“…There is a cost function associated with these systems, which is often related to QoS. Hence, we consider a stochastic task model based on the one presented in [16]. Then, we represent each soft-real-time task using a tuple τ i = (r i , s i , a i , d i ) where: r i is the release time of the task, s i is the service time, which follows an exponential distribution of average µ −1 (i.e., µ is the number of serviced jobs of τ i per unit time), a i is the arrival time; tasks arrive according to a renewal process with exponential distribution of average λ −1 , and d i is the absolute deadline; the relative deadline is…”