arXiv subjects

Philippe Nain

Publications and source records attributed to Philippe Nain.

At least 19 recordsLinked to original sources

arXiv2026

Quickest Change Detection in Discrete-Time in Presence of a Covert Adversary

We study the problem of covert quickest change detection in a discrete-time setting, where a sequence of observations undergoes a distributional change at an unknown time. Unlike classical formulations, we consider a covert adversary who has knowledge of the detector's false alarm constraint parameter $\gamma$ and selects a stationary post-change distribution that depends on it, seeking to remain undetected for as long as possible. Building on the theoretical foundations of the CuSum procedure, we rigorously characterize the asymptotic behavior of the average detection delay (ADD) and the average time to false alarm (AT2FA) when the post-change distribution converges to the pre-change distribution as $\gamma \to \infty$. Our analysis establishes exact asymptotic expressions for these quantities, extending and refining classical results that no longer hold in this regime. We identify the critical scaling laws governing covert behavior and derive explicit conditions under which an adversary can maintain covertness, defined by ADD = $\Theta(\gamma)$, whereas in the classical setting, ADD grows only as $\mathcal{O}(\log \gamma)$. In particular, for Gaussian and Exponential models under adversarial perturbations of their respective parameters, we asymptotically characterize ADD as a function of the Kullback--Leibler divergence between the pre- and post-change distributions and $\gamma$.

cs.IT↗

arXiv2025

Quickest Change Detection in Continuous-Time in Presence of a Covert Adversary

We investigate the problem of covert quickest change detection in a continuous-time setting, where a Brownian motion experiences a drift change at an unknown time. Unlike classical formulations, we consider a covert adversary who adjusts the post-change drift $\mu = \mu(\gamma)$ as a function of the false alarm constraint parameter $\gamma$, with the goal of remaining undetected for as long as possible. Leveraging the exact expressions for the average detection delay (ADD) and average time to false alarm (AT2FA) known for the continuous-time CuSum procedure, we rigorously analyze how the asymptotic behavior of ADD evolves as $\mu(\gamma) \to 0$ with increasing $\gamma$. Our results reveal that classical detection delay characterizations no longer hold in this regime. We derive sharp asymptotic expressions for the ADD under various convergence rates of $\mu(\gamma)$, identify precise conditions for maintaining covertness, and characterize the total damage inflicted by the adversary. We show that the adversary achieves maximal damage when the drift scales as $\mu(\gamma) = \Theta(1/\sqrt{\gamma})$, marking a fundamental trade-off between stealth and impact in continuous-time detection systems.

cs.IT↗

arXiv2022

On the Analysis of a Multipartite Entanglement Distribution Switch

We study a quantum switch that distributes maximally entangled multipartite states to sets of users. The entanglement switching process requires two steps: first, each user attempts to generate bipartite entanglement between itself and the switch; and second, the switch performs local operations and a measurement to create multipartite entanglement for a set of users. In this work, we study a simple variant of this system, wherein the switch has infinite memory and the links that connect the users to the switch are identical. Further, we assume that all quantum states, if generated successfully, have perfect fidelity and that decoherence is negligible. This problem formulation is of interest to several distributed quantum applications, while the technical aspects of this work result in new contributions within queueing theory. Via extensive use of Lyapunov functions, we derive necessary and sufficient conditions for the stability of the system and closed-form expressions for the switch capacity and the expected number of qubits in memory.

quant-ph↗

arXiv2021

A New Upper Bound on Cache Hit Probability for Non-anticipative Caching Policies

Caching systems have long been crucial for improving the performance of a wide variety of network and web based online applications. In such systems, end-to-end application performance heavily depends on the fraction of objects transferred from the cache, also known as the cache hit probability. Many caching policies have been proposed and implemented to improve the hit probability. In this work, we propose a new method to compute an upper bound on hit probability for all non-anticipative caching policies, i.e., for policies that have no knowledge of future requests. Our key insight is to order the objects according to the ratio of their Hazard Rate (HR) function values to their sizes and place in the cache the objects with the largest ratios till the cache capacity is exhausted. Under some statistical assumptions, we prove that our proposed HR to size ratio based ordering model computes the maximum achievable hit probability and serves as an upper bound for all non-anticipative caching policies. We derive closed form expressions for the upper bound under some specific object request arrival processes. We also provide simulation results to validate its correctness and to compare it to the state-of-the-art upper bounds. We find it to be tighter than state-of-the-art upper bounds for a variety of object request arrival processes.

cs.PF↗

arXiv2020

Resource Allocation in One-dimensional Distributed Service Networks with Applications

We consider assignment policies that allocate resources to users, where both resources and users are located on a one-dimensional line. First, we consider unidirectional assignment policies that allocate resources only to users located to their left. We propose the Move to Right (MTR) policy, which scans from left to right assigning nearest rightmost available resource to a user, and contrast it to the Unidirectional Gale-Shapley (UGS) matching policy. While both policies among all unidirectional policies, minimize the expected distance traveled by a request (request distance), MTR is fairer. Moreover, we show that when user and resource locations are modeled by statistical point processes, and resources are allowed to satisfy more than one user, the spatial system under unidirectional policies can be mapped into bulk service queueing systems, thus allowing the application of many queueing theory results that yield closed form expressions. As we consider a case where different resources can satisfy different numbers of users, we also generate new results for bulk service queues. We also consider bidirectional policies where there are no directional restrictions on resource allocation and develop an algorithm for computing the optimal assignment which is more efficient than known algorithms in the literature when there are more resources than users. Numerical evaluation of performance of unidirectional and bidirectional allocation schemes yields design guidelines beneficial for resource placement. \np{Finally, we present a heuristic algorithm, which leverages the optimal dynamic programming scheme for one-dimensional inputs to obtain approximate solutions to the optimal assignment problem for the two-dimensional scenario and empirically yields request distances within a constant factor of the optimal solution.

cs.PF↗

arXiv2020

Covert Cycle Stealing in a Single FIFO Server

Consider a setting where Willie generates a Poisson stream of jobs and routes them to a single server that follows the first-in first-out discipline. Suppose there is an adversary Alice, who desires to receive service without being detected. We ask the question: what is the number of jobs that she can receive covertly, i.e. without being detected by Willie? In the case where both Willie and Alice jobs have exponential service times with respective rates $\mu_1$ and $\mu_2$, we demonstrate a phase-transition when Alice adopts the strategy of inserting a single job probabilistically when the server idles : over $n$ busy periods, she can achieve a covert throughput, measured by the expected number of jobs covertly inserted, of $\mathcal{O}(\sqrt{n})$ when $\mu_1 < 2\mu_2$, $\mathcal{O}(\sqrt{n/\log n})$ when $\mu_1 = 2\mu_2$, and $\mathcal{O}(n^{\mu_2/\mu_1})$ when $\mu_1 > 2\mu_2$. When both Willie and Alice jobs have general service times we establish an upper bound for the number of jobs Alice can execute covertly. This bound is related to the Fisher information. More general insertion policies are also discussed.

math.PR↗

arXiv2020

Resource Allocation in One-dimensional Distributed Service Networks

We consider assignment policies that allocate resources to users, where both resources and users are located on a one-dimensional line. First, we consider unidirectional assignment policies that allocate resources only to users located to their left. We propose the Move to Right (MTR) policy, which scans from left to right assigning nearest rightmost available resource to a user, and contrast it to the Unidirectional Gale-Shapley (UGS) matching policy. While both these policies are optimal among all unidirectional policies, we show that they are equivalent with respect to the expected distance traveled by a request (request distance), although MTR is fairer. Moreover, we show that when user and resource locations are modeled by statistical point processes, and resources are allowed to satisfy more than one user, the spatial system under unidirectional policies can be mapped into bulk service queuing systems, thus allowing the application of a plethora of queuing theory results that yield closed form expressions. As we consider a case where different resources can satisfy different numbers of users, we also generate new results for bulk service queues. We also consider bidirectional policies where there are no directional restrictions on resource allocation and develop an algorithm for computing the optimal assignment which is more efficient than known algorithms in the literature when there are more resources than users. Finally, numerical evaluation of performance of unidirectional and bidirectional allocation schemes yields design guidelines beneficial for resource placement.

cs.PF↗

arXiv2019

On the Stochastic Analysis of a Quantum Entanglement Switch

We study a quantum entanglement switch that serves $k$ users in a star topology. We model variants of the system using Markov chains and standard queueing theory and obtain expressions for switch capacity and the expected number of qubits stored in memory at the switch. While it is more accurate to use a discrete-time Markov chain (DTMC) to model such systems, we quickly encounter practical constraints of using this technique and switch to using continuous-time Markov chains (CTMCs). Using CTMCs allows us to obtain a number of analytic results for systems in which the links are homogeneous or heterogeneous and for switches that have infinite or finite buffer sizes. In addition, we can model the effects of decoherence of quantum states fairly easily using CTMCs. We also compare the results we obtain from the DTMC against the CTMC in the case of homogeneous links and infinite buffer, and learn that the CTMC is a reasonable approximation of the DTMC. From numerical observations, we discover that decoherence has little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating close to stability constraints, buffer size and decoherence can have significant effects on performance metrics. We also learn that in general, increasing the buffer size from one to two qubits per link is advantageous to most systems, while increasing the buffer size further yields diminishing returns.

quant-ph↗

arXiv2019

On the Capacity Region of Bipartite and Tripartite Entanglement Switching

We study a quantum entanglement distribution switch serving a set of users in a star topology with equal-length links. The quantum switch, much like a quantum repeater, can perform entanglement swapping to extend entanglement across longer distances. Additionally, the switch is equipped with entanglement switching logic, enabling it to implement switching policies to better serve the needs of the network. In this work, the function of the switch is to create bipartite or tripartite entangled states among users at the highest possible rates at a fixed ratio. Using Markov chains, we model a set of randomized switching policies. Discovering that some are better than others, we present analytical results for the case where the switch stores one qubit per user, and find that the best policies outperform a time division multiplexing (TDM) policy for sharing the switch between bipartite and tripartite state generation. This performance improvement decreases as the number of users grows. The model is easily augmented to study the capacity region in the presence of quantum state decoherence and associated cut-off times for qubit storage, obtaining similar results. Moreover, decoherence-associated quantum storage cut-off times appear to have little effect on capacity in our identical-link system. We also study a smaller class of policies when the switch stores two qubits per user.

cs.NI↗

arXiv2018

On a Class of Stochastic Multilayer Networks

In this paper, we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of $M$ networks (one per layer) where each is a subgraph of a foundational network $G$. Each layer network is the result of probabilistically removing links and nodes from $G$. The resulting network includes any link that appears in at least $K$ layers. This model is an instance of a non-standard site-bond percolation model. Two sets of results are obtained: first, we derive the probability distribution that the $M$-layer network is in a given configuration for some particular graph structures (explicit results are provided for a line and an algorithm is provided for a tree), where a configuration is the collective state of all links (each either active or inactive). Next, we show that for appropriate scalings of the node and link selection processes in a layer, links are asymptotically independent as the number of layers goes to infinity, and follow Poisson distributions. Numerical results are provided to highlight the impact of having several layers on some metrics of interest (including expected size of the cluster a node belongs to in the case of the line). This model finds applications in wireless communication networks with multichannel radios, multiple social networks with overlapping memberships, transportation networks, and, more generally, in any scenario where a common set of nodes can be linked via co-existing means of connectivity.

cs.SI↗

arXiv2018

On the Convergence of the TTL Approximation for an LRU Cache under Independent Stationary Request Processes

The modeling and analysis of an LRU cache is extremely challenging as exact results for the main performance metrics (e.g. hit rate) are either lacking or cannot be used because of their high computational complexity for large caches. As a result, various approximations have been proposed. The state-of-the-art method is the so-called TTL approximation, first proposed and shown to be asymptotically exact for IRM requests by Fagin. It has been applied to various other workload models and numerically demonstrated to be accurate but without theoretical justification. In this paper we provide theoretical justification for the approximation in the case where distinct contents are described by independent stationary and ergodic processes. We show that this approximation is exact as the cache size and the number of contents go to infinity. This extends earlier results for the independent reference model. Moreover, we establish results not only for the aggregate cache hit probability but also for every individual content. Last, we obtain bounds on the rate of convergence.

cs.PF↗

arXiv2017

Sharing LRU Cache Resources among Content Providers: A Utility-Based Approach

In this paper, we consider the problem of allocating cache resources among multiple content providers. The cache can be partitioned into slices and each partition can be dedicated to a particular content provider, or shared among a number of them. It is assumed that each partition employs the LRU policy for managing content. We propose utility-driven partitioning, where we associate with each content provider a utility that is a function of the hit rate observed by the content provider. We consider two scenarios: i)~content providers serve disjoint sets of files, ii)~there is some overlap in the content served by multiple content providers. In the first case, we prove that cache partitioning outperforms cache sharing as cache size and numbers of contents served by providers go to infinity. In the second case, It can be beneficial to have separate partitions for overlapped content. In the case of two providers, it is usually always beneficial to allocate a cache partition to serve all overlapped content and separate partitions to serve the non-overlapped contents of both providers. We establish conditions when this is true asymptotically but also present an example where it is not true asymptotically. We develop online algorithms that dynamically adjust partition sizes in order to maximize the overall utility and prove that they converge to optimal solutions, and through numerical evaluations, we show they are effective.

cs.NI↗

arXiv2016

Spanning connectivity in a multilayer network and its relationship to site-bond percolation

We analyze the connectivity of an $M$-layer network over a common set of nodes that are active only in a fraction of the layers. Each layer is assumed to be a subgraph (of an underlying connectivity graph $G$) induced by each node being active in any given layer with probability $q$. The $M$-layer network is formed by aggregating the edges over all $M$ layers. We show that when $q$ exceeds a threshold $q_c(M)$, a giant connected component appears in the $M$-layer network---thereby enabling far-away users to connect using `bridge' nodes that are active in multiple network layers---even though the individual layers may only have small disconnected islands of connectivity. We show that $q_c(M) \lesssim \sqrt{-\ln(1-p_c)}\,/{\sqrt{M}}$, where $p_c$ is the bond percolation threshold of $G$, and $q_c(1) \equiv q_c$ is its site percolation threshold. We find $q_c(M)$ exactly for when $G$ is a large random network with an arbitrary node-degree distribution. We find $q_c(M)$ numerically for various regular lattices, and find an exact lower bound for the kagome lattice. Finally, we find an intriguingly close connection between this multilayer percolation model and the well-studied problem of site-bond percolation, in the sense that both models provide a smooth transition between the traditional site and bond percolation models. Using this connection, we translate known analytical approximations of the site-bond critical region, which are functions only of $p_c$ and $q_c$ of the respective lattice, to excellent general approximations of the multilayer connectivity threshold $q_c(M)$.

cond-mat.stat-mech↗

arXiv2013

Computing Traversal Times on Dynamic Markovian Paths

In source routing, a complete path is chosen for a packet to travel from source to destination. While computing the time to traverse such a path may be straightforward in a fixed, static graph, doing so becomes much more challenging in dynamic graphs, in which the state of an edge in one time slot (i.e., its presence or absence) is random, and may depend on its state in the previous time step. The traversal time is due to both time spent waiting for edges to appear and time spent crossing them once they become available. We compute the expected traversal time (ETT) for a dynamic path in a number of special cases of stochastic edge dynamics models, and for three edge failure models, culminating in a surprisingly challenging yet realistic setting in which the initial configuration of edge states for the entire path is known. We show that the ETT for this "initial configuration" setting can be computed in quadratic time, by an algorithm based on probability generating functions. We also give several linear-time upper and lower bounds on the ETT.

cs.NI↗

arXiv2012

Characterizing Continuous Time Random Walks on Time Varying Graphs

In this paper we study the behavior of a continuous time random walk (CTRW) on a stationary and ergodic time varying dynamic graph. We establish conditions under which the CTRW is a stationary and ergodic process. In general, the stationary distribution of the walker depends on the walker rate and is difficult to characterize. However, we characterize the stationary distribution in the following cases: i) the walker rate is significantly larger or smaller than the rate in which the graph changes (time-scale separation), ii) the walker rate is proportional to the degree of the node that it resides on (coupled dynamics), and iii) the degrees of node belonging to the same connected component are identical (structural constraints). We provide examples that illustrate our theoretical findings.

cs.SI↗

arXiv2012

A retrial system with two input streams and two orbit queues

Two independent Poisson streams of jobs flow into a single-server service system having a limited common buffer that can hold at most one job. If a type-i job (i=1,2) finds the server busy, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. This creates a system with three dependent queues. Such a queueing system serves as a model for two competing job streams in a carrier sensing multiple access system. We study the queueing system using multi-dimensional probability generating functions, and derive its necessary and sufficient stability conditions while solving a boundary value problem. Various performance measures are calculated and numerical results are presented.

cs.DM↗

arXiv2012

Optimal Threshold Control by the Robots of Web Search Engines with Obsolescence of Documents

A typical web search engine consists of three principal parts: crawling engine, indexing engine, and searching engine. The present work aims to optimize the performance of the crawling engine. The crawling engine finds new web pages and updates web pages existing in the database of the web search engine. The crawling engine has several robots collecting information from the Internet. We first calculate various performance measures of the system (e.g., probability of arbitrary page loss due to the buffer overflow, probability of starvation of the system, the average time waiting in the buffer). Intuitively, we would like to avoid system starvation and at the same time to minimize the information loss. We formulate the problem as a multi-criteria optimization problem and attributing a weight to each criterion. We solve it in the class of threshold policies. We consider a very general web page arrival process modeled by Batch Marked Markov Arrival Process and a very general service time modeled by Phase-type distribution. The model has been applied to the performance evaluation and optimization of the crawler designed by INRIA Maestro team in the framework of the RIAM INRIA-Canon research project.

cs.NI↗

arXiv2011

Predicting the Impact of Measures Against P2P Networks on the Transient Behaviors

The paper has two objectives. The first is to study rigorously the transient behavior of some P2P networks whenever information is replicated and disseminated according to epidemic-like dynamics. The second is to use the insight gained from the previous analysis in order to predict how efficient are measures taken against peer-to-peer (P2P) networks. We first introduce a stochastic model which extends a classical epidemic model and characterize the P2P swarm behavior in presence of free riding peers. We then study a second model in which a peer initiates a contact with another peer chosen randomly. In both cases the network is shown to exhibit a phase transition: a small change in the parameters causes a large change in the behavior of the network. We show, in particular, how the phase transition affects measures that content provider networks may take against P2P networks that distribute non-authorized music or books, and what is the efficiency of counter-measures.

cs.NI↗