Adversarial Queueing Model for Continuous Network Dynamics

Abstract

Abstract. In this paper we start the study of generalizing the Adversarial Queueing Theory (aqt) model towards a continuous scenario in which the usually assumed synchronicity of the evolution is not required anymore. We consider a model, named continuous AQT (caqt), in which packets can have arbitrary lengths, and the network links may have different speeds (or bandwidths) and propagation delays. We show that, in such a general model, having bounded queues implies bounded endto-end packet delays and vice versa. From the network point of view, we show that networks with directed acyclic topologies are universally stable, i.e., stable independently of the protocols and the traffic patterns used in it, and that this even holds for traffic patterns that make links to be fully loaded. Concerning packet scheduling protocols, we show that the well-known lis, sis, ftg and nfs protocols remain universally stable in our model. We also show that the caqt model is strictly stronger than the aqt model by presenting scheduling policies that are unstable under the former while they are universally stable under the latter.

A Universally Stable and Energy-Efficient Scheduling Protocol for Packet Switching Network

“…The paths will be specified by the adversary rather than the protocol. This is a typical assumption for the existing AQT models (e.g., [8]- [10]). It allows us to focus on the scheduling protocol.…”

“…To generalize the original AQT, some new AQT models have been proposed [5], [10]. In [10], Blesa et al proposed the Continuous AQT (CAQT) model, which allows arbitrary packet lengths and link speeds.…”

“…In [10], Blesa et al proposed the Continuous AQT (CAQT) model, which allows arbitrary packet lengths and link speeds. However, this model doesn't enable the links to vary their speeds dynamically.…”

“…RA-CAQT). Our model is mainly based on the continuous AQT (CAQT) model [10], and adopts some features of the Temporary Session Model [5]. It can verify the stability of network protocol in the worst case with the adversarial input, and allows arbitrary packet lengths and dynamically adaptive transmission rates.…”

“…The original AQT [8], [9] assumes that the network packets transmission behaves synchronously [10], i.e., the lengths of the packets are assumed to be uniform and the network devices can only work at uniform speed. By abandoning these assumptions, in this paper we provide a new AQT model which is more suitable for developing the energy-efficient scheduling protocol.…”