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Michel Mandjes

Publications and source records attributed to Michel Mandjes.

At least 19 recordsLinked to original sources
arXiv2026

Analysis of Triggered Packet Streams: A Matrix-Analytic Method for Exponential Triggering Delays

In many communication networks, the transmission of a packet may automatically trigger the transmission of a subsequent packet from the same source after a (possibly random) delay, without requiring acknowledgment or feedback. Such behavior arises in multi-stage status updating, proactive protocols, and other applications where users generate causally dependent packet streams. In this paper, in order to analyze these systems, we introduce the $\mathrm{M^T/G/1}$ queue. In this model, primary customers arrive according to a Poisson process, and each primary customer triggers a secondary customer to join the queue after an independent delay. This arrival mechanism falls outside the scope of classical queueing models with renewal arrival processes. When the triggering delays follow an exponential distribution, we exploit the memoryless property to set up a tractable Markov description. By truncating the number of pending secondary customers, we derive a finite system of linear algebraic equations in the Laplace--Stieltjes transform domain and solve them using matrix-analytic methods. Based on the resulting workload distribution, we compute class-specific performance metrics using PASTA for primary customers and Palm conditioning for secondary customers. Finally, we validate the accuracy of this truncation through numerical experiments.

math.PR↗
arXiv2026

Sample-path Large deviations for Scheduled Arrival Processes with Unpunctuality

We study a scheduled-arrival process in which deterministic arrival times are perturbed by i.i.d. unpunctuality random variables. For the empirical mean of independent copies of the resulting counting process, we prove a sample-path large deviations principle on $D([0,T])$, equipped with the Skorokhod topology. As an application, we derive large deviation principles for the corresponding workload process under deterministic and random service setting. In the deterministic service case, we also identify the exponentially tilted arrival path associated with a rare workload overflow event.

math.PR↗
arXiv2026

Parameter inference for partially observed branching processes

In this paper, we study an age-dependent branching process. In the simplest setting, the population is divided into two age groups, namely juveniles and adults. Our objective is to estimate the model parameters using observations of the total population size only (i.e., juveniles plus adults). Focusing on the ergodic regime of the model, we introduce a method-of-moments estimator and establish its asymptotic normality. Several extensions are discussed, including models with more than two age groups.

math.ST↗
arXiv2026

Analysis of a maximum-entropy based estimator for dynamic random graph models

We study dynamic random graphs in which the set of nodes is fixed, but edges evolve over time according to an underlying stochastic mechanism. Using a maximum-entropy approach, we define a probability distribution on graph trajectories that is consistent with observed constraints, capturing the inherent uncertainty in partially observed networks. We introduce a moment-based estimator for the parameters of this distribution and establish its statistical properties, such as consistency and asymptotic normality, with explicit formulas for the covariance structure. Numerical experiments demonstrate the estimator's accuracy and robustness across various dynamic network scenarios. Our framework bridges probabilistic modeling and statistical inference in time-varying networks, providing practical tools for understanding and predicting complex edge dynamics.

math.ST↗
arXiv2026

Insurance risk models in a heterogeneous time-dependent population: scaling limits and ruin probabilities

Epidemic dynamics introduce time-varying heterogeneity into insured populations, as individuals' risk profiles depend on their evolving health status, thereby challenging classical insurance models based on homogeneity. Motivated by this phenomenon, we develop in this paper actuarial risk models in which the claim process is directly linked to an underlying general stochastic population dynamics, resulting in interacting subpopulations with different claim frequencies and severities. We propose both collective and individual modeling frameworks that track the changing composition of the insured population and its impact on aggregate claims. For these models, we derive scaling limits and provide bounds and approximations for ruin probabilities, offering tractable tools for risk assessment. Applications in an SIS context are detailed for different classes of risk processes, thereby contributing to a better understanding of how contagion-driven changes in population structure affect insurer solvency and supporting more realistic modeling of insurance portfolios in the presence of epidemic risk.

math.PR↗
arXiv2026

Dynamic Core Allocation for Malleable Jobs with Unknown Speed-up Parameters

We study dynamic resource allocation in a multicore computing system with a fixed number of processing cores and a stream of malleable jobs. Each job may adjust its level of parallelism during execution, allowing adaptive redistribution of resources across concurrently active jobs. Jobs belong to one of two observable classes, each characterized by a distinct speed-up function with unknown parameters. The objective is to learn a core-allocation policy that minimizes the long-run mean number of jobs in the system, equivalently the mean response time in steady state. \noindent To address this uncertainty, we develop an iterative learning-and-control framework. The system alternates between estimating the unknown speed-up parameters from observed job completions and solving the associated Markov decision process (MDP) to update the allocation policy. Within each job class, cores are shared equally among active jobs; the fraction of capacity assigned to each class is obtained from the MDP formulation of \cite{berg2017}, evaluated at the current parameter estimates. We construct a maximum likelihood estimator based on state-dependent inter-departure times and prove its strong consistency under a fixed allocation policy. We further propose two learning algorithms that combine this estimation step with dynamic programming-based policy updates, and illustrate their through numerical experiments.

math.OC↗
arXiv2026

General perturbative framework for kinetics of rare transitions in 1-dimensional active particle systems

We present a theoretical framework that enables investigating rare transitions in a general model of an active particle in an external potential, with the thermal Active Ornstein-Uhlenbeck Particle (AOUP) appearing as a special case. Using a projection-operator formalism, we compute transition rates perturbatively in two distinct asymptotic regimes. In the regime of small persistence times-where the activity evolves much faster than the particle's position-integrating out the activity reproduces the rates previously reported in the literature. In the opposite regime of large persistence times, we instead integrate out the position and obtain the corresponding rates analytically. Together, these asymptotic expansions uniquely specify a rational approximation that remains accurate across intermediate persistence times. As a result, we obtain an analytic expression for the rate valid across all persistence times and activity strengths in the rare-event limit, which are in excellent agreement with numerical simulations. The presented framework applies to rare transitions in a broad class of driven systems.

cond-mat.stat-mech↗
arXiv2026

A stochastic optimization algorithm for revenue maximization in a service system with balking customers

This paper analyzes a service system modeled as a single-server queue, in which the service provider aims to dynamically maximize the expected revenue per unit of time. This is achieved by constructing a stochastic gradient descent algorithm that dynamically adjusts the price. A key feature of our modeling framework is that customers may choose to balk - that is, decide not to join - when facing high congestion. A notable strength of our approach is that the revenue-maximizing algorithm relies solely on information about effective arrivals, meaning that only the behavior of customers who choose not to balk is observable and used in decision-making. This results in an elaborate interplay between the pricing policy and the effective arrival process, yielding a non-standard state dependent queueing process. An important contribution of our work concerns a novel Infinitesimal Perturbation Analysis (IPA) procedure that is able to consistently estimate the stationary effective arrival rate. This is further leveraged to construct an iterative algorithm that converges, under mild regularity conditions, to the optimal price with provable asymptotic guarantees.

math.OC↗
arXiv2026

Estimating Graph Dynamics from Population Observations

In this paper we consider a population process evolving on a dynamic random graph. The dynamic random graph is an Erdős--Rényi graph that is resampled every time unit, independently of the previous ones, with `edge existence probability' $p$. The population process consists of $M$ individuals which reside at the vertices of the dynamic graph. At each point in time any of the $M$ individuals, supposing it resides at a vertex with $k$ neighbors, jumps to an adjacent vertex with probability $k/(k+1)$ (where this adjacent vertex is picked uniformly at random), and with probability $1/(k+1)$ it stays where it is. We suppose we observe the numbers of individuals at each of the vertices, but not the evolving random graph itself. We propose two estimators for $p$, and establish their consistency and asymptotic normality.

math.PR↗
arXiv2026

Infection models on dense dynamic random graphs

We consider Susceptible-Infected-Recovered (SIR) models on dense dynamic random graphs, in which the joint dynamics of vertices and edges are co-evolutionary, i.e., they influence each other bidirectionally. In particular, edges appear and disappear over time depending on the states of the two connected vertices, on how long they have been infected, and on the total density of susceptible and infected vertices. Our main results establish functional laws of large numbers for the densities of susceptible, infected, and recovered vertices, jointly with the underlying evolving random graphs in the graphon space. Our results are supported by simulations, which characterize the limiting size of the epidemics, i.e., the limiting density of susceptible vertices, and how the peak of the epidemics depends on the rate of the evolution of the underlying graph. The proofs of our main results rely on the careful construction of a mimicking process, obtained by approximating the two-way feedback interaction between vertex and edge dynamics with a mean-field type interaction, acting only as one-way feedback, that remains sufficiently close to the original co-evolutionary process. To treat the more general setting in which edge dynamics are affected by the proportions of susceptible and infected individuals, we introduce a methodological extension of existing techniques. We thus show that our model exhibits multiple epidemic peaks -- a phenomenon observed in real-world epidemics -- which can emerge in models that incorporate mutual feedback between vertex and edge dynamics.

math.PR↗
arXiv2026

Exact analysis of transient behavior of finite-capacity MAP-driven queues

This paper studies the workload distribution of a finite-capacity queue driven by a spectrally one-sided Markov additive process (MAP). Our main result provides the Laplace-Stieltjes transform of the workload at an exponentially distributed time, thereby uniquely characterizing its transient distribution. The proposed approach combines several decompositions with established fluctuation-theoretic results for spectrally one-sided Lévy processes. For the special case of Markov-modulated compound Poisson input, we additionally derive results for the idle time and the cumulative amount of lost work. We conclude this paper with a series of numerical experiments.

math.PR↗
arXiv2026

Lévy-driven queuing networks in multi-scale light and heavy traffic

We study a queueing network with a strictly upper-triangular routing matrix, where each column contains at most one non-negative entry, and the root node receives input from a spectrally positive Lévy process. Our aim is to characterize the distribution of the multivariate stationary workload under a specific scaling of the service rates. Under mild conditions on the Laplace exponent of the driving Lévy process, we identify the limiting law of an appropriately scaled joint stationary workload in both light-traffic and heavy-traffic regimes. In particular, we establish conditions under which certain queueing workloads within the network asymptotically decouple, becoming independent in the limiting regime.

math.PR↗
arXiv2026

A framework for window design in delivery schedules

This paper develops a structured framework for the design and dynamic updating of service time windows in delivery and appointment-based systems. We consider a single-server setting with stochastic service and travel times, where customers are promised a time window in which the provider will arrive. The first part of the paper introduces a static window construction method based on a probabilistic threshold criterion, using an analytical approximation of residual travel and service time distributions. Building on this, we develop a dynamic update mechanism that monitors residual system uncertainty, where time windows are revised during execution only when the remaining time until the window's start falls below a predefined threshold. This threshold-based approach enables communication-efficient scheduling while substantially improving delivery accuracy. Numerical experiments demonstrate significant performance gains of the dynamic approach in both stylized and real-world settings.

math.OC↗
arXiv2025

Functional Central Limit Theorem for the simultaneous subgraph count of dynamic Erdős-Rényi random graphs

In this paper we consider a dynamic Erdős-Rényi random graph with independent identically distributed edge processes. Our aim is to describe the joint evolution of the entries of a subgraph count vector. The main result of this paper is a functional central limit theorem: we establish, under an appropriate centering and scaling, the joint functional convergence of the vector of subgraph counts to a specific multidimensional Gaussian process. The result holds under mild assumptions on the edge processes, most notably a Lipschitz-type condition.

math.PR↗
arXiv2025

Estimation of on- and off-time distributions in a dynamic Erdős-Rényi random graph

In this paper we consider a dynamic Erdős-Rényi graph in which edges, according to an alternating renewal process, change from present to absent and vice versa. The objective is to estimate the on- and off-time distributions while only observing the aggregate number of edges. This inverse problem is dealt with, in a parametric context, by setting up an estimator based on the method of moments. We provide conditions under which the estimator is asymptotically normal, and we point out how the corresponding covariance matrix can be identified. It is also demonstrated how to adapt the estimation procedure if alternative subgraph counts are observed, such as the number of wedges or triangles.

math.ST↗
arXiv2025

Parameter estimation in a dynamic Chung-Lu random graph

In this paper we consider a dynamic version of the Chung-Lu random graph in which the edges alternate between being present and absent. The main contribution concerns a technique by which one can estimate the underlying dynamics from partial information, in particular from snapshots of the total number of edges present. The efficacy of our inference method is demonstrated through a series of numerical experiments.

math.PR↗
arXiv2025

Delayed Hawkes birth-death processes

We introduce, and formally establish, a variant of the Hawkes-fed birth-death process -- the delayed Hawkes birth-death process -- in which the conditional intensity does not increase at arrivals but at departures from the system. In a scaling limit where sojourn times are stretched out by a factor $\sqrt T$, after which time gets contracted by a factor $T$, the delayed Hawkes process behaves markedly differently from its classical counterpart. We design a family of models admitting a cluster representation and containing the Hawkes and delayed Hawkes processes as special cases. The cluster representation allows for transform characterizations by a fixed-point equation and for analysis of heavy-tailed asymptotics. We compare the delayed Hawkes process to the classical Hawkes process using stochastic ordering, which enables us to describe stationary distributions and heavy-traffic behavior. In the Markovian network case, a recursive procedure is presented to calculate the $d$th-order moments analytically.

math.PR↗