D. Manjunath

On the connectivity in finite ad hoc networks

Connectivity and capacity analysis of ad hoc networks has usually focused on asymptotic results in the number of nodes in the network. In this letter we analyze finite ad hoc networks. With the standard assumption of uniform distribution of nodes in [0, z], z > 0, for a one-dimensional network, we obtain the exact formula for the probability that the network is connected. We then extend this result to find bounds for the connectivity in a two-dimensional network in [0, z]/sup 2/.

Routing and wavelength assignment in optical networks from edge disjoint path algorithms

Routing and wavelength assignment (RWA) problems in wavelength-routed optical networks are typically solved using a combination of integer programming and graph coloring. Such techniques are complex and make extensive use of heuristics. We explore an alternative solution technique in the well-known maximum edge disjoint paths (EDP) problem which can be naturally adapted to the RWA problem. Maximum EDP is NP-hard, but now it is known that simple greedy algorithms for it are as good as any of the more complex heuristic solutions. In this paper we investigate the performance of a simple greedy maximum edge disjoint paths algorithm applied to the RWA problem and compare it with a previously known solution method.

On Distributed Computation in Noisy Random Planar Networks

We consider distributed computation of functions of distributed data in random planar networks with noisy wireless links. We present a new algorithm for computation of the maximum value which is order optimal in the number of transmissions and computation time. We also adapt the histogram computation algorithm of Ying et al [1] to make the histogram computation time optimal.

On connectivity thresholds in superposition of random key graphs on random geometric graphs

In a random key graph (RKG) of n nodes each node is randomly assigned a key ring of K_n cryptographic keys from a pool of P_n keys. Two nodes can communicate directly if they have at least one common key in their key rings. We assume that the n nodes are distributed uniformly in [0, l]². In addition to the common key requirement, we require two nodes to also be within r_n of each other to be able to have a direct edge. Thus we have a random graph in which the RKG is superposed on the familiar random geometric graph (RGG). For such a random graph, we obtain tight bounds on the relation between K_n, P_n and r_n for the graph to be asymptotically almost surely connected.

Data Delivery Properties of Human Contact Networks

Pocket Switched Networks take advantage of social contacts to opportunistically create data paths over time. This work employs empirical traces to examine the effect of the human contact process on data delivery in such networks. The contact occurrence distribution is found to be highly uneven: contacts between a few node pairs occur too frequently, leading to inadequate mixing in the network, while the majority of contacts occur rarely, but are essential for global connectivity. This distribution of contacts leads to a significant variation in the fraction of node pairs that can be connected over time windows of similar duration. Good time windows tend to have a large clique of nodes that can all reach each other. It is shown that the clustering coefficient of the contact graph over a time window is a good predictor of achievable connectivity. We then examine all successful paths found by flooding and show that though delivery times vary widely, randomly sampling a small number of paths between each source and destination is sufficient to yield a delivery time distribution close to that of flooding over all paths. This result suggests that the rate at which the network can deliver data is remarkably robust to path failures.

The queueing network analysis tool (QNAT)

In this paper we describe QNAT, a software tool developed at Indian Institute of Technology, Kanpur, India, for the analysis and simulation of queueing networks. Arbitrary configurations of open or closed networks of multi-server queues with infinite or finite capacity, fork-join queues with or without synchronization queues can be analyzed or simulated using QNAT. Queueing Networks with multiple classes of customers mall be specified with each class being a closed or an open class independently if there are finite capacity queues in the system, the type of blocking mechanism-transfer, repetitive service or rejection, can also be specified. For the applications where the accuracy of the results is important, an option to simulate the network is also provided. QNAT has proved to be a useful tool for the design of telecommunication systems, computer networks, modeling of industrial systems, design of banking systems, teaching courses and research on queueing theory etc. QNAT is a user-friendly analysis tool, developed with a Windows based Graphical User Interface (GUI). Mathematica forms the computing platform for QNAT due to its ability to perform symbolic computation.

On distributed function computation in structure-free random networks

We consider in-network computation of MAX in a structure-free random multihop wireless network. Nodes do not know their relative or absolute locations and use the Aloha MAC protocol. For one-shot computation, we describe a protocol in which the MAX value becomes available at the origin in O(radicn/ log n) slots with high probability. This is within a constant factor of that required by the best coordinated protocol. A minimal structure (knowledge of hop-distance from the sink) is imposed on the network and with this structure, we describe a protocol for pipelined computation of MAX that achieves a rate of Omega(1/(log2 n)).

Load balancing via random local search in closed and open systems

In this paper, we analyze the performance of random load resampling and migration strategies in parallel server systems. Clients initially attach to an arbitrary server, but may switch servers independently at random instants of time in an attempt to improve their service rate. This approach to load balancing contrasts with traditional approaches where clients make smart server selections upon arrival (e.g., Join-the-Shortest-Queue policy and variants thereof). Load resampling is particularly relevant in scenarios where clients cannot predict the load of a server before being actually attached to it. An important example is in wireless spectrum sharing where clients try to share a set of frequency bands in a distributed manner. We first analyze the natural Random Local Search (RLS) strategy. Under this strategy, after sampling a new server randomly, clients only switch to it if their service rate is improved. In closed systems, where the client population is fixed, we derive tight estimates of the time it takes under RLS strategy to balance the load across servers. We then study open systems where clients arrive according to a random process and leave the system upon service completion. In this scenario, we analyze how client migrations within the system interact with the system dynamics induced by client arrivals and departures. We compare the load-aware RLS strategy to a load-oblivious strategy in which clients just randomly switch server without accounting for the server loads. Surprisingly, we show that both load-oblivious and load-aware strategies stabilize the system whenever this is at all possible. We further demonstrate, using large-system asymptotics, that the average client sojourn time under the load-oblivious strategy is not considerably reduced when clients apply smarter load-aware strategies.

Control and management plane in a multi-stage software router architecture

Software routers based on personal computer (PC) architectures are receiving increasing attention in the research community. However, a router based on a single PC suffers from limited bus and central processing unit (CPU) bandwidth, high memory access latency, limited scalability in terms of number of network interface cards, and lack of resilience mechanisms. Multi-stage architectures created by interconnecting several PCs are an interesting alternative since they allow to i) increase the performance of single-software routers, ii) scale router size, iii) distribute packet-forwarding and control functionalities, iv) recover from single-component failures, and v) incrementally upgrade router performance. However, a crucial issue is to hide the internal details of the interconnected architecture so that the architecture behaves externally as a single router, especially when considering the control and the management plane. In this paper, we describe a control protocol for a previously proposed multi-stage architecture based on PC interconnection. The protocol permits information exchange among internal PCs to support: i) configuration of the interconnected architecture, ii) packet forwarding, iii) routing table distribution, iv) management of the internal devices. The protocol is operating system independent, since it interacts with software routing suites such as Quagga and Xorp, and it is under test in our labs on a small-scale prototype of the multi-stage router.

Traffic management and resource allocation in small wired/wireless networks

We consider the problem of traffic management in small networks with both wireless and wired devices, connected to the Internet through a single gateway. Examples of such networks are small office networks or residential networks, where typically traffic management is limited to flow prioritization through port-based filtering. We propose a practical resource allocation framework that provides simple mechanisms to applications and users to enable traffic management functionality currently not present due to the distributed nature of the system and various technology or protocol limitations. To allow for control irrespective of whether traffic flows cross wireless, wired or even broadband links, the proposed framework jointly optimizes rate allocations across wireless and wired devices in a weighted fair manner. Additionally, we propose a model for estimating the achievable capacity regions in wireless networks. This model is used by the controller to achieve a specific rate allocation. We evaluate a decentralized, host-based implementation of the proposed framework. The controller is incrementally deployable by not requiring modifications to existing network protocols and equipment or the wireless MAC. Using analytical methods and experimental results with realistic traffic, we show that our controller is stable with fast convergence for both UDP and TCP traffic, achieves weighted fairness, and mitigates scheduling inefficiencies of the existing hardware.