Reduced Load Equivalence under Subexponentiality

AbstractThe stationary workload WA+Bφ 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 $$e^{ - \sqrt x } $$ , we show that WA+Bφ is asymptotically equal to the reduced load queue WAφ−b, where b is the mean rate of B. Given that this property does not hold when both processes have lighter than $$e^{ - \sqrt x } $$ deviation decay rates, our result establishes the criticality of $$e^{ - \sqrt x } $$ 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.