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) -> 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/root gamma), marking a fundamental trade-off between stealth and impact in continuous-time detection systems.

This paper investigates the damage that an adversary can effect while remaining covert in the presence of the Cumulative Sum (CuSum) procedure. An adversary is covert if the time to detection is on the same order as the time to false alarm. Damage is given as an increasing function of the KL-divergence of the adversarial actions and the normal distribution prior to the adversarial attack. By analyzing the problem with a focus on the growth function g(n), which measures the cumulative expected log-likelihood ratio after n time slots following the change, we establish conditions under which the adversary remains covert and provide an analysis of the impact of different adversarial strategies on damage.

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 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.

In Section 4.3 (Analysis), the last few lines of the proof of Claim 3 should be replaced with the following

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 and 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. When object request processes are conditionally independent, we prove that this cache allocation based on the HR-to-size ratio rule guarantees the maximum achievable expected number of object hits across all non-anticipative caching policies. Further, the HR ordering rule serves as an upper bound on cache hit probability when object request processes follow either independent delayed renewal process or a Markov modulated Poisson process. We also derive closed form expressions for the upper bound under some specific object request arrival processes. We provide simulation results to validate its correctness and to compare it to the state-of-the-art upper bounds, such as produced by Bélády’s algorithm. We find it to be tighter than state-of-the-art upper bounds for some specific object request arrival processes such as independent renewal, Markov modulated, and shot noise processes.

We state and prove the square root scaling laws for the amount of traffic injected by a covert attacker into a network from a set of homes under the assumption that traffic descriptors follow a multivariate Gaussian distribution. We numerically evaluate the obtained result under realistic settings wherein traffic is collected from real users, leveraging detectors that exploit multiple features. Under such circumstances, we observe that phase transitions predicted by the model still hold.

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.

The proliferation of smart devices, computational and storage resources is predicted to continue aggressively in the near future. Such “networked” devices and resources which are distributed in a physical space and provide services are collectively referred to as a distributed service network . Assigning users or applications to available resources is important to sustain high performance of the distributed service network. In this work, we consider a one-dimensional service network where both users and resources are located on a line, and analyze a unidirectional assignment policy Move To Right (MTR), which sequentially assigns users to resources available to their right. We express the communication cost for a user-resource assignment as an increasing function of the distance traveled by the user request ( request distance ) and analyze the expected communication cost for the service network when locations of users and resources are modeled by different spatial point processes. We use results from the literature that map the request distance of an assigned user in a one-dimensional service network to the sojourn time of a customer in an exceptional service accessible batch queueing system. We compute the Laplace–Stieltjes transform of the sojourn time distribution for this queueing system for Poisson distributed users with general inter-resource distance distributions and in the process also generate new results for batch service queues. Unlike previous work (Panigrahy et al. in Perform Eval 142:102, 2020), our framework not only captures the first-order moment of the request distance, but also the request distance distribution itself, thus allowing us to compute the expected communication cost under different cost models.

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 μ 1 and μ 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 O (√ n ) when μ 1 < 2 μ 2 , O (√ n log n ) when μ 1 = 2μ 2 , and O ( n μ 2 /μ 1 ) when μ 1 > 2μ 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.

The Internet has become an indispensable commodity in the last several years. This achievement was parallel to the growth of sophistication that home networks have undergone, nowadays hosting a variety of devices such as PCs, tablets, mobile phones and specialized apparatus such as smart thermostats and other Internet of things (IoT) devices. While these devices offer users an array of services and conveniences, they come at the cost of increasing the attack surface of the home network.Because of the vulnerabilities of such devices, they have been increasingly used as the source of Distributed Denial-of-Service (DDoS) attacks.

The MISTRAL project is devoted to the elaboration and the analysis of mathematical models for performance evaluation of communication systems and of parallel and distributed systems. The research of the project focuses on two main formalisms: queueing networks and Petri nets. Two complementary approaches are used: the development of (stochastic) mathematical models, and simulation. The research consists of analytical and probabilistic studies of discrete event dynamic systems, scheduling and mapping studies in multiprocessor networks, and control and optimization problems in communication networks.

This work investigates distributed transmission scheduling in wireless networks. Due to interference constraints, “neighboring links” cannot be simultaneously activated, otherwise transmissions will fail. Here, we consider any binary model of interference. We use the model described by Bui et al. in [L. X. Bui, S. Sanghavi and R. Srikant, Distributed link scheduling with constant overhead, IEEE/ACM Trans. Netw. 17(5) (2009) 1467–1480; S. Sanghavi, L. Bui and R. Srikant, Distributed link scheduling with constant overhead, in Proc. ACM Sigmetrics (San Diego, CA, USA, 2007), pp. 313–324.]. We assume that time is slotted and during each slot there are two phases: one control phase in which a link scheduling algorithm determines a set of non-interfering links to be activated, and a data phase in which data is sent through these links. We assume random arrivals on each link during each slot, so that a queue is associated to each link. Since nodes do not have a global knowledge of the queues sizes, our aim (like in [L. X. Bui, S. Sanghavi and R. Srikant, Distributed link scheduling with constant overhead, IEEE/ACM Trans. Netw. 17(5) (2009) 1467–1480; S. Sanghavi, L. Bui and R. Srikant, Distributed link scheduling with constant overhead, in Proc. ACM Sigmetrics (San Diego, CA, USA, 2007), pp. 313–324.]) is to design a distributed link scheduling algorithm. To be efficient, the control phase should be as short as possible; this is done by exchanging control messages during a constant number of mini-slots (constant overhead). In this paper, we design the first fully distributed local algorithm with the following properties: it works for any arbitrary binary interference model; it has a constant overhead (independent of the size of the network and the values of the queues), and it does not require any knowledge of the queue-lengths. We prove that this algorithm gives a maximal set of active links, where for any non-active link there exists at least one active link in its interference set. We also establish sufficient conditions for stability under general Markovian assumptions. Finally, the performance of our algorithm (throughput, stability) is investigated and compared via simulations to that of previously proposed schemes.

Protocols that exploit quantum communication technology offer two advantages: they can either extend or render feasible the capabilities of their classical counterparts, or they exhibit functionality entirely unachievable through classical means alone. For an example of the former, quantum key distribution protocols such as E91 [2] and BBM92 [1] can in principle yield information-theoretic security by using entanglement to generate secure key bits. These raw secret key bits can then be distilled into a one-time pad to encode messages sent between two parties. For an example of the latter, distributed quantum sensing frameworks such as [3] and [11] employ entanglement to overcome the standard quantum limit [4].

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 least recently used policy for managing content. We propose utility-driven partitioning, where we associate with each content provide a utility that is a function of the hit rate observed by the content provider. We consider two scenarios: 1) content providers serve disjoint sets of files and 2) 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 a number 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.

We study a quantum switch serving a set of users. The function of the switch is to convert bipartite entanglement generated over individual links connecting each user to the switch, into bipartite or tripartite entangled states among (pairs or groups of) users at the highest possible rates at a fixed ratio. Such entanglement can then be converted to quantum-secure shared secret bits among pairs or triples of users using E91-like Quantum Key Distribution (QKD) protocols. The switch can store a certain number of qubits in a quantum memory for a certain length of time, and can make two-qubit Bell-basis measurements or three-qubit GHZ-basis projective measurements on qubits held in the memory. 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 at a given time step, and find that the best policies outperform a time division multiplexing (TDM) policy for sharing the switch between bipartite and tripartite entanglement 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 qubit decoherence, obtaining similar results. Moreover, decoherence appears to have little effect on capacity. We also study a smaller class of policies when the switch can store two qubits per user. The full manuscript can be found at https://arxiv.org/abs/1901.06786.

In this article, we study a quantum entanglement distribution switch that serves $k$ users in a star topology. We model variants of the system as continuous-time Markov chains and obtain expressions for switch capacity, expected number of qubits stored in memory at the switch, and the quantum memory occupancy distribution. We obtain a number of analytic results for systems in which measurements are imperfect, the links are homogeneous or heterogeneous and for switches that have an infinite or finite number of quantum memories or buffers. In addition, we model the effect of decoherence of quantum states and associated cutoff times on their storage using a simple model. From numerical observations, we discover that decoherence-associated cutoff times have little effect on capacity and expected number of stored qubits for homogeneous systems. For heterogeneous systems, especially those operating near the boundaries of their stability regions (i.e., systems that are nearly unstable), 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, whereas increasing the buffer size further yields diminishing returns. The analytical results obtained in this work can serve as a useful guide toward the future design of quantum switches—e.g., by allowing the designer to determine how many quantum memories suffice for a given number of users—as well as provide valuable insight on the performance of these and similar devices.

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.

A propos du centre ou de la direction fonctionnelle Le centre Inria Sophia Antipolis Méditerranée compte 37 équipes de recherche, ainsi que 9 services d’appui à la recherche. Le personnel du centre (600 personnes environ dont 400 salariés Inria) est composé de scientifiques de différentes nationalités (250 personnes étrangères sur 50 nationalités), d’Ingénieurs, de Techniciens et d’Administratifs. 1/3 du personnel est fonctionnaire, les autres sont contractuels. La majorité des équipes de recherche du centre sont localisées à Sophia Antipolis et Nice dans les Alpes-Maritimes. Six équipes sont implantées à Montpellier et une équipe est hébergée par le département d'informatique de l'université de Bologne en Italie. Le Centre est membre de la Communauté d’Université et d’Établissement (ComUE) « Université Côte d’Azur (UCA) ».

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.