Reduced Load Equivalence under Subexponentiality

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