Local Queuing Under Contention

We study stability of local packet scheduling policies in a distributed system of n nodes. The local policies at nodes may only access their local queues, and have no other feedback from the underlying distributed system. The packets arrive at queues according to arrival patterns controlled by an adversary restricted only by injection rate rho and burstiness b. In this work, we assume that the underlying distributed system is a shared channel, in which in order to get rid of a packet from the queue, a node needs to schedule it for transmission on the channel and no other packet is scheduled for transmission at the same time. We show that there is a local adaptive scheduling policy with relatively small memory, which is universally stable on a shared channel, that is, it has bounded queues for any rho= 0. On the other hand, without memory the maximal stable injection rate is O(1/log n). We show a local memoryless (non-adaptive) scheduling policy based on novel idea of ultra strong selectors which is stable for slightly smaller injection c/log^2 n, for some constant c>0

Stable routing scheduling algorithms in multi-hop wireless networks

Stability is an important issue in order to characterize the performance of a network, and it has become a major topic of study in the last decade. Roughly speaking, a communication network system is said to be stableif the number of packets waiting to be delivered (backlog) is finitely bounded at any one time. In this paper we introduce a number of routing scheduling algorithms which, making use of certain knowledge about the network’s structure, guarantee stability for certain injection rates. First, we introduce two new families of combinatorial structures, which we call universally strong selectorsand generalized universally strong selectors, that are used to provide a set of transmission schedules. Making use of these structures, we propose two local-knowledgepacket-oblivious routing scheduling algorithms. The first proposed routing scheduling algorithm onlyneeds to know some upper bounds on the number of links and on the network’s degree, and is asymptotically optimal regarding the injection rate for which stability is guaranteed. The second proposed routing scheduling algorithm isclose to be asymptotically optimal, but it only needs to know an upper bound on the number of links. For such algorithms, we also provide some results regarding both the maximum latencies and queue lengths. Furthermore, we also evaluate how the lack of global knowledge about the system topology affects the performance of the routing scheduling algorithms.Funding for open access charge: CRUE-Universitat Jaume

Robust and Listening-Efficient Contention Resolution

This paper shows how to achieve contention resolution on a shared communication channel using only a small number of channel accesses -- both for listening and sending -- and the resulting algorithm is resistant to adversarial noise. The shared channel operates over a sequence of synchronized time slots, and in any slot agents may attempt to broadcast a packet. An agent's broadcast succeeds if no other agent broadcasts during that slot. If two or more agents broadcast in the same slot, then the broadcasts collide and both broadcasts fail. An agent listening on the channel during a slot receives ternary feedback, learning whether that slot had silence, a successful broadcast, or a collision. Agents are (adversarially) injected into the system over time. The goal is to coordinate the agents so that each is able to successfully broadcast its packet. A contention-resolution protocol is measured both in terms of its throughput and the number of slots during which an agent broadcasts or listens. Most prior work assumes that listening is free and only tries to minimize the number of broadcasts. This paper answers two foundational questions. First, is constant throughput achievable when using polylogarithmic channel accesses per agent, both for listening and broadcasting? Second, is constant throughput still achievable when an adversary jams some slots by broadcasting noise in them? Specifically, for $N$ packets arriving over time and $J$ jammed slots, we give an algorithm that with high probability in $N+J$ guarantees $\Theta(1)$ throughput and achieves on average $O(\texttt{polylog}(N+J))$ channel accesses against an adaptive adversary. We also have per-agent high-probability guarantees on the number of channel accesses -- either $O(\texttt{polylog}(N+J))$ or $O((J+1) \texttt{polylog}(N))$, depending on how quickly the adversary can react to what is being broadcast