Fast Discrete Consensus Based on Gossip for Makespan Minimization in Networked Systems

In this paper we propose a novel algorithm to solve the discrete consensus problem, i.e., the problem of distributing evenly a set of tokens of arbitrary weight among the nodes of a networked system. Tokens are tasks to be executed by the nodes and the proposed distributed algorithm minimizes monotonically the makespan of the assigned tasks. The algorithm is based on gossip-like asynchronous local interactions between the nodes. The convergence time of the proposed algorithm is superior with respect to the state of the art of discrete and quantized consensus by at least a factor O(n) in both theoretical and empirical comparisons

A new analytical method for parallel, diffusion-type load balancing

We propose a new proof technique which can be used to analyze many parallel load balancing algorithms. The technique is designed to handle concurrent load balancing actions, which are often the main obstacle in the analysis. We demonstrate the usefulness of the approach by analyzing various natural diffusion-type protocols. Our results are similar to, or better than, previously existing ones, while our proofs are much easier. The key idea is to first sequentialize the original, concurrent load transfers, analyze this new, sequential system, and then to bound the gap between both.

Discrete Load Balancing in Heterogeneous Networks with a Focus on Second-Order Diffusion

In this paper we consider a wide class of discrete diffusion load balancing algorithms. The problem is defined as follows. We are given an interconnection network and a number of load items, which are arbitrarily distributed among the nodes of the network. The goal is to redistribute the load in iterative discrete steps such that at the end each node has (almost) the same number of items. In diffusion load balancing nodes are only allowed to balance their load with their direct neighbors. We show three main results. Firstly, we present a general framework for randomly rounding the flow generated by continuous diffusion schemes over the edges of a graph in order to obtain corresponding discrete schemes. Compared to the results of Rabani, Sinclair, and Wanka, FOCS'98, which are only valid w.r.t. the class of homogeneous first order schemes, our framework can be used to analyze a larger class of diffusion algorithms, such as algorithms for heterogeneous networks and second order schemes. Secondly, we bound the deviation between randomized second order schemes and their continuous counterparts. Finally, we provide a bound for the minimum initial load in a network that is sufficient to prevent the occurrence of negative load at a node during the execution of second order diffusion schemes. Our theoretical results are complemented with extensive simulations on different graph classes. We show empirically that second order schemes, which are usually much faster than first order schemes, will not balance the load completely on a number of networks within reasonable time. However, the maximum load difference at the end seems to be bounded by a constant value, which can be further decreased if first order scheme is applied once this value is achieved by second order scheme.Comment: Full version of paper submitted to ICDCS 201

Performance controls for distributed telecommunication services

As the Internet and Telecommunications domains merge, open telecommunication service architectures such as TINA, PARLAY and PINT are becoming prevalent. Distributed Computing is a common engineering component in these technologies and promises to bring improvements to the scalability, reliability and flexibility of telecommunications service delivery systems. This distributed approach to service delivery introduces new performance concerns. As service logic is decomposed into software components and distnbuted across network resources, significant additional resource loading is incurred due to inter-node communications. This fact makes the choice of distribution of components in the network and the distribution of load between these components critical design and operational issues which must be resolved to guarantee a high level of service for the customer and a profitable network for the service operator. Previous research in the computer science domain has addressed optimal placement of components from the perspectives of minimising run time, minimising communications costs or balancing of load between network resources. This thesis proposes a more extensive optimisation model, which we argue, is more useful for addressing concerns pertinent to the telecommunications domain. The model focuses on providing optimal throughput and profitability of network resources and on overload protection whilst allowing flexibility in terms of the cost of installation of component copies and differentiation in the treatment of service types, in terms of fairness to the customer and profitability to the operator. Both static (design-time) component distribution and dynamic (run-time) load distribution algorithms are developed using Linear and Mixed Integer Programming techniques. An efficient, but sub-optimal, run-time solution, employing Market-based control, is also proposed. The performance of these algorithms is investigated using a simulation model of a distributed service platform, which is based on TINA service components interacting with the Intelligent Network through gateways. Simulation results are verified using Layered Queuing Network analytic modelling Results show significant performance gains over simpler methods of performance control and demonstrate how trade-offs in network profitability, fairness and network cost are possible

Consensus Algorithms for Estimation and Discrete Averaging in Networked Control Systems

In this thesis several topics on consensus and gossip algorithms for multi-agent systems are addressed. An agent is a dynamical system that can be fully described by a state-space representation of its dynamics. A multi-agent system is a network of agents whose pattern of interactions or couplings is described by a graph. Consensus problems in multi-agent systems consist in the study of local interaction rules between the agents such that as global emergent behavior the network converges to the so called "consensus" or "agreement" state where the value of each agent's state is the same and it is possibly a function of the initial network state, for instance the average. A consensus algorithm is thus a set of local interaction rules that solve the consensus problem under some assumptions on the network topology. A gossip algorithm is a set of local state update rules between the agents that, disregarding their objective, are supposed to be implemented in a totally asynchronous way between pairs of neighboring agents, thus resembling the act of "gossiping" in a crowd of people. In this thesis several algorithms based on gossip that solve the consensus and other related problems are presented. In the �first part, several solutions to the consensus problem based on gossip under different sets of assumptions are proposed. In the fi�rst case, it is assumed that the state of the agents is discretized and represents a collection of tasks of different size. In the second case, under the same discretization assumptions of the �rst case, it is assumed that the network is represented by a Hamiltonian graph and it is shown how under this assumption the convergence speed can be improved. In the third case, a solution for the consensus problem for networks represented by arbitrary strongly connected directed graphs is proposed, assuming that the state of the agents is a real number. In the fourth case, a coordinate-free consensus algorithm based on gossip is designed and applied to a network of vehicles able to sense the relative distance between each other but with no access to absolute position information or to a common coordinate system. The proposed algorithm is then used to build in a decentralized way a common reference frame for the network of vehicles. In the second part, a novel local interaction rule based on the consensus equation is proposed together with an algorithm to estimate in a decentralized way the spectrum of the Laplacian matrix that encodes the network topology. As emergent behavior, each agent's state oscillates only at frequencies corresponding to the eigenvalues of the Laplacian matrix thus mapping the spectrum estimation problem into a signal processing problem solvable using the Fourier Transform. It is further shown that the constant component of the emergent behavior in the frequency domain solves the consensus on the average problem. The spectrum estimation algorithm is then applied to leader-follower networks of mobile vehicles to infer in a decentralized way properties such as controllability, osservability and other topological features of the network such as its topology. Finally, a fault detection and recovery technique for sensor networks based on the so called motion-probes is presented to address the inherent lack of robustness against outlier agents in networks implementing consensus algorithms to solve the distributed averaging problem

A simple approach for adapting continuous load balancing processes to discrete settings

We consider the neighbourhood load balancing problem. Given a network of processors and an arbitrary distribution of tasks over the network, the goal is to balance load by exchanging tasks between neighbours. In the continuous model, tasks can be arbitrarily divided and perfectly balanced state can always be reached. This is not possible in the discrete model where tasks are non-divisible. In this paper we consider the problem in a very general setting, where the tasks can have arbitrary weights and the nodes can have different speeds. Given a continuous load balancing algorithm that balances the load perfectly in (Formula presented.) rounds, we convert the algorithm into a discrete version. This new algorithm is deterministic and balances the load in  (Formula presented.) rounds so that the difference between the average and the maximum load is at most (Formula presented.) , where d is the maximum degree of the network and  (Formula presented.) is the maximum weight of any task. For general graphs, these bounds are asymptotically lower compared to the previous results. The proposed conversion scheme can be applied to a wide class of continuous processes, including first and second order diffusion, dimension exchange, and random matching processes. For the case of identical tasks, we present a randomized version of our algorithm that balances the load up to a discrepancy of  (Formula presented.) provided that the initial load on every node is large enough.Hoda Akbari, Petra Berenbrink and Thomas Sauerwald work was supported by an NSERC Discovery Grant “Analysis of Randomized Algorithms”