10 citations · 72 across the 46 of their papers we have counts for
27 papers · 1 filter
Matrix-analytic methods for queues with Marshall--Olkin dependent servers
Qihui Bu, Suman Thapa, Yiqiang Q. Zhao
We study multiserver queues with Marshall--Olkin dependent service mechanisms, heterogeneous servers, and fixed idle-set assignment. An explicit matrix-analytic solution links the…
Markov Modelling Approach for Queues with Correlated Service Times -- the Model
Suman Thapa, Yiqiang Q. Zhao
Demand for studying queueing systems with multiple servers providing correlated services was created about 60 years ago, motivated by various applications. In recent years, the imp…
Matrix-analytic methods for solving Poisson's equation with applications to Markov chains of GI/G/1-type
Jinpeng Liu, Yuanyuan Liu, Yiqiang Q. Zhao
In this paper, we are devoted to developing matrix-analytic methods for solving Poisson's equation for irreducible and positive recurrent discrete-time Markov chains (DTMCs). Two s…
Local stability of McKean-Vlasov equations arising from heterogeneous Gibbs systems using limit of relative entropies
D. A. Dawson, A. Sid-Ali, Y. Q. Zhao
A family of heterogeneous mean-field systems with jumps is analyzed. These systems are constructed as a Gibbs measure on block graphs. When the total number of particles goes to in…
Large-time behavior of finite-state mean-field systems with multi-classes
Donald A. Dawson, Ahmed Sid-Ali, Yiqiang Q. Zhao
We study in this paper the large-time asymptotics of the empirical vector associated with a family of finite-state mean-field systems with multi-classes. The empirical vector is co…
GTH Algorithm, Censored Markov Chains, and -Factorization
Yiqiang Q. Zhao
In this paper, we provide a review on the GTH algorithm, which is a numerically stable algorithm for computing stationary probabilities of a Markov chain. Mathematically the GTH al…
Construction of New Copulas with Queueing Application
Suman Thapa, Yiqiang Q. Zhao
In this paper, we construct a bound copula, which can reach both Frechet's lower and upper bounds for perfect positive and negative dependence cases. Since it covers a wide range o…
Equilibrium and Socially optimal of a double-sided queueing system with two-mass point matching time
Zhen Wang, Cheryl Yang, Liwei Liu +1
We study a passenger-taxi double-ended queue with impatient passengers and two-point matching time in this paper. The system considered in this paper is different from those consid…
Kernel Method -- An Analytic Approach for Tail Asymptotics in Stationary Probabilities of 2-Dimensional Queueing Systems
Yiqiang Q. Zhao
In this paper, we provide a review on the kernel method, which is one of the options for characterizing so-called exact tail asymptotic properties in stationary probabilities of tw…
Augmented truncation approximations to the solution of Poisson's equation for Markov chains
Jinpeng Liu, Yuanyuan Liu, Yiqiang Q. Zhao
Poisson's equation has a lot of applications in various areas. Usually it is hard to derive the explicit expression of the solution of Poisson's equation for a Markov chain on an i…
Propagation of chaos and large deviations in mean-field models with jumps on block-structured networks
Donald A. Dawson, Ahmed Sid-Ali, Yiqiang Q. Zhao
A system of interacting multiclass finite-state jump processes is analyzed. The model under consideration consists of a block-structured network with dynamically changing multi-col…
Equilibrium customer and socially optimal balking strategies in a constant retrial queue with multiple vacations and -policy
Zhen Wang, Liwei Liu, Yiqiang Q. Zhao
In this paper, equilibrium strategies and optimal balking strategies of customers in a constant retrial queue with multiple vacations and the -policy under two information level…
Multidimensional Sticky Brownian Motions: Tail Behaviour of the Joint Stationary Distribution
Hongshuai Dai, Yiqiang Q. Zhao
Sticky Brownian motions, as time-changed semimartingale reflecting Brownian motions, have various applications in many fields, including queuing theory and mathematical finance. In…
Tail Asymptotics for the Retrial Queue with Priority
Bin Liu, Yiqiang Q. Zhao
Stochastic networks with complex structures are key modelling tools for many important applications. In this paper, we consider a specific type of network: the retrial queueing sys…
Exact tail asymptotics for a three dimensional Brownian-driven tandem queue with intermediate inputs
Hongshuai Dai, Dawson A. Donald, Yiqiang Q. Zhao
The semimartingale reflecting Brownian motion (SRBM) can be a heavy traffic limit for many server queueing networks. Asymptotic properties for stationary probabilities of the SRBM…
Exact tail asymptotics for fluid models driven by an queue
Wendi Li, Yuanyuan Liu, Yiqiang Q. Zhao
In this paper, we investigate exact tail asymptotics for the stationary distribution of a fluid model driven by the queue, which is a two-dimensional queueing system with a…
Stationary Distributions for Two-Dimensional Sticky Brownian Motions: Exact Tail Asymptotics and Extreme Value Distributions
Hongshuai Dai, Yiqiang Q. Zhao
In this paper, we consider a two-dimensional sticky Brownian motion. Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions, which find ap…
Join-the-Shortest-Queue Model as a Mean Field Approximation to a Local Balancing Network
Qihui Bu, Liwei Liu, Yiqiang Q. Zhao
In this paper, we consider a queueing network with nodes, each of which has a fixed number of neighboring nodes, referred to as the node network with local balancing. W…
Tail Asymptotics for a Retrial Queue with Bernoulli Schedule
Bin Liu, Yiqiang Q. Zhao
In this paper, we study the asymptotic behavior of the tail probability of the number of customers in the steady-state retrial queue with Bernoulli schedule, under the assu…
Mean Field Approximations to a Queueing System with Threshold-Based Workload Control Scheme
Qihui Bu, Liwei Liuand Yiqiang Q. Zhao
In this paper, motivated by considerations of server utilization and energy consumptions in cloud computing, we investigate a homogeneous queueing system with a threshold-based wor…
Second Order Asymptotic Properties for the Tail Probability of the Number of Customers in the M/G/1 Retrial Queue
Bin Liu, Yiqiang Q. Zhao
When an explicit expression for a probability distribution function can not be found, asymptotic properties of the tail probability function are very val…
Refined Tail Asymptotic Properties for the Retrial Queue
Bin Liu, Jie Min, Yiqiang Q. Zhao
In the literature, retrial queues with batch arrivals and heavy service times have been studied and the so-called equivalence theorem has been established under the condition that…
A Kernel Method for Exact Tail Asymptotics --- Random Walks in the Quarter Plane
Hui Li, Yiqiang Q. Zhao
In this paper, we propose a kernel method for exact tail asymptotics of a random walk to neighborhoods in the quarter plane. This is a two-dimensional method, which does not requir…
Exact Tail Asymptotics --- Revisit of a Retrial Queue with Two Input Streams and Two Orbits
Yang Song, Zaiming Liu, Yiqiang Q. Zhao
We revisit a single-server retrial queue with two independent Poisson streams (corresponding to two types of customers) and two orbits. The size of each orbit is infinite. The expo…