Overflow behavior in queues with many long-tailed inputs (Q2713162)

This paper is concerned with a fluid queue fed by \(n\) on-off sources which arrives at a buffered space \(bn\) having a constant depletion rate \(cn\). Explicit asymptotic results are obtained for the case where the on periods have a subexponential distribution, \(b\) being taken as large. These show a sharp dichotomy in behaviour depending on the behaviour of the function \(v(t) = -\log P(A^* > t)\) for large \(t\), \(A^*\) representing the residual on period. If \(v\) is regularly varying of index 0, the time to overflow will increase faster than the buffer size, while if the regular variation is of index strictly between 0 and 1, then the time to overflow is roughly proportional to the buffer size. Approximations are also obtained for the overflow probability.