Virag Shah

Splitting algorithms for fast relay selection: Generalizations, analysis, and a unified view

Relay selection for cooperative communications promises significant performance improvements, and is, therefore, attracting considerable attention. While several criteria have been proposed for selecting one or more relays, distributed mechanisms that perform the selection have received relatively less attention. In this paper, we develop a novel, yet simple, asymptotic analysis of a splitting-based multiple access selection algorithm to find the single best relay. The analysis leads to simpler and alternate expressions for the average number of slots required to find the best user. By introducing a new `contention load¿ parameter, the analysis shows that the parameter settings used in the existing literature can be improved upon. New and simple bounds are also derived. Furthermore, we propose a new algorithm that addresses the general problem of selecting the best Q ¿ 1 relays, and analyze and optimize it. Even for a large number of relays, the scalable algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. We also propose a new and simple scheme for the practically relevant case of discrete metrics. Altogether, our results develop a unifying perspective about the general problem of distributed selection in cooperative systems and several other multi-node systems.

Performance evaluation and asymptotics for Content Delivery Networks.

Large scale Content Delivery Networks (CDNs) are one of the key components of todays information infrastructure. This paper proposes and analyzes a simple stochastic model for a file-server system wherein servers can work together, as a pooled resource, to meet individual user requests. In such systems basic questions include: How and where to replicate files? What is the impact of dynamic service allocation across request types, and whether it can provide substantial gains over simpler load balancing policies? What are tradeoffs amongst performance, reliability and recovery costs, and energy? The paper provides both explicit and asymptotic approximations for large systems towards addressing these basic questions.

Network flows for functions

We consider in-network computation of an arbitrary function over an arbitrary communication network. A network with capacity constraints on the links is given. Some nodes in the network generate data, e.g., sensor nodes in a sensor network. An arbitrary function of this distributed data is to be obtained at a terminal node. The structure of the function is described by a given computation schema, which in turn is represented by a directed tree. We define a new notion of conservation of flow suitable in this setup and design computing and communicating schemes to obtain the function at the terminal at the maximum rate. For this, we formulate linear programs to determine network flows that maximize the computation rate. Our approach introduces the network flow techniques to the distributed function computation setup where such a scope was hitherto unsuspected due to the lack of traditional conservation of flow.

Analysis, Insights and Generalization of a Fast Decentralized Relay Selection Mechanism

Relay selection for cooperative communications has attracted considerable research interest recently. While several criteria have been proposed for selecting one or more relays and analyzed, mechanisms that perform the selection in a distributed manner have received relatively less attention. In this paper, we analyze a splitting algorithm for selecting the single best relay amongst a known number of active nodes in a cooperative network. We develop new and exact asymptotic analysis for computing the average number of slots required to resolve the best relay. We then propose and analyze a new algorithm that addresses the general problem of selecting the best Q ≥ 1 relays. Regardless of the number of relays, the algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. Our analysis also brings out an intimate relationship between multiple access selection and multiple access control algorithms.

High-performance centralized content delivery infrastructure: models and asymptotics

We consider a centralized content delivery infrastructure where a large number of storage-intensive files are replicated across several collocated servers. To achieve scalable mean delays in file downloads under stochastic loads, we allow multiple servers to work together as a pooled resource to meet individual download requests. In such systems, basic questions include: How and where to replicate files? What is the impact of dynamic service allocation across request types, and whether such allocations can provide substantial gains over simpler load balancing policies? What are tradeoffs among performance, reliability and recovery costs, and energy? This paper provides a simple performance model for large systems towards addressing these basic questions.

Performance of a Fast, Distributed Multiple Access Based Relay Selection Algorithm Under Imperfect Statistical Knowledge

Cooperative wireless systems can exploit spatial diversity by opportunistically selecting the best relay to forward data to a destination. However, determining the best relay is a challenging task and requires a selection algorithm because the relays are geographically separated and only have local channel knowledge. Selecting the best relay is equivalent to finding the relay with the largest metric, where each relay computes its metric using local channel knowledge. We analyze the performance of a fast, distributed, and scalable multiple access based selection algorithm when it assumes incorrect values for two fundamental parameters that it requires to operate efficiently - the number of available relays and the cumulative distribution function (CDF) of the metrics. Such imperfect knowledge will invariably arise in practice. We develop new expressions for the time required to select the best relay as a function of the assumed and actual parameters. We show that imperfect knowledge can significantly slow down the selection algorithm. Further, in a system that uses its observations to update its CDF estimate, we determine the minimum number of observations required to limit the performance degradation. We also develop a minimax formulation that makes the algorithm robust to uncertainties in the number of relays in the system.

Asymptotic independence of servers' activity in queueing systems with limited resource pooling

We consider multi-class multi-server queuing systems where a subset of servers, called a server pool, may collaborate in serving jobs of a given class. The pools of servers associated with different classes may overlap, so the sharing of server resources across classes is done via a dynamic allocation policy based on a fairness criterion. We consider an asymptotic regime where the total load increases proportionally with the system size. We show that under limited scaling in size of server pools the stationary distribution for activity of a fixed finite subset of servers has asymptotically a product form, which in turn implies a concentration result for server activity. In particular, we establish a clear connection between the scaling of server pools’ size and asymptotic independence. Further, these results are robust to the service requirement distribution of jobs. For large-scale cloud systems where heterogeneous pools of servers collaborate in serving jobs of diverse classes, a concentration in server activity indicates that the overall power and network capacity that need to be provisioned may be substantially lower than the worst case, thus reducing costs.

Impact of fairness and heterogeneity on delays in large-scale centralized content delivery systems

We consider multiclass queueing systems where the per class service rates depend on the network state, fairness criterion, and is constrained to be in a symmetric polymatroid capacity region. We develop new comparison results leading to explicit bounds on the mean service time under various fairness criteria and possibly heterogeneous loads. We then study large-scale systems with a growing number of service classes n (for example, files),

On optimal timer-based distributed selection for rate-adaptive multi-user diversity systems

m = \left\lceil {bn} \right\rceil