We consider the problem of throughput-optimal packet dissemination, in the presence of an arbitrary mix of unicast, broadcast, multicast, and anycast traffic, in an arbitrary wireless network. We propose an online dynamic policy, called Universal Max-Weight (UMW), which solves the problem efficiently. To the best of our knowledge, UMW is the first known throughput-optimal policy of such versatility in the context of generalized network flow problems. Conceptually, the UMW policy is derived by relaxing the precedence constraints associated with multi-hop routing and then solving a min-cost routing and max-weight scheduling problem on a virtual network of queues . When specialized to the unicast setting, the UMW policy yields a throughput-optimal cycle-free routing and link scheduling policy. This is in contrast with the well-known throughput-optimal back-pressure (BP) policy which allows for packet cycling, resulting in excessive latency. Extensive simulation results show that the proposed UMW policy incurs a substantially smaller delay as compared with the BP policy. The proof of throughput-optimality of the UMW policy combines ideas from the stochastic Lyapunov theory with a sample path argument from adversarial queueing theory and may be of independent theoretical interest.

Adaptive packet scheduling over a wireless channel under constrained jamming

Adversarial Queueing Theory (AQT) has shown that seemingly innocent traffic injection rates might lead to unbounded queues in packet-switched networks - depending on scheduling strategies as well as topological characteristics. Little attention has been given to quantifying these effects in realistic network configurations. In particular, the existing AQT literature makes two unrealistic assumptions: infinite buffers and perfect synchrony. Because finite buffers inherently limit queue sizes, adversarial effects ultimately lead to packet loss which we address in this work. In addition, we study the effect of imperfect network synchronization under the packet loss metric. Our results, using analysis and simulation, indicate that classical AQT examples appear harmless under realistic assumptions but for a novel class of adversaries considerably higher loss can be observed. We introduce this class by giving examples of two new AQT concepts to construct loss-efficient network adversaries. Our analysis proves the robustness of these new adversaries against randomized de-synchronization effects in terms of variable link delays and nodal processing.

The robustness of stability under link and node failures

In this paper, we study stability and latency of routing in wireless networks where it is assumed that no collision will occur. Our approach is inspired by the adversarial queuing theory, which is amended in order to model wireless communication. More precisely, there is an adversary that specifies transmission rates of wireless links and injects data in such a way that an average number of data injected in a single round and routed through a single wireless link is at most r, for a given r ∈ (0, 1). We also assume that the additional "burst" of data injected during any time interval and scheduled via a single link is bounded by a given parameter b. Under this scenario, we show that the nodes following so called work-conserving scheduling policies, not necessarily the same, are guaranteed stability (i.e., bounded queues) and reasonably small data latency (i.e., bounded time on data delivery), for injection rates r <; 1/d, where d is the maximum length of a routing path. Furthermore, we also show that such a bound is asymptotically optimal on d.

Adversarial queuing theory with setups

An adversarial queueing model for online server routing

We consider packet networks and make use of the "adversarial queuing theory" model [10]. We are interested in the question of guaranteeing that all packets are actually delivered to destination, and of having an upper bound on the delivery times of all packets. Whether this is possible against all adversarial queuing theory rate-1 adversaries was previously posed as an open question [13],[10]. Among other things, we give a queuing policy that guarantees bounded delivery time whenever the rate-1 adversary injects a sequence of packets for which there exists a schedule with a finite upper bound on the delivery times of all packets, and adheres to certain additional conditions. On the negative side we show that there exist rate-1 sequences of packets for which there is no schedule with a finite upper bound on the delivery times of all packets. We thus answer an open question posed by Gamarnik [13]. We further show that delivering all packets while maintaining stability (we coin the term "reliability" for this property) can be done by an offline scheduler whenever the injection of packets is done at rate of at most 1. However, on the other hand, we also show that there is no online protocol (even centralized) that can achieve that property against all rate-1 adversaries. We thus answer an open question of Borodin et al. [10].

Tight bounds for the performance of Longest In System on DAGs

We consider the model of "adversarial queuing theory" for packet networks introduced by Borodin et al. [J. ACM, 48 (2001), pp. 13--38].We show that the scheduling protocol first-in-first-out (FIFO) can be unstable at any injection rate larger than 1/2 and that it is always stable if the injection rate is less than 1/d, where d is the length of the longest route used by any packet. We further show that every work-conserving (i.e., greedy) scheduling policy is stable if the injection rate is less than 1/(d+1).

Abstract The adversarial queueing theory model for packet routing was suggested by Borodin et al. We give a complete and simple characterization of all networks that are universally stable in this model. We show that the same characterization also holds for networks which are stable given that the packet forwarding protocol is FIFO (First in First out). We also show that a specific greedy protocol, SIS (Shortest in System), is stable against 0/1 stochastic adversaries. © 2001 John Wiley & Sons, Inc.

We consider packet routing when packets are injected continuously into a network. We develop an adversarial theory of queuing aimed at addressing some of the restrictions inherent in probabilistic analysis and queuing theory based on time-invariant stochastic generation. We examine the stability of queuing networks and policies when the arrival process is adversarial, and provide some preliminary results in this direction. Our approach sheds light on various queuing policies in simple networks, and paves the way for a systematic study of queuing with few or no probabilistic assumptions.

Adaptive Packet Routing for Bursty Adversarial Traffic