Reduced load equivalence under subexponentiality
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abstract
The stationary workload W A+B of a queue with capacity loaded by two independent processes A and B is investigated. When the probability of load deviation in process A decays slower v than both in B and e -x , we show that W A+B is asymptotically equal to the reduced load queue W A-b , where b is the mean rate of B. Given that this property does not hold when both processes have lighter than e -x deviation decay rates, our result establishes the criticality of e -x in the functional behavior of the workload distribution. Furthermore, using the same methodology, we show that under an equivalent set of conditions the results on sampling at subexponential times hold.