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 than both in B and e^-, we show that W^_A+B is asymptotically equal to the reduced load queue W^-b_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^- 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.
