffer overflows for Jackson networks in which the recurrence times of buffer overflows in a network are expressed in terms of the recurrence times for overflows of individual buffers, isolated from the network. This result is applied to the buffer allocation problem for queueing networks, providing extensions and further justification for a previously derived heuristic approach to this problem