Stability of two families of real-time queueing networks

We study open multiclass queueing networks with renewal arrival streams and general service time distributions. Upon arrival to the network, customers from each class are assigned a random deadline drawn from a distribution associated with this class.We show that preemptive subcritical EDF networks with fixed customer routes are stable. We also prove that a broad class of (not necessarily subcritical) networks with reneging and Markovian routing, including EDF, FIFO, LIFO, SRPT, fixed priorities and processor sharing, is stable.