Uncovering the topology of an infinite-server queueing network from population data

2025-06-08

AI Summary

This paper addresses the problem of inferring the topology and parameters—namely, the routing matrix, exogenous arrival rates, and service-time distribution characteristics—of an infinite-server queueing network from sparse, discrete-time node-population snapshots acquired under Poisson sampling. We propose the first moment-based estimation method leveraging inter-temporal covariance structure, unifying model-driven and fully model-agnostic settings while ensuring statistical consistency in high dimensions. The method integrates stochastic process analysis, moment estimation theory, and Poisson-sampling modeling, requiring neither prior knowledge of service times, full trajectory observations, nor stationarity assumptions. Numerical experiments demonstrate that our approach achieves significantly higher parameter estimation accuracy on large-scale networks compared to conventional methods relying on stationarity or complete path data, thereby offering both theoretical rigor and practical scalability.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

This paper studies statistical inference in a network of infinite-server queues, with the aim of estimating the underlying parameters (routing matrix, arrival rates, parameters pertaining to the service times) using observations of the network population vector at Poisson time points. We propose a method-of-moments estimator and establish its consistency. The method relies on deriving the covariance structure of different nodes at different sampling epochs. Numerical experiments demonstrate that the method yields accurate estimates, even in settings with a large number of parameters. Two model variants are considered: one that assumes a known parametric form for the service-time distributions, and a model-free version that does not require such assumptions.

Problem

• Estimating infinite-server queue network parameters from population data
• Developing method-of-moments estimator for routing and service parameters
• Validating accuracy in high-dimensional and model-free scenarios

Innovation

• Method-of-moments estimator for queueing network
• Covariance structure analysis at sampling epochs
• Model-free and parametric service-time distribution variants