Percolation and Connectivity on the Signal to Interference Ratio Graph

A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater than a threshold. Assuming that the nodes of the wireless network are distributed as a Poisson point process (PPP), percolation (unbounded connected cluster) on the resulting SIR graph is studied as a function of the density of the PPP. For both the path-loss as well as path-loss plus fading model of signal propagation, it is shown that for a small enough threshold, there exists a closed interval of densities for which percolation happens with non-zero probability. Conversely, for the path-loss model of signal propagation, it is shown that for a large enough threshold, there exists a closed interval of densities for which the probability of percolation is zero. Restricting all nodes to lie in an unit square, connectivity properties of the SIR graph are also studied. Assigning separate frequency bands or time-slots proportional to the logarithm of the number of nodes to different nodes for transmission/reception is sufficient to guarantee connectivity in the SIR graph.Comment: To appear in the Proceedings of the IEEE Conference on Computer Communications (INFOCOM 2012), to be held in Orlando Florida Mar. 201

Online Knapsack Problem under Expected Capacity Constraint

Online knapsack problem is considered, where items arrive in a sequential fashion that have two attributes; value and weight. Each arriving item has to be accepted or rejected on its arrival irrevocably. The objective is to maximize the sum of the value of the accepted items such that the sum of their weights is below a budget/capacity. Conventionally a hard budget/capacity constraint is considered, for which variety of results are available. In modern applications, e.g., in wireless networks, data centres, cloud computing, etc., enforcing the capacity constraint in expectation is sufficient. With this motivation, we consider the knapsack problem with an expected capacity constraint. For the special case of knapsack problem, called the secretary problem, where the weight of each item is unity, we propose an algorithm whose probability of selecting any one of the optimal items is equal to $1-1/e$ and provide a matching lower bound. For the general knapsack problem, we propose an algorithm whose competitive ratio is shown to be $1/4e$ that is significantly better than the best known competitive ratio of $1/10e$ for the knapsack problem with the hard capacity constraint.Comment: To appear in IEEE INFOCOM 2018, April 2018, Honolulu H

Finite-Horizon Optimal Transmission Policies for Energy Harvesting Sensors

In this paper, we derive optimal transmission policies for energy harvesting sensors to maximize the utility obtained over a finite horizon. First, we consider a single energy harvesting sensor, with discrete energy arrival process, and a discrete energy consumption policy. Under this model, we show that the optimal finite horizon policy is a threshold policy, and explicitly characterize the thresholds, and the thresholds can be precomputed using a recursion. Next, we address the case of multiple sensors, with only one of them allowed to transmit at any given time to avoid interference, and derive an explicit optimal policy for this scenario as well.Comment: Appeared in IEEE ICASSP 201

Long term Throughput and Approximate Capacity of Transmitter-Receiver Energy Harvesting Channel with Fading

We first consider an energy harvesting channel with fading, where only the transmitter harvests energy from natural sources. We bound the optimal long term throughput by a constant for a class of energy arrival distributions. The proposed method also gives a constant approximation to the capacity of the energy harvesting channel with fading. Next, we consider a more general system where both the transmitter and the receiver employ energy harvesting to power themselves. In this case, we show that finding an approximation to the optimal long term throughput is far more difficult, and identify a special case of unit battery capacity at both the transmitter and the receiver for which we obtain a universal bound on the ratio of the upper and lower bound on the long term throughput.Comment: To appear in ICCS 2014, Macau in Nov. 201