On Resource Aware Algorithms in Epidemic Live Streaming

Epidemic-style diffusion schemes have been previously proposed for achieving peer-to-peer live streaming. Their performance trade-offs have been deeply analyzed for homogeneous systems, where all peers have the same upload capacity. However, epidemic schemes designed for heterogeneous systems have not been completely understood yet. In this report we focus on the peer selection process and propose a generic model that encompasses a large class of algorithms. The process is modeled as a combination of two functions, an aware one and an agnostic one. By means of simulations, we analyze the awareness-agnostism trade-offs on the peer selection process and the impact of the source distribution policy in non-homogeneous networks. We highlight that the early diffusion of a given chunk is crucial for its overall diffusion performance, and a fairness trade-off arises between the performance of heterogeneous peers, as a function of the level of awareness

Early Experiences in Traffic Engineering Exploiting Path Diversity: A Practical Approach

Recent literature has proved that stable dynamic routing algorithms have solid theoretical foundation that makes them suitable to be implemented in a real protocol, and used in practice in many different operational network contexts. Such algorithms inherit much of the properties of congestion controllers implementing one of the possible combination of AQM/ECN schemes at nodes and flow control at sources. In this paper we propose a linear program formulation of the multi-commodity flow problem with congestion control, under max-min fairness, comprising demands with or without exogenous peak rates. Our evaluations of the gain, using path diversity, in scenarios as intra-domain traffic engineering and wireless mesh networks encourages real implementations, especially in presence of hot spots demands and non uniform traffic matrices. We propose a flow aware perspective of the subject by using a natural multi-path extension to current congestion controllers and show its performance with respect to current proposals. Since flow aware architectures exploiting path diversity are feasible, scalable, robust and nearly optimal in presence of flows with exogenous peak rates, we claim that our solution rethinked in the context of realistic traffic assumptions performs as better as an optimal approach with all the additional benefits of the flow aware paradigm

Size Does Matter (in P2P Live Streaming)

Optimal dissemination schemes have previously been studied for peer-to-peer live streaming applications. Live streaming being a delay-sensitive application, fine tuning of dissemination parameters is crucial. In this report, we investigate optimal sizing of chunks, the units of data exchange, and probe sets, the number peers a given node probes before transmitting chunks. Chunk size can have significant impact on diffusion rate (chunk miss ratio), diffusion delay, and overhead. The size of the probe set can also affect these metrics, primarily through the choices available for chunk dissemination. We perform extensive simulations on the so-called random-peer, latest-useful dissemination scheme. Our results show that size does matter, with the optimal size being not too small in both cases

Forwarding Tables Verification through Representative Header Sets

Forwarding table verification consists in checking the distributed data-structure resulting from the forwarding tables of a network. A classical concern is the detection of loops. We study this problem in the context of software-defined networking (SDN) where forwarding rules can be arbitrary bitmasks (generalizing prefix matching) and where tables are updated by a centralized controller. Basic verification problems such as loop detection are NP-hard and most previous work solves them with heuristics or SAT solvers. We follow a different approach based on computing a representation of the header classes, i.e. the sets of headers that match the same rules. This representation consists in a collection of representative header sets, at least one for each class, and can be computed centrally in time which is polynomial in the number of classes. Classical verification tasks can then be trivially solved by checking each representative header set. In general, the number of header classes can increase exponentially with header length, but it remains polynomial in the number of rules in the practical case where rules are constituted with predefined fields where exact, prefix matching or range matching is applied in each field (e.g., IP/MAC addresses, TCP/UDP ports). We propose general techniques that work in polynomial time as long as the number of classes of headers is polynomial and that do not make specific assumptions about the structure of the sets associated to rules. The efficiency of our method rely on the fact that the data-structure representing rules allows efficient computation of intersection, cardinal and inclusion. Finally, we propose an algorithm to maintain such representation in presence of updates (i.e., rule insert/update/removal). We also provide a local distributed algorithm for checking the absence of black-holes and a proof labeling scheme for locally checking the absence of loops

Efficient Loop Detection in Forwarding Networks and Representing Atoms in a Field of Sets

The problem of detecting loops in a forwarding network is known to be NP-complete when general rules such as wildcard expressions are used. Yet, network analyzer tools such as Netplumber (Kazemian et al., NSDI'13) or Veriflow (Khurshid et al., NSDI'13) efficiently solve this problem in networks with thousands of forwarding rules. In this paper, we complement such experimental validation of practical heuristics with the first provably efficient algorithm in the context of general rules. Our main tool is a canonical representation of the atoms (i.e. the minimal non-empty sets) of the field of sets generated by a collection of sets. This tool is particularly suited when the intersection of two sets can be efficiently computed and represented. In the case of forwarding networks, each forwarding rule is associated with the set of packet headers it matches. The atoms then correspond to classes of headers with same behavior in the network. We propose an algorithm for atom computation and provide the first polynomial time algorithm for loop detection in terms of number of classes (which can be exponential in general). This contrasts with previous methods that can be exponential, even in simple cases with linear number of classes. Second, we introduce a notion of network dimension captured by the overlapping degree of forwarding rules. The values of this measure appear to be very low in practice and constant overlapping degree ensures polynomial number of header classes. Forwarding loop detection is thus polynomial in forwarding networks with constant overlapping degree