Rena Bakhshi

MeanField analysis for the evaluation of gossip protocols

Gossip protocols are designed to operate in very large, decentralised networks. A node in such a network bases its decision to interact (gossip) with another node on its partial view of the global system. Because of the size of these networks, analysis of gossip protocols is mostly done using simulations, that tend to be expensive in computation time and memory consumption. We employ mean-¿eld approximation for an analytical evaluation of gossip protocols. Nodes in the network are represented by small identical stochastic models. Joining all nodes would result in an enormous stochastic process. If the number of nodes goes to in¿nity, however, mean-¿eld analysis allows us to replace this intractably large stochastic process by a small deterministic process. This process approximates the behaviour of very large gossip networks, and can be evaluated using simple matrix-vector multiplications.

Formal analysis techniques for gossiping protocols

We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them.

Mean-Field Analysis for the Evaluation of Gossip Protocols

Gossip protocols are designed to operate in very large, decentralised networks. A node in such a network bases its decision to interact (gossip) with another node on its partial view of the global system. Because of the size of these networks, analysis of gossip protocols is mostly done using simulations, that tend to be expensive in computation time and memory consumption. We employ mean-?eld approximation for an analytical evaluation of gossip protocols. Nodes in the network are represented by small identical stochastic models. Joining all nodes would result in an enormous stochastic process. If the number of nodes goes to in?nity, however, mean-?eld analysis allows us to replace this intractably large stochastic process by a small deterministic process. This process approximates the behaviour of very large gossip networks, and can be evaluated using simple matrix-vector multiplications.

An Analytical Model of Information Dissemination for a Gossip-Based Protocol

We develop an analytical model of information dissemination for a gossip protocol. With this model we analyse how fast an item is replicated through a network. We also determine the optimal size of the exchange buffer, to obtain fast replication. Our results are confirmed by large-scale simulation experiments.

Mean-field framework for performance evaluation of push-pull gossip protocols

Gossip protocols are designed to operate in very large, decentralised networks. A node in such a network bases its decision to interact (gossip) with another node on its partial view of the global system. Because of the size of these networks, analysis of gossip protocols is mostly done using simulations, but these tend to be expensive in computation time and memory consumption. We employ mean-field analysis techniques for the evaluation of gossip protocols. Nodes in the network are represented by small identical stochastic processes. Joining all nodes would result in an enormous stochastic process. If the number of nodes goes to infinity, however, mean-field analysis allows us to replace this intractably large stochastic process by a small deterministic process. This process approximates the behaviour of very large gossip networks, and can be evaluated using simple matrix-vector multiplications.

Automating the Mean-Field Method for Large Dynamic Gossip Networks

We investigate an abstraction method, called mean-field method, for the performance evaluation of dynamic networks with pairwise communication between nodes. It allows us to evaluate systems with very large numbers of nodes, that is, systems of a size where traditional performance evaluation methods fall short. While the mean-field analysis is well-established in epidemics and for chemical reaction systems, it is rarely used for communication networks because a mean-field model tends to abstract away the underlying topology. To represent topological information, however, we extend the mean-field analysis with the concept of classes of states. At the abstraction level of classes we define the network topology by means of connectivity between nodes. This enables us to encode physical node positions and model dynamic networks by allowing nodes to change their class membership whenever they make a local state transition. Based on these extensions, we derive and implement algorithms for automating a mean-field based performance evaluation.

Leader Election in Anonymous Rings: Franklin Goes Probabilistic

We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin, augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size.

Reliable localised event detection in a wireless distributed radio telescope

We consider a large wireless network constituting a radio telescope. Each of the anticipated 3000 nodes is triggered to collect data for further analysis at a rate of more than 200 Hz, mostly caused by noisy environmental sources. However, relevant cosmic rays occur only a few times a day. As every trigger has an associated 12.5 KB of data, and considering the size of the telescope in number of nodes and covered area, centralised processing is not an option. We propose a fully decentralised event detection algorithm based on collaborative local data analysis, effectively filtering out only those triggers that need further centralised processing. As we show through performance evaluations, the crux in the design is finding the right balance between accuracy and efficient use of resources such as the communication bandwidth in the unreliable communication environment.

Mechanized extraction of topology anti-patterns in wireless networks

Exhaustive and mechanized formal verification of wireless networks is hampered by the huge number of possible topologies and the large size of the actual networks. However, the generic communication structure in such networks allows for reducing the root causes of faults to faulty (sub-)topologies, called anti-patterns, of small size. We propose techniques to find such anti-patterns using a combination of model-checking and automated debugging. We apply the proposed technique on two well-known protocols for wireless sensor networks and show that the techniques indeed find the root causes in terms of canonical topologies featuring the fault.

Fast leader election in anonymous rings with bounded expected delay

We propose a probabilistic network model, called asynchronous bounded expected delay (ABE), which requires a known bound on the expected message delay. In ABE networks all asynchronous executions are possible, but executions with extremely long delays are less probable. Thus, the ABE model captures asynchrony that occurs in sensor networks and ad-hoc networks. At the example of an election algorithm, we show that the minimal assumptions of ABE networks are sufficient for the development of efficient algorithms. For anonymous, unidirectional ABE rings of known size n we devise a probabilistic election algorithm having average message and time complexityO(n).