The uncertainty in user locations and channel conditions makes the deployment and performance analysis of wireless networks challenging. stochastic geometry has emerged as a powerful tool for analyzing the performance...
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The uncertainty in user locations and channel conditions makes the deployment and performance analysis of wireless networks challenging. stochastic geometry has emerged as a powerful tool for analyzing the performance of wireless networks, assuming certain stochastic models for the distribution of both users and base stations (BSs). In this letter, seeking further precision, we derive the downlink rate coverage probability of a wireless network with deterministically known BS locations. Then, we use this result to optimize the placement of BSs while keeping the downlink rate coverage probability above a certain threshold.
We consider a class of packing problems with uncertain data, which we refer to as the chance-constrained binary packing problem. In this problem, a subset of items is selected that maximizes the total profit so that a...
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We consider a class of packing problems with uncertain data, which we refer to as the chance-constrained binary packing problem. In this problem, a subset of items is selected that maximizes the total profit so that a generic packing constraint is satisfied with high probability. Interesting special cases of our problem include chance-constrained knapsack and set packing problems with random coefficients. We propose a problem formulation in its original space based on the so-called probabilistic covers. We focus our solution approaches on the special case in which the uncertainty is represented by a finite number of scenarios. In this case, the problem can be formulated as an integer program by introducing a binary decision variable to represent feasibility of each scenario. We derive a computationally efficient coefficient strengthening procedure for this formulation, and demonstrate how the scenario variables can be efficiently projected out of the linear programming relaxation. We also study how methods for lifting deterministic cover inequalities can be leveraged to perform approximate lifting of probabilistic cover inequalities. We conduct an extensive computational study to illustrate the potential benefits of our proposed techniques on various problem classes.
Using results from parametric optimization, we derive for chance-constrainedstochastic programs quantitative stability properties for locally optimal values and sets of local minimizers when the underlying probabilit...
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Using results from parametric optimization, we derive for chance-constrainedstochastic programs quantitative stability properties for locally optimal values and sets of local minimizers when the underlying probability distribution is subjected to perturbations in a metric space of probability measures. Emphasis is placed on verifiable sufficient conditions for the constraint-set mapping to fulfill a Lipschitz property which is essential for the stability results. Both convex and nonconvex problems are investigated. For a chance-constrained model of power dispatch, where the power demand enters as a random vector with incompletely known probability distribution, we discuss consequences of our general results for the stability of optimal generation costs and optimal generation policies.
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