Upper and Lower Class Functions for Maximum Likelihood Estimator for Single server Queues

Nonparametric estimation of service time characteristics in infinite-server queues with nonstationary Poisson input

This paper provides a mathematical framework for estimation of the service time distribution and the expected service time of an infinite-server queueing system with a nonhomogeneous Poisson arrival process, in the case of partial information, where only the number of busy servers are observed over time. The problem is reduced to a statistical deconvolution problem, which is solved by using Laplace transform techniques and kernels for regularization. Upper bounds on the mean squared error of the proposed estimators are derived. Some concrete simulation experiments are performed to illustrate h…

从总体数据中揭示无限服务排队网络的拓扑结构

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

本文针对无限服务排队网络，提出矩估计方法并证明其一致性，结合协方差结构推导完成参数估计，经数值实验验证方法在多参数场景下仍能准确估计，还涵盖含已知服务时间分布与无模型两种变体。

Statistical analysis of single-server loss queueing systems

In this article statistical bounds for certain output characteristics of the $M/GI/1/n$ and $GI/M/1/n$ loss queueing systems are derived on the basis of large samples of an input characteristic of these systems, such as service time in the $M/GI/1/n$ queueing system or interarrival time in the $GI/M/1/n$ queueing system. The analysis of this article is based on application of Kolmogorov's statistics for empirical probability distribution functions.