1,111 research outputs found
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 and
provide a matching lower bound. For the general knapsack problem, we propose an
algorithm whose competitive ratio is shown to be that is significantly
better than the best known competitive ratio of for the knapsack
problem with the hard capacity constraint.Comment: To appear in IEEE INFOCOM 2018, April 2018, Honolulu H
A Model of Inter-Regional Trade in Grains with Storage
When there is spatial arbitrage between food markets, the price differential between the markets should equal the cost of transfer. This simple arbitrage rule has formed the basis of many empirical tests of the performance of developing countries’ food markets. Here, a more complex structure to regional food markets is hypothesised. By including commodity storage into a model of inter-regional trade, it is shown that, in an optimal dynamic program, trade is intermittent. The possibility of periods without trade casts doubt on the validity of using tests for correlation in market prices as indicators of market performance.Food markets, optimal control, storage, spatial equilibrium.
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
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