arXiv subjects

Luis Guijarro

Publications and source records attributed to Luis Guijarro.

At least 19 recordsLinked to original sources

arXiv2026

Economic feasibility of virtual operators in 5G via network slicing

The provision of services by more than one operator over a common network infrastructure, as enabled by 5G network slicing, is analyzed. Two business models to be implemented by a network operator, who owns the network, and a virtual operator, who does not, are proposed. In one business model, named \emph{strategic}, the network operator provides service to its user base and the virtual operator provides service to its user base and pays a per-subscriber fee to the network operator. In the other business model, named \emph{monopolistic}, the network operator provides service to both user bases. The two proposals are analyzed by means of a model that captures both system and economic features. As regards the systems features, the slicing of the network is modeled by means of a Discriminatory Processor Sharing queue. As regards the economic features, the incentives are modeled by means of the user utilities and the operators' revenues; and game theory is used to model the strategic interaction between the users' subscription decision and the operators' pricing decision. In both business models, it is shown that the network operator can be provided with the appropriate economic incentives so that it acquiesces in serving the virtual operator's user base (monopolistic model) and in allowing the virtual operator to provide service over the network operator's infrastructure (strategic model). From the point of view of the users, the strategic model results in a higher subscription rate than the monopolistic model.

cs.NI↗

arXiv2026

Energy-Based Cell Association in Nonuniform Renewable Energy-Powered Cellular Networks: Analysis and Optimization of Carbon Efficiency

The increasing global push for carbon reduction highlights the importance of integrating renewable energy into the supply chain of cellular networks. However, due to the stochastic nature of renewable energy generation and the uneven load distribution across base stations, the utilization rate of renewable energy remains low. To address these challenges, this paper investigates the trade-off between carbon emissions and downlink throughput in cellular networks, offering insights into optimizing both network performance and sustainability. The renewable energy state of base station batteries and the number of occupied channels are modeled as a quasi-birth-death process. We construct models for the probability of channel blocking, average successful transmission probability for users, downlink throughput, carbon emissions, and carbon efficiency based on stochastic geometry. Based on these analyses, an energy-based cell association scheme is proposed to optimize the carbon efficiency of cellular networks. The results show that, compared to the closest cell association scheme, the energy-based cell association scheme is capable of reducing the carbon emissions of the network by 13.0% and improving the carbon efficiency by 11.3%.

eess.SP↗

arXiv2026

A user subscription model in mobile radio access networks with network slicing

Network slicing is an architectural enabling technology that logically decouples the current cellular networks into infrastructure providers (InPs) and Network Slice Tenants (NSTs). The network resources (e.g., radio access resources at each cell) are owned by the InP, and are shared by the NSTs to provide a service to their mobile users. In this context, we proposed a business model that includes resource allocation and user subscription to NSTs in a competitive setting, and provides, among other things, closed-form expressions for the subscription indicators in equilibrium of each NST at each cell. This model relies on the widely adopted logit model to characterize user subscriptions. However, as a consequence of user mobility and radio propagation, some of the underlying assumptions in the logit model do not hold. Therefore, further research is needed to assess the accuracy of the results provided by the logit model in a mobile radio scenario. We carry out a thorough evaluation of the validity of the model by comparing its results against those obtained through computer simulation. Our simulation model includes complete and realistic characterizations of user mobility and radio propagation. From the results, we conclude in most cases the logit model provides valid results in a mobile radio scenario.

cs.NI↗

arXiv2025

Policy Gradient Algorithms for Age-of-Information Cost Minimization

Recent developments in cyber-physical systems have increased the importance of maximizing the freshness of the information about the physical environment. However, optimizing the access policies of Internet of Things devices to maximize the data freshness, measured as a function of the Age-of-Information (AoI) metric, is a challenging task. This work introduces two algorithms to optimize the information update process in cyber-physical systems operating under the generate-at-will model, by finding an online policy without knowing the characteristics of the transmission delay or the age cost function. The optimization seeks to minimize the time-average cost, which integrates the AoI at the receiver and the data transmission cost, making the approach suitable for a broad range of scenarios. Both algorithms employ policy gradient methods within the framework of model-free reinforcement learning (RL) and are specifically designed to handle continuous state and action spaces. Each algorithm minimizes the cost using a distinct strategy for deciding when to send an information update. Moreover, we demonstrate that it is feasible to apply the two strategies simultaneously, leading to an additional reduction in cost. The results demonstrate that the proposed algorithms exhibit good convergence properties and achieve a time-average cost within 3% of the optimal value, when the latter is computable. A comparison with other state-of-the-art methods shows that the proposed algorithms outperform them in one or more of the following aspects: being applicable to a broader range of scenarios, achieving a lower time-average cost, and requiring a computational cost at least one order of magnitude lower.

cs.NI↗

arXiv2025

Entry deterrence by exploiting economies of scope in data aggregation

We model a market for data where an incumbent and a challenger compete for data from a producer. The incumbent has access to an exclusive data producer, and it uses this exclusive access, together with economies of scope in the aggregation of the data, as a strategy against the potential entry by the challenger. We assess the incumbent incentives to either deter or accommodate the entry of the challenger. We show that the incumbent will accommodate when the exclusive access is costly and when the economies of scope are low, and it will blockade or deter otherwise. The results would justify an access regulation that incentivizes the entry of the challenger, e.g., by increasing production costs for the exclusive data.

econ.TH↗

arXiv2024

Economics of Integrated Sensing and Communication service provision in 6G networks

In Beyond5G and 6G networks, a common theme is that sensing will play a more significant role than ever before. Over this trend, Integrated Sensing and Communications (ISAC) is focused on unifying the sensing functionalities and the communications ones and to pursue direct tradeoffs between them as well as mutual performance gains. We frame the resource tradeoff between the SAC functionalities within an economic setting. We model a service provision by one operator to the users, the utility of which is derived from both SAC functionalities. The tradeoff between the resources that the operator assigns to the SAC functionalities is analyzed from the point of view of the service prices, quantities and profits. We demonstrate that equilibrium quantities and prices exist. And we provide relevant recommendations for enforcing regulatory limits of both power and bandwidth.

cs.NI↗

arXiv2024

Competitive advantage of URLLC vs. eMBB for supporting timeliness-relevant services

5G specifications promise a common and flexible-enough network infrastructure capable of satisfying diverse requirements of both current and future use cases. Two service types standardized in 5G are eMBB, without stringent delay guarantee, and URLLC, with stringent delay guarantee. We focus on a use case where data timeliness is the relevant quality parameter. We provide an economic rationale for the support of data-based services, that is, from the point of view of the profits attained by the service providers and operators (SP). More specifically, we focus on data-based services the quality of which is related to the Age of Information, and we assess two alternatives for the support of this sort of services by means of a 5G network: one that is based on the eMBB service type, and one that is based on the URLLC service type. These assessment is conducted in a duopoly scenario. We conclude that URLLC support provides a competitive advantage to an SP against a competitor SP that supports its service offering on eMBB. And that there is a slightly better situation for the users when the URLLC QoS constraint is stringent.

cs.NI↗

arXiv2024

Homogenization on parallelizable Riemannian manifolds

We consider the problem of finding the homogenization limit of oscillating linear elliptic equations on an arbitrary parallelizable manifold $(M,g,Γ)$. We replicate the concept of two-scale convergence by pulling back tensors $T$ defined on the torus bundle $\mathbb{T}M$ to $M$. The process consist of two steps: localization in the slow variable through Voronoi domains, and inducing local periodicity in the fast variable from the local exponential map in combination with the geometry of the torus bundle. The procedure yields explicit cell formulae for the homogenization limit and as a byproduct a theory of two-scale convergence of tensors of arbitrary order.

math.AP↗

arXiv2024

ISP pricing and Platform pricing interaction under net neutrality

We analyze the effects of enforcing vs. exempting access ISP from net neutrality regulations when platforms are present and operate two-sided pricing in their business models. This study is conducted in a scenario where users and Content Providers (CPs) have access to the internet by means of their serving ISPs and to a platform that intermediates and matches users and CPs, among other service offerings. Our hypothesis is that platform two-sided pricing interacts in a relevant manner with the access ISP, which may be allowed (an hypothetical non-neutrality scenario) or not (the current neutrality regulation status) to apply two-sided pricing on its service business model. We preliminarily conclude that the platforms are extracting surplus from the CPs under the current net neutrality regime for the ISP, and that the platforms would not be able to do so under the counter-factual situation where the ISPs could apply two-sided prices.

econ.TH↗

arXiv2023

Decompositions of three-dimensional Alexandrov spaces

We extend basic results in $3$-manifold topology to general three-dimensional Alexandrov spaces (or Alexandrov $3$-spaces for short), providing a unified framework for manifold and non-manifold spaces. We generalize the connected sum to non-manifold $3$-spaces and prove a prime decomposition theorem, exhibit an infinite family of closed, prime non-manifold $3$-spaces which are not irreducible, and establish a conjecture of Mitsuishi and Yamaguchi on the structure of closed, simply-connected Alexandrov $3$-spaces with non-negative curvature. Additionally, we define a notion of generalized Dehn surgery for Alexandrov $3$-spaces and show that any closed Alexandrov $3$-space may be obtained by performing generalized Dehn surgery on a link in $S^3$ or the non-trivial $S^2$-bundle over $S^1$. As an application of this result, we show that every closed Alexandrov $3$-space is homeomorphic to the boundary of a $4$-dimensional Alexandrov space.

math.GT↗

arXiv2023

Topological Data Analysis in Air Traffic Management: the shape of big flight data sets

Analyzing flight trajectory data sets poses challenges due to the intricate interconnections among various factors and the high dimensionality of the data. Topological Data Analysis (TDA) is a way of analyzing big data sets focusing on the topological features this data sets have as point clouds in some metric space. Techniques as the ones that TDA provides are suitable for dealing with high dimensionality and intricate interconnections. This paper introduces TDA and its tools and methods as a way to derive meaningful insights from ATM data. Our focus is on employing TDA to extract valuable information related to airports. Specifically, by utilizing persistence landscapes (a potent TDA tool) we generate footprints for each airport. These footprints, obtained by averaging over a specific time period, are based on the deviation of trajectories and delays. We apply this method to the set of Spanish' airports in the Summer Season of 2018. Remarkably, our results align with the established Spanish airport classification and raise intriguing questions for further exploration. This analysis serves as a proof of concept, showcasing the potential application of TDA in the ATM field. While previous works have outlined the general applicability of TDA in aviation, this paper marks the first comprehensive application of TDA to a substantial volume of ATM data. Finally, we present conclusions and guidelines to address future challenges in the ATM domain.

math.AT↗

arXiv2022

Upper and lower bounds on the filling radius

We give a curvature dependent lower bound for the filling radius of all closed Riemannian manifolds as well as an upper one for manifolds which are the total space of a Riemannian submersion. The latter applies also to the case of submetries. We also see that the reach (in the sense of Federer) of the image of the Kuratowski embedding vanishes, and we finish by giving some inequalities involving the k-intermediate filling radius.

math.DG↗

arXiv2022

Basic Metric Geometry of the Bottleneck Distance

Given a metric pair $(X,A)$, i.e. a metric space $X$ and a distinguished closed set $A \subset X$, one may construct in a functorial way a pointed pseudometric space $\mathcal{D}_\infty(X,A)$ of persistence diagrams equipped with the bottleneck distance. We investigate the basic metric properties of the spaces $\mathcal{D}_\infty(X,A)$ and obtain characterizations of their metrizability, completeness, separability, and geodesicity.

math.MG↗

arXiv2021

Metric Geometry of Spaces of Persistence Diagrams

Persistence diagrams are objects that play a central role in topological data analysis. In the present article, we investigate the local and global geometric properties of spaces of persistence diagrams. In order to do this, we construct a family of functors $\mathcal{D}_p$, $1\leq p \leq\infty$, that assign, to each metric pair $(X,A)$, a pointed metric space $\mathcal{D}_p(X,A)$. Moreover, we show that $\mathcal{D}_{\infty}$ is sequentially continuous with respect to the Gromov-Hausdorff convergence of metric pairs, and we prove that $\mathcal{D}_p$ preserves several useful metric properties, such as completeness and separability, for $p \in [1,\infty)$, and geodesicity and non-negative curvature in the sense of Alexandrov, for $p=2$. For the latter case, we describe the metric of the space of directions at the empty diagram. We also show that the Fr\'echet mean set of a Borel probability measure on $\mathcal{D}_p(X,A)$, $1\leq p \leq\infty$, with finite second moment and compact support is non-empty. As an application of our geometric framework, we prove that the space of Euclidean persistence diagrams, $\mathcal{D}_{p}(\mathbb{R}^{2n},\Delta_n)$, $1\leq n$ and $1\leq p<\infty$, has infinite covering, Hausdorff, asymptotic, Assouad, and Assouad-Nagata dimensions.

math.MG↗

arXiv2020

Bounded distance geodesic foliations in Riemannian planes

A conjecture of Burns and Knieper asks whether a 2-plane with a metric without conjugate points, and with a geodesic foliation whose lines are at bounded Hausdorff distance, is necessarily flat. We prove this conjecture in two cases: under the hypothesis that the plane admits total curvature, and under the hypothesis of visibility at some point. Along the way, we show that all geodesic line foliations on a Riemannian 2-plane must be homeomorphic to the standard one.

math.DG↗

arXiv2020

A softer connectivity principle

We give soft, quantitatively optimal extensions of the classical Sphere Theorem, Wilking's connectivity principle and Frankel's Theorem to the context of ${k}$-th Ricci curvature. The hypotheses are soft in the sense that they are satisfied on sets of metrics that are open in the $C^{2}$-topology.

math.DG↗

arXiv2019

Competition between service providers with strategic resource allocation: application to network slicing

We propose and analyze a business model for 5G operators. Each operator is entitled to a share of a network operated by an Infrastructure Provider (InP) and use network slicing mechanisms to request network resources as needed for service provision. The network operators become Network Slice Tenants (NSTs). The InP performs the resource allocation based on a vector of weights chosen strategically by each NST. The weights distribute the NST's share of resources between its subscribers in each cell. We propose a strategy profile in which the NST chooses weights equal to the product of its share by the ratio between the total number of subscribers in the cell and the total number of subscribers in the network. We characterize the proposed solution in terms of subscription ratios and fractions of subscribers, for different cell capacities and user sensitivities. The proposed solution provides the exact values for the Nash equilibrium if the cells are homogeneous in terms of normalized capacity, which is a measure of the total amount of resources available in the cell. Otherwise, if the cells are heterogeneous, it provides an accurate approximation. We quantify the deviation from the equilibrium and conclude that it is highly accurate.

cs.NI↗

arXiv2019

Restrictions on Submanifolds via Focal Radius Bounds

We give an optimal estimate for the norm of any submanifold's second fundamental form in terms of its focal radius and the lower sectional curvature bound of the ambient manifold. This is a special case of a similar theorem for intermediate Ricci curvature, and leads to a $C^{1,α}$ compactness result for submanifolds, as well as a "soul-type" structure theorem for manifolds with nonnegative $k^{th}$--intermediate Ricci curvature that have a closed submanifold with dimension $\geq k$ and infinite focal radius. To prove these results, we use the comparison lemma for Jacobi fields from arXiv:1603.04050 that exploits Wilking's transverse Jacobi equation. The comparison lemma also yields new information about group actions, Riemannian submersions, and submetries, including generalizations to intermediate Ricci curvature of results of Chen and Grove.

math.DG↗