114 citations · 348 across the 55 of their papers we have counts for
29 papers · 1 filter
Asymptotic product-form steady-state for generalized Jackson networks in multi-scale heavy traffic
J. G. Dai, Peter Glynn, Yaosheng Xu
We prove that under a multi-scale heavy traffic condition, the stationary distribution of the scaled queue length vector process in any generalized Jackson network has a product-fo…
Gaussian Limits for Scheduled Traffic with Super-Heavy Tailed Perturbations
Victor F. Araman, Peter W. Glynn
A scheduled arrival model is one in which customers are scheduled to arrive at constant interarrival times, but each customer actual arrival time is perturbed from her scheduled ar…
Stability of a Queue Fed by Scheduled Traffic at Critical Loading
Victor F. Araman, Peter W. Glynn
Consider the workload process for a single server queue with deterministic service times in which customers arrive according to a scheduled traffic process. A scheduled arrival seq…
A New Truncation Algorithm for Markov Chain Equilibrium Distributions with Computable Error Bounds
Alex Infanger, Peter W. Glynn
This paper introduces a new algorithm for numerically computing equilibrium (i.e. stationary) distributions for Markov chains and Markov jump processes with either a very large fin…
A Short Proof of a Convex Representation for Stationary Distributions of Markov Chains with an Application to State Space Truncation
Zeyu Zheng, Alex Infanger, Peter W. Glynn
In an influential paper, Courtois and Semal (1984) establish that when is an irreducible substochastic matrix for which , then the stationary di…
On Convergence of a Truncation Scheme for Approximating Stationary Distributions of Continuous State Space Markov Chains and Processes
Alex Infanger, Peter W. Glynn
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is ma…
On Convergence of General Truncation-Augmentation Schemes for Approximating Stationary Distributions of Markov Chains
Alex Infanger, Peter W. Glynn, Yuanyuan Liu
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is ma…
Solutions of Poisson's Equation for Stochastically Monotone Markov Chains
Peter W. Glynn, Alex Infanger
Stochastically monotone Markov chains arise in many applied domains, especially in the setting of queues and storage systems. Poisson's equation is a key tool for analyzing additiv…
Solving Poisson's Equation: Existence, Uniqueness, Martingale Structure, and CLT
Peter W. Glynn, Alex Infanger
The solution of Poisson's equation plays a key role in constructing the martingale through which sums of Markov correlated random variables can be analyzed. In this paper, we study…
Distributionally Robust Martingale Optimal Transport
Zhengqing Zhou, Jose Blanchet, Peter W. Glynn
We study the problem of bounding path-dependent expectations (within any finite time horizon ) over the class of discrete-time martingales whose marginal distributions lie withi…
Efficient Steady-state Simulation of High-dimensional Stochastic Networks
Jose Blanchet, Xinyun Chen, Peter Glynn +1
We propose and study an asymptotically optimal Monte Carlo estimator for steady-state expectations of a d-dimensional reflected Brownian motion. Our estimator is asymptotically opt…
A Probabilistic Proof of the Perron-Frobenius Theorem
Peter W. Glynn, Paritosh Y. Desai
The Perron-Frobenius theorem plays an important role in many areas of management science and operations research. This paper provides a probabilistic perspective on the theorem, by…
Approximating Performance Measures for Slowly Changing Non-stationary Markov Chains
Zeyu Zheng, Harsha Honnappa, Peter W. Glynn
This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabi…
Probabilistic Contraction Analysis of Iterated Random Operators
Abhishek Gupta, Rahul Jain, Peter Glynn
In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algor…
On Gaussian Limits and Large Deviations for Queues Fed by High Intensity Randomly Scattered Traffic
Peter W. Glynn, Harsha Honnappa
We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are inde- pendent and identically distributed. We ca…
Lyapunov Conditions for Differentiability of Markov Chain Expectations: the Absolutely Continuous Case
Chang-Han Rhee, Peter Glynn
We consider a family of Markov chains whose transition dynamics are affected by model parameters. Understanding the parametric dependence of (complex) performance measures of such…
Likelihood Ratio Gradient Estimation for Steady-State Parameters
Peter W. Glynn, Mariana Olvera-Cravioto
We consider a discrete-time Markov chain on a general state-space , whose transition probabilities are parameterized by a real-valued vector .…
Selecting the best system and multi-armed bandits
Peter Glynn, Sandeep Juneja
Consider the problem of finding a population or a probability distribution amongst many with the largest mean when these means are unknown but population samples can be simulated o…
On the Limiting Ratio of Current Age to Total Life for Null Recurrent Renewal Processes
Jose Blanchet, Peter Glynn, Hermann Thorisson
If the inter-arrival time distribution of a renewal process is regularly varying with index (i.e. the inter-arrival times have infinite mean) and if $A\lef…
Theoretical analysis of a Stochastic Approximation approach for computing Quasi-Stationary distributions of general state space Markov chains
Jose H. Blanchet, Peter Glynn, Shuheng Zheng
An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that wo…
Theoretical analysis of a Stochastic Approximation approach for computing Quasi-Stationary distributions
Jose Blanchet, Peter Glynn, Shuheng Zheng
This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in e…
Shape-constrained Estimation of Value Functions
Mohammad Mousavi, Peter W. Glynn
We present a fully nonparametric method to estimate the value function, via simulation, in the context of expected infinite-horizon discounted rewards for Markov chains. Estimating…
Exact Simulation of Non-stationary Reflected Brownian Motion
Mohammad Mousavi, Peter W. Glynn
This paper develops the first method for the exact simulation of reflected Brownian motion (RBM) with non-stationary drift and infinitesimal variance. The running time of generatin…
Central Limit Theorems and Large Deviations for Additive Functionals of Reflecting Diffusion Processes
Peter W. Glynn, Rob J. Wang
This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a…