arXiv subjects

Andres Ferragut

Publications and source records attributed to Andres Ferragut.

5 recordsLinked to original sources

arXiv2026

Measure-valued fluid limits for partial service queues with correlated patience and service times

We consider a many-server queue where tasks with general patience and service times arrive as a renewal process. Contrary to the standard assumptions, we allow for preemption and abandonment during service, relevant in applications such as electric vehicle charging and anytime algorithms in cloud computing. Moreover, we do not assume independence of patience and service times, which has been a critical assumption in the literature. We describe the state of the system using a discrete measure on a two-dimensional orthant, such that the coordinates of its atoms represent the attained service and time in the system of tasks. Under mild assumptions, we derive the fluid limit as the number of servers approaches infinity and the arrival rate of tasks grows proportionally. The limit is given by a measure-valued integral transport equation that we solve explicitly when the initial condition is the null measure. We also prove that all solutions, regardless of the initial condition, converge to the same fixed point, which admits a closed-form expression. Our results focus on the preemptive Last-Come-First-Served (LCFS) policy, which has been identified as practically appealing in recent work.

math.PR↗

arXiv2025

Geometric lower bounds for the steady-state occupancy of processing networks with limited connectivity

We consider processing networks where multiple dispatchers are connected to single-server queues by a bipartite compatibility graph, modeling constraints that are common in data centers and cloud networks due to geographic reasons or data locality issues. We prove lower bounds for the steady-state occupancy, i.e., the complementary cumulative distribution function of the empirical queue length distribution. The lower bounds are geometric with ratios given by two flexibility metrics: the average degree of the dispatchers and a novel metric that averages the minimum degree over the compatible dispatchers across the servers. Using these lower bounds, we establish that the asymptotic performance of a growing processing network cannot match that of the classic Power-of-$d$ or JSQ policies unless the flexibility metrics approach infinity in the large-scale limit.

math.PR↗

arXiv2024

Optimal local storage policy based on stochastic intensities and its large scale behavior

In this paper, we analyze the optimal management of local memory systems, using the tools of stationary point processes. We provide a rigorous setting of the problem, building upon recent work, and characterize the optimal causal policy that maximizes the hit probability. We specialize the result for the case of renewal request processes and derive a suitable large scale limit as the catalog size N grows to infinity, when a fixed fraction c of items can be stored. We prove that in the limiting regime, the optimal policy amounts to comparing the stochastic intensity (observed hazard rate) of the process with a fixed threshold, defined by a quantile of an appropriate limit distribution, and derive asymptotic performance metrics, as well as sharp estimates for the pre-limit case. Moreover, we establish a connection with optimal timer based policies for the case of monotonic hazard rates. We also present detailed validation examples of our results, including some close form expressions for the miss probability that are compared to simulations. We also use these examples to exhibit the significant superiority of the optimal policy for the case of regular traffic patterns.

math.PR↗

arXiv2024

Dynamics and Optimization in Spatially Distributed Electrical Vehicle Charging

We consider a spatially distributed demand for electrical vehicle recharging, that must be covered by a fixed set of charging stations. Arriving EVs receive feedback on transport times to each station, and waiting times at congested ones, based on which they make a selfish selection. This selection determines total arrival rates in station queues, which are represented by a fluid state; departure rates are modeled under the assumption that clients have a given sojourn time in the system. The resulting differential equation system is analyzed with tools of optimization. We characterize the equilibrium as the solution to a specific convex program, which has connections to optimal transport problems, and also with road traffic theory. In particular a price of anarchy appears with respect to a social planner's allocation. From a dynamical perspective, global convergence to equilibrium is established, with tools of Lagrange duality and Lyapunov theory. An extension of the model that makes customer demand elastic to observed delays is also presented, and analyzed with extensions of the optimization machinery. Simulations to illustrate the global behavior are presented, which also help validate the model beyond the fluid approximation.

math.OC↗

arXiv2020

Minimal-Variance Distributed Deadline Scheduling

Many modern schedulers can dynamically adjust their service capacity to match the incoming workload. At the same time, however, unpredictability and instability in service capacity often incur operational and infrastructure costs. In this paper, we seek to characterize optimal distributed algorithms that maximize the predictability, stability, or both when scheduling jobs with deadlines. Specifically, we show that Exact Scheduling minimizes both the stationary mean and variance of the service capacity subject to strict demand and deadline requirements. For more general settings, we characterize the minimal-variance distributed policies with soft demand requirements, soft deadline requirements, or both. The performance of the optimal distributed policies is compared to that of the optimal centralized policy by deriving closed-form bounds and by testing centralized and distributed algorithms using real data from the Caltech electrical vehicle charging facility and many pieces of synthetic data from different arrival distribution. Moreover, we derive the Pareto-optimality condition for distributed policies that balance the variance and mean square of the service capacity. Finally, we discuss a scalable partially-centralized algorithm that uses centralized information to boost performance and a method to deal with missing information on service requirements.

math.OC↗