Performance of scheduling policies in adversarial networks with non synchronized clocks

In this paper we generalize the Continuous Adversarial Queuing Theory (CAQT) model by considering the possibility that the router clocks in the network are not synchronized. Clearly, this new extension to the model only affects those scheduling policies that use some form of timing. First, if all clocks run at the same speed, maintaining constant differences, we show that all universally stable policies in CAQT that use the injection time and the remaining path to schedule packets remain universally stable. These policies include, for instance, Shortest in System (SIS) and Longest in System (LIS). Then, if clock differences can vary over time, but difference is bounded, we show the universal stability of SIS and a family of policies related to LIS. The bounds we obtain in this case depend on the maximum difference between clocks. We then present a new policy that we call Longest in Queues (LIQ), which gives priority to the packet that has been waiting the longest in edge queues. This policy is universally stable and, if clocks maintain constant differences, the bounds do not depend on them. To finish, we provide with simulation results that compare the behavior of some of these protocols in a network with stochastic injection of packets.