arXiv subjects

Tijani Chahed

Publications and source records attributed to Tijani Chahed.

At least 19 recordsLinked to original sources

arXiv2026

Stochastic Multi-Robot Monitoring on Graphs under Markovian Mobility

We study a stochastic multi-robot monitoring problem on a connected graph $G=(V,E)$, where each robot moves according to a Markov chain on $G$ and monitors the closed neighborhood of its current vertex. The performance of $r$ robots is evaluated in steady state via two objectives: average-case coverage (the expected number of covered vertices) and worst-case coverage (the minimum coverage probability over all vertices). We consider three models: independent homogeneous strategies, where all robots share the same stationary distribution; independent heterogeneous strategies, where robots use different stationary distributions; and centralized strategies, allowing arbitrary correlations between robot locations. For the heterogeneous model, we prove that maximizing average coverage is NP-hard even for two robots, and that replicating an easy-to-compute optimal homogeneous strategy yields a $\left(1-\left(1-\frac{1}{r}\right)^r\right)$-approximation for both objective functions in the heterogeneous setting; moreover, no polynomial-time algorithm can achieve a ratio better than $1-\nicefrac{1}{e}$ unless $\text{P}=\text{NP}$. Centralized strategies can exploit correlations to reduce redundancy. We develop a hierarchy of approximation factors: for any positive integer $r'\le r$, writing $r=hr'+b$ with $0\le b<r'$, block coordination yields a $1-\left(1-\frac{r'}{r}\right)^h\left(1-\frac{b}{r}\right)$ approximation for both objectives. We also establish NP-hardness and a tight $1-\nicefrac{1}{e}$ inapproximability bound. Moreover, we prove diminishing-returns properties with respect to the number of robots: a non-increasing-ratio property holds for the average-case objective in all settings, but not for the heterogeneous worst-case objective.

cs.DS↗

arXiv2026

From Individual to Shared Ownership: A Coalitional Game Approach to Sustainable Co-investment

This paper proposes a cooperative game-theoretic framework for sustainable co-investment in shared infrastructure under regulatory incentives. Multiple heterogeneous operators co-invest in a common infrastructure whose production capability evolves over time and is subject to operational variability. A regulator supports the deployment through incentive mechanisms designed to align individual economic investment objectives with the coalitional one. We formulate the co-investment problem as a transferable-utility (TU) coalitional game in which the value generated by cooperation depends on heterogeneous operational profiles, dynamic resource availability, investment costs, and regulatory incentive level. We show that the proposed coalitional game can be reformulated as a linear production game (LPG), whose dual prices yield a constructive and stable allocation of the cooperative surplus. Finally, we illustrate the proposed framework through a case study on co-investment among data center operators in shared renewable energy infrastructure, supported by government subsidies promoting renewable energy consumption.

cs.GT↗

arXiv2026

Shared Infrastructure Investment and Pricing: Stackelberg Equilibria in Risk-Aware Take-or-Pay Contracts

We study a shared infrastructure deployed by an Infrastructure Provider (InP) and used by multiple firms generating revenues through resource usage. We focus on a challenging setting where (i) infrastructure deployment requires substantial upfront investment, which the InP recovers via payments by firms that depend on their uncertain future revenues; (ii) firms' resource usage is jointly influenced by exogenous factors, infrastructure pricing, operational costs, and resource congestion; and (iii) firms exhibit heterogeneous risk aversion. These aspects are typical of emerging technologies, such as Mobile Edge Computing (MEC). Yet, their joint effect on the InP's capacity dimensioning and pricing decisions and the firms' usage commitments remains poorly understood. We establish conditions for the uniqueness of the equilibrium among the firms. We do so by introducing a Stackelberg game with risk-aware take-or-pay contracting and firm-side operational and congestion costs, in which the InP acts as the leader, while firms act as followers that share the infrastructure and commit upfront to future resource usage under uncertain revenues. Followers' heterogeneous risk aversion is modeled through Conditional Value-at-Risk (CVaR). We prove the existence of a Stackelberg equilibrium (SE), in which the followers' decisions constitute a generalized Nash equilibrium, and develop a polynomial-time algorithm that boundedly approximates the SE. We derive a lower bound on the followers' Probability of Profit (PoP). Simulations in a realistic MEC scenario show that higher followers' risk aversion reduces capacity, pricing, and leader profit, while increasing the lower bound on PoP.

cs.GT↗

arXiv2026

Continuity of VaR and Continuous Differentiability of CVaR under Decision-Dependent Losses

Value-at-risk (VaR) and conditional value-at-risk (CVaR) are widely used in risk-aware optimization and equilibrium models. When the loss depends on a decision variable, the induced distribution, the VaR threshold, and the CVaR tail set all change with the decision. This makes the regularity of the VaR and CVaR maps nontrivial. We give simple sufficient conditions under which the VaR map is continuous and the corresponding CVaR map is continuously differentiable. The assumptions are local around the VaR level and rely on dominated pathwise differentiability of the scenario-wise loss. We also derive the CVaR gradient formula, thereby justifying first-order analysis for decision-dependent tail-risk models.

cs.GT↗

arXiv2026

Constrained Online Convex Optimization with Memory and Predictions

We study Constrained Online Convex Optimization with Memory (COCO-M), where both the loss and the constraints depend on a finite window of past decisions made by the learner. This setting extends the previously studied unconstrained online optimization with memory framework and captures practical problems such as the control of constrained dynamical systems and scheduling with reconfiguration budgets. For this problem, we propose the first algorithms that achieve sublinear regret and sublinear cumulative constraint violation under time-varying constraints, both with and without predictions of future loss and constraint functions. Without predictions, we introduce an adaptive penalty approach that guarantees sublinear regret and constraint violation. When short-horizon and potentially unreliable predictions are available, we reinterpret the problem as online learning with delayed feedback and design an optimistic algorithm whose performance improves as prediction accuracy improves, while remaining robust when predictions are inaccurate. Our results bridge the gap between classical constrained online convex optimization and memory-dependent settings, and provide a versatile learning toolbox with diverse applications.

cs.LG↗

arXiv2025

Co-Investment in Mobile Edge Computing with Infrastructure Update and Dynamic Participation

Mobile Edge Computing (MEC) requires Network Operators (NOs) to undertake substantial infrastructure investments, while most revenues are captured by Service Providers (SPs) offering end-user applications. This cost-revenue imbalance discourages NOs from investing in MEC deployment, despite increasing demand for low-latency and bandwidth-intensive services. This paper proposes a co-investment scheme in which players, i.e., one NO and multiple SPs, jointly deploy, maintain, and share MEC infrastructure over multiple decision epochs. We devise a new coalitional game model that captures the planning of resources, their allocation among players, and cost and revenue sharing. To address fluctuating user demand and evolving participation incentives, we design a mechanism that updates resources and allows the dynamic entrance and exit of players over time. We sustain cooperation through a compensation scheme. Numerical results show that combining resource updates with dynamic participation increases the total payoff and strengthens the NO's incentive to invest.

cs.GT↗

arXiv2025

Co-Investment under Revenue Uncertainty Based on Stochastic Coalitional Game Theory

The introduction of new services, such as Mobile Edge Computing (MEC), requires a massive investment that cannot be assumed by a single stakeholder, for instance the Infrastructure Provider (InP). Service Providers (SPs) however also have an interest in the deployment of such services. We hence propose a co-investment scheme in which all stakeholders, i.e., the InP and the SPs, form the so-called grand coalition composed of all the stakeholders with the aim of sharing costs and revenues and maximizing their payoffs. The challenge comes from the fact that future revenues are uncertain. We devise in this case a novel stochastic coalitional game formulation which builds upon robust game theory and derive a lower bound on the probability of the stability of the grand coalition, wherein no player can be better off outside of it. In the presence of highly dependent fluctuations of revenues however, stability can be too conservative. In this case, we make use also of profitability, in which payoffs of players are non-negative, as a necessary condition for co-investment, and we derive a lower bound on the probability that co-investment is profitable. The proposed framework is showcased for MEC deployment, where computational resources need to be deployed in nodes at the edge of a telecommunication network. Numerical results show high lower bound on the probability of stability when the SPs' revenues are of similar magnitude, even with high levels of uncertainty. In the case where revenues are highly variable however, the lower bound on stability can be trivially low whereas co-investment is still profitable.

cs.GT↗

arXiv2023

Multiple Resource Allocation in Multi-Tenant Edge Computing via Sub-modular Optimization

Edge Computing (EC) allows users to access computing resources at the network frontier, which paves the way for deploying delay-sensitive applications such as Mobile Augmented Reality (MAR). Under the EC paradigm, MAR users connect to the EC server, open sessions and send continuously frames to be processed. The EC server sends back virtual information to enhance the human perception of the world by merging it with the real environment. Resource allocation arises as a critical challenge when several MAR Service Providers (SPs) compete for limited resources at the edge of the network. In this paper, we consider EC in a multi-tenant environment where the resource owner, i.e., the Network Operator (NO), virtualizes the resources and lets SPs run their services using the allocated slice of resources. Indeed, for MAR applications, we focus on two specific resources: CPU and RAM, deployed in some edge node, e.g., a central office. We study the decision of the NO about how to partition these resources among several SPs. We model the arrival and service dynamics of users belonging to different SPs using Erlang queuing model and show that under perfect information, the interaction between the NO and SPs can be formulated as a sub-modular maximization problem under multiple Knapsack constraints. To solve the problem, we use an approximation algorithm, guaranteeing a bounded gap with respect to the optimal theoretical solution. Our numerical results show that the proposed algorithm outperforms baseline proportional allocation in terms of the number of sessions accommodated at the edge for each SP.

cs.DC↗

arXiv2023

RIS-assisted Cell-Free MIMO with Dynamic Arrivals and Departures of Users: A Novel Network Stability Approach

Reconfigurable Intelligent Surfaces (RIS) have recently emerged as a hot research topic, being widely advocated as a candidate technology for next generation wireless communications. These surfaces passively alter the behavior of propagation environments enhancing the performance of wireless communication systems. In this paper, we study the use of RIS in cell-free multiple-input multiple-output (MIMO) setting where distributed service antennas, called Access Points (APs), simultaneously serve the users in the network. While most existing works focus on the physical layer improvements RIS carry, less attention has been paid to the impact of dynamic arrivals and departures of the users. In such a case, ensuring the stability of the network is the main goal. For that, we propose an optimization framework of the phase shifts, for which we derived a low-complexity solution. We then provide a theoretical analysis of the network stability and show that our framework stabilizes the network whenever it is possible. We also prove that a low complexity solution of our framework stabilizes a guaranteed fraction (higher than 78.5%) of the stability region. We provide also numerical results that corroborate the theoretical claims.

cs.IT↗

arXiv2023

Initial Access Optimization for RIS-assisted Millimeter Wave Wireless Networks

Reconfigurable Intelligent Surfaces (RIS) are considered a key enabler to achieve the vision of Smart Radio Environments, where the propagation environment can be programmed and controlled to enhance the efficiency of wireless systems. These surfaces correspond to planar sheets comprising a large number of small and low-cost reflecting elements whose parameters are adaptively selected with a programmable controller. Hence, by optimizing these coefficients, the information signals can be directed in a customized fashion. On the other hand, the initial access procedure used in 5G is beam sweeping, where the base station sequentially changes the active beam direction in order to scan all users in the cell. This conventional protocol results in an initial access latency. The aim of this paper is to minimize this delay by optimizing the activated beams in each timeslot, while leveraging the presence of the RIS in the network. The problem is formulated as a hard optimization problem. We propose an efficient solution based on jointly alternating optimization and Semi Definite Relaxation (SDR) techniques. Numerical results are provided to assess the superiority of our scheme as compared to conventional beam sweeping.

cs.NI↗

arXiv2022

Coalitional Game-Theoretical Approach to Coinvestment with Application to Edge Computing

We propose in this paper a coinvestment plan between several stakeholders of different types, namely a physical network owner, operating network nodes, e.g. a network operator or a tower company, and a set of service providers willing to use these resources to provide services as video streaming, augmented reality, autonomous driving assistance, etc. One such scenario is that of deployment of Edge Computing resources. Indeed, although the latter technology is ready, the high Capital Expenditure (CAPEX) cost of such resources is the barrier to its deployment. For this reason, a solid economical framework to guide the investment and the returns of the stakeholders is key to solve this issue. We formalize the coinvestment framework using coalitional game theory. We provide a solution to calculate how to divide the profits and costs among the stakeholders, taking into account their characteristics: traffic load, revenues, utility function. We prove that it is always possible to form the grand coalition composed of all the stakeholders, by showing that our game is convex. We derive the payoff of the stakeholders using the Shapley value concept, and elaborate on some properties of our game. We show our solution in simulation.

cs.GT↗

arXiv2022

Cache Allocation in Multi-Tenant Edge Computing via online Reinforcement Learning

We consider in this work Edge Computing (EC) in a multi-tenant environment: the resource owner, i.e., the Network Operator (NO), virtualizes the resources and lets third party Service Providers (SPs - tenants) run their services, which can be diverse and with heterogeneous requirements. Due to confidentiality guarantees, the NO cannot observe the nature of the traffic of SPs, which is encrypted. This makes resource allocation decisions challenging, since they must be taken based solely on observed monitoring information. We focus on one specific resource, i.e., cache space, deployed in some edge node, e.g., a base station. We study the decision of the NO about how to partition cache among several SPs in order to minimize the upstream traffic. Our goal is to optimize cache allocation using purely data-driven, model-free Reinforcement Learning (RL). Differently from most applications of RL, in which the decision policy is learned offline on a simulator, we assume no previous knowledge is available to build such a simulator. We thus apply RL in an \emph{online} fashion, i.e., the policy is learned by directly perturbing the actual system and monitoring how its performance changes. Since perturbations generate spurious traffic, we also limit them. We show in simulation that our method rapidly converges toward the theoretical optimum, we study its fairness, its sensitivity to several scenario characteristics and compare it with a method from the state-of-the-art.

cs.DC↗

arXiv2019

A Stochastic Game Framework for Analyzing Computational Investment Strategies in Distributed Computing

We study a stochastic game framework with dynamic set of players, for modeling and analyzing their computational investment strategies in distributed computing. Players obtain a certain reward for solving the problem or for providing their computational resources, while incur a certain cost based on the invested time and computational power. We first study a scenario where the reward is offered for solving the problem, such as in blockchain mining. We show that, in Markov perfect equilibrium, players with cost parameters exceeding a certain threshold, do not invest; while those with cost parameters less than this threshold, invest maximal power. Here, players need not know the system state. We then consider a scenario where the reward is offered for contributing to the computational power of a common central entity, such as in volunteer computing. Here, in Markov perfect equilibrium, only players with cost parameters in a relatively low range in a given state, invest. For the case where players are homogeneous, they invest proportionally to the 'reward to cost' ratio. For both the scenarios, we study the effects of players' arrival and departure rates on their utilities using simulations and provide additional insights.

cs.GT↗

arXiv2019

Optimal Policies of Advanced Sleep Modes for Energy-Efficient 5G networks

We study in this paper optimal control strategy for Advanced Sleep Modes (ASM) in 5G networks. ASM correspond to different levels of sleep modes ranging from deactivation of some components of the base station for several micro-seconds to switching off of almost all of them for one second or more. ASMs are made possible in 5G networks thanks to the definition of so-called lean carrier radio access which allows for configurable signaling periodicities. We model such a system using Markov Decision Processes (MDP) and find optimal sleep policy in terms of a trade-off between saved power consumption versus additional incurred delay for user traffic which has to wait for the network components to be woken-up and serve it. Eventually, for the system not to oscillate between sleep levels, we add a switching component in the cost function and show its impact on the energy reduction versus delay trade-off.

cs.IT↗

arXiv2019

A Two Phase Investment Game for Competitive Opinion Dynamics in Social Networks

We propose a setting for two-phase opinion dynamics in social networks, where a node's final opinion in the first phase acts as its initial biased opinion in the second phase. In this setting, we study the problem of two camps aiming to maximize adoption of their respective opinions, by strategically investing on nodes in the two phases. A node's initial opinion in the second phase naturally plays a key role in determining the final opinion of that node, and hence also of other nodes in the network due to its influence on them. More importantly, this bias also determines the effectiveness of a camp's investment on that node in the second phase. To formalize this two-phase investment setting, we propose an extension of Friedkin-Johnsen model, and hence formulate the utility functions of the camps. There is a tradeoff while splitting the budget between the two phases. A lower investment in the first phase results in worse initial biases for the second phase, while a higher investment spares a lower available budget for the second phase. We first analyze the non-competitive case where only one camp invests, for which we present a polynomial time algorithm for determining an optimal way to split the camp's budget between the two phases. We then analyze the case of competing camps, where we show the existence of Nash equilibrium and that it can be computed in polynomial time under reasonable assumptions. We conclude our study with simulations on real-world network datasets, in order to quantify the effects of the initial biases and the weightage attributed by nodes to their initial biases, as well as that of a camp deviating from its equilibrium strategy. Our main conclusion is that, if nodes attribute high weightage to their initial biases, it is advantageous to have a high investment in the first phase, so as to effectively influence the biases to be harnessed in the second phase.

cs.SI↗

arXiv2018

Optimal Investment Strategies for Competing Camps in a Social Network: A Broad Framework

We study the problem of optimally investing in nodes of a social network in a competitive setting, wherein two camps aim to drive the average opinion of the population in their own favor. Using a well-established model of opinion dynamics, we formulate the problem as a zero-sum game with its players being the two camps. We derive optimal investment strategies for both camps, and show that a random investment strategy is optimal when the underlying network follows a popular class of weight distributions. We study a broad framework, where we consider various well-motivated settings of the problem, namely, when the influence of a camp on a node is a concave function of its investment on that node, when a camp aims at maximizing competitor's investment or deviation from its desired investment, and when one of the camps has uncertain information about the values of the model parameters. We also study a Stackelberg variant of this game under common coupled constraints on the combined investments by the camps and derive their equilibrium strategies, and hence quantify the first-mover advantage. For a quantitative and illustrative study, we conduct simulations on real-world datasets and provide results and insights.

cs.SI↗

arXiv2018

Optimal Multiphase Investment Strategies for Influencing Opinions in a Social Network

We study the problem of optimally investing in nodes of a social network in a competitive setting, where two camps aim to maximize adoption of their opinions by the population. In particular, we consider the possibility of campaigning in multiple phases, where the final opinion of a node in a phase acts as its initial biased opinion for the following phase. Using an extension of the popular DeGroot-Friedkin model, we formulate the utility functions of the camps, and show that they involve what can be interpreted as multiphase Katz centrality. Focusing on two phases, we analytically derive Nash equilibrium investment strategies, and the extent of loss that a camp would incur if it acted myopically. Our simulation study affirms that nodes attributing higher weightage to initial biases necessitate higher investment in the first phase, so as to influence these biases for the terminal phase. We then study the setting in which a camp's influence on a node depends on its initial bias. For single camp, we present a polynomial time algorithm for determining an optimal way to split the budget between the two phases. For competing camps, we show the existence of Nash equilibria under reasonable assumptions, and that they can be computed in polynomial time.

cs.SI↗

arXiv2016

Performance Analysis of Small Cells' Deployment under Imperfect Traffic Hotspot Localization

Heterogeneous Networks (HetNets), long been considered in operators' roadmaps for macrocells' network improvements, still continue to attract interest for 5G network deployments. Understanding the efficiency of small cell deployment in the presence of traffic hotspots can further draw operators' attention to this feature. In this context, we evaluate the impact of imperfect small cell positioning on the network performances. We show that the latter is mainly impacted by the position of the hotspot within the cell: in case the hotspot is near the macrocell, even a perfect positioning of the small cell will not yield improved performance due to the interference coming from the macrocell. In the case where the hotspot is located far enough from the macrocell, even a large error in small cell positioning would still be beneficial in offloading traffic from the congested macrocell.

cs.NI↗