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 with very low computational cost is presented for calculating the recurrence times of buffer overflows in 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. Equivalent results are given for continuous and discrete-time networks. 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.
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