Abstract—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-field 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 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. I.

Abstract—We investigate an abstraction method, called meanfield 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 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. I.

Abstract. 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. 1

We evaluate an asynchronous gossiping middleware for wireless users that propagates messages from any group member to all the other group members. This propagation can either be implemented through distributed mechanisms or can be mediated through servers. Our analysis of asynchronous mechanisms using wireless user availability traces from an university, corporation and a hot spot federation shows that the fundamental impediment to the system performance is the wireless user availability patterns. We then investigate the relative performance for several distributed as well as server mediated approaches. We show that pull mechanisms effectively randomizes the times when messages are propagated and thus achieves better performance than push based mechanisms. We then develop an adaptive approach that customizes the propagation frequency using the last session duration and show that this mechanism exhibits good performance when the required propagation intervals are large. We also show that for a given number of gossips, it is preferable to propagate messages to all available nodes rather than increasing the frequency while correspondingly reducing the number of nodes to propagate messages. Our results allow middleware developers to choose the appropriate propagation model to satisfy their application constraints.

The Dutch company Chess develops a wireless sensor network (WSN) architecture using an epidemic communication model. One of the greatest challenges in the design is to find suitable mechanisms for clock synchronization. In this paper, we study a clock synchronization protocol for the Chess WSN. First, we model the protocol as a network of timed automata and verify various instances using the Uppaal model checker. Next, we present a full parametric analysis of the protocol for the special case of cliques (networks with full connectivity), that is, we give constraints on the parameters that are both necessary and sufficient for correctness. These results have been checked using the proof assistant Isabelle. Finally, we present a negative result for the special case of line topologies: for any instantiation of the parameters, the protocol will eventually fail if the network grows.

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 mostlydoneusingsimulations, but eventheytendtobeexpensive incomputation timeand memory consumption. We employ mean-field approximation for an analytical 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 beevaluated using simple matrix-vector multiplications. 1

Many software systems today are designed for deployment on a range of architectures. However, in formal models it is typically assumed that the architecture is known and fixed; for example, that the software is sequential or concurrent, that the communication environment is synchronous or asynchronous but ordered, etc. In order to specify and analyze models which range over different deployment scenarios, it is interesting to lift aspects of low-level deployment variability to the abstraction level of the modeling language. In this paper, we propose a technique for introducing explicit resource constraints on concurrent objects in a timed extension of Creol, a formally defined high-level object-oriented modeling language. The technique is demonstrated by examples concerning rate restrictions on communication between objects. These restrictions are compositional and non-invasive: no change to the functional parts of the model is required, and restrictions can be selectively applied to parts of the model. In fact, the rate restrictions are captured by parameters in the model, which allows timed simulations to be performed with varying rate restrictions. We demonstrate the usefulness of explicit rate restrictions on communication in the model by a case study of wireless sensor networks. In this domain, rate restrictions may be understood as an abstraction over the collision patterns of broadcast data packets. Simulation results with different rate restrictions show how the timed throughput of data to the sink node in the network varies depending on the available rates. Keywords: bandwidth modeling, simulation, object-oriented models, deployment scenarios

Wireless access is increasingly ubiquitous while mobile devicesthatusethemareresourcerich.Thesetrends allow wireless users to collaborate with each other. We investigate various group communication paradigms that underly collaboration applications. We synthesize durations when members collaborate using wireless device availability traces. Wireless users operate from a variety of locations. Hence, we analyzed the behavior of wireless users in universities, corporations, conference venues, and city-wide hotspots. We show that the availability durations are longer in corporations followed by university and then in hotspots. The number of simultaneously available wireless users is small in all the scenarios. The session lengths are becoming smaller while the durations between sessions are becoming larger. We observed user churn in all the scenarios. We show that synchronous mechanisms require less effort to maintain update synchronicity among the group members. However, distributed mechanisms require a large number of replicas in order to propagate updates among the users. For asynchronous mechanisms, we show that pull-based mechanisms naturally randomize the times when updates are propagated and thus achieve better performance than push based mechanisms. We develop an adaptive approach that customizes the update frequencyusingthelastsessiondurationandshow that this mechanism exhibits goodperformancewhentherequiredupdatefrequencyintervalsarelarge.We also show that for a given number of gossips, it is preferable to propagate updates to all available nodes rather than increasing the frequency while correspondingly reducing the number of nodes to propagate updates. We develop a middleware to illustrate the practicality of our approach. Keywords: Wireless LAN, group communication mechanisms

Abstract. Gossip protocols have been proposed as a robust and efficient method for disseminating information throughout large-scale networks. In this paper, we propose a compositional analysis technique to study formal probabilistic models of gossip protocols in the context of wireless sensor networks. We introduce a simple probabilistic timed process calculus for modelling wireless sensor networks. A simulation theory is developed to compare probabilistic protocols that have similar behaviour up to a certain probability. This theory is used to prove a number of algebraic laws which revealed to be very effective to evaluate the performances of gossip networks with and without communication collisions. 1