The Decay Parameter and Invariant Measures for Markovian Bulk-Arrival Queues with Control at Idle Time

2011 ◽  
Vol 15 (2) ◽  
pp. 467-484 ◽  
Author(s):  
Li Junping ◽  
Chen Anyue
Keyword(s):  
Invariant Measures ◽  
Idle Time ◽  
Decay Parameter ◽  
Bulk Arrival

scholarly journals Decay property of stopped Markovian bulk-arriving queues

2008 ◽  
Vol 40 (1) ◽  
pp. 95-121 ◽  
Author(s):  
Junping Li ◽  
Anyue Chen
Keyword(s):  
Generating Functions ◽  
Busy Period ◽  
Invariant Measures ◽  
Geometric Interpretation ◽  
Decay Property ◽  
Decay Parameter ◽  
Decay Properties ◽  
Invariant Vectors ◽  
Quasistationary Distributions

We consider decay properties including the decay parameter, invariant measures, invariant vectors, and quasistationary distributions of a Markovian bulk-arriving queue that stops immediately after hitting the zero state. Investigating such behavior is crucial in realizing the busy period and some other related properties of Markovian bulk-arriving queues. The exact value of the decay parameter λC is obtained and expressed explicitly. The invariant measures, invariant vectors, and quasistationary distributions are then presented. We show that there exists a family of invariant measures indexed by λ ∈ [0, λC]. We then show that, under some conditions, there exists a family of quasistationary distributions, also indexed by λ ∈ [0, λC]. The generating functions of these invariant measures and quasistationary distributions are presented. We further show that a stopped Markovian bulk-arriving queue is always λC-transient and some deep properties are revealed. The clear geometric interpretation of the decay parameter is explained. A few examples are then provided to illustrate the results obtained in this paper.

Uniqueness and Decay Properties of Markov Branching Processes with Disasters

2014 ◽  
Vol 51 (03) ◽  
pp. 613-624 ◽  
Author(s):  
Anyue Chen ◽  
Kai Wang Ng ◽  
Hanjun Zhang
Keyword(s):  
Branching Process ◽  
Invariant Measures ◽  
Branching Processes ◽  
Decay Parameter ◽  
Markov Branching Process ◽  
Decay Properties ◽  
Invariant Vectors ◽  
Quasistationary Distributions

In this paper we discuss the decay properties of Markov branching processes with disasters, including the decay parameter, invariant measures, and quasistationary distributions. After showing that the corresponding q-matrix Q is always regular and, thus, that the Feller minimal Q-process is honest, we obtain the exact value of the decay parameter λ C . We show that the decay parameter can be easily expressed explicitly. We further show that the Markov branching process with disaster is always λ C -positive. The invariant vectors, the invariant measures, and the quasidistributions are given explicitly.

scholarly journals Uniqueness and Decay Properties of Markov Branching Processes with Disasters

2014 ◽  
Vol 51 (3) ◽  
pp. 613-624 ◽  
Author(s):  
Anyue Chen ◽  
Kai Wang Ng ◽  
Hanjun Zhang
Keyword(s):  
Branching Process ◽  
Invariant Measures ◽  
Branching Processes ◽  
Decay Parameter ◽  
Markov Branching Process ◽  
Decay Properties ◽  
Invariant Vectors ◽  
Quasistationary Distributions

In this paper we discuss the decay properties of Markov branching processes with disasters, including the decay parameter, invariant measures, and quasistationary distributions. After showing that the corresponding q-matrix Q is always regular and, thus, that the Feller minimal Q-process is honest, we obtain the exact value of the decay parameter λC. We show that the decay parameter can be easily expressed explicitly. We further show that the Markov branching process with disaster is always λC-positive. The invariant vectors, the invariant measures, and the quasidistributions are given explicitly.

scholarly journals Decay property of stopped Markovian bulk-arriving queues

2008 ◽  
Vol 40 (01) ◽  
pp. 95-121 ◽  
Author(s):  
Junping Li ◽  
Anyue Chen
Keyword(s):  
Generating Functions ◽  
Busy Period ◽  
Invariant Measures ◽  
Geometric Interpretation ◽  
Decay Property ◽  
Decay Parameter ◽  
Decay Properties ◽  
Invariant Vectors ◽  
Quasistationary Distributions

We consider decay properties including the decay parameter, invariant measures, invariant vectors, and quasistationary distributions of a Markovian bulk-arriving queue that stops immediately after hitting the zero state. Investigating such behavior is crucial in realizing the busy period and some other related properties of Markovian bulk-arriving queues. The exact value of the decay parameter λCis obtained and expressed explicitly. The invariant measures, invariant vectors, and quasistationary distributions are then presented. We show that there exists a family of invariant measures indexed by λ ∈ [0, λC]. We then show that, under some conditions, there exists a family of quasistationary distributions, also indexed by λ ∈ [0, λC]. The generating functions of these invariant measures and quasistationary distributions are presented. We further show that a stopped Markovian bulk-arriving queue is always λC-transient and some deep properties are revealed. The clear geometric interpretation of the decay parameter is explained. A few examples are then provided to illustrate the results obtained in this paper.

Decay parameter for general stopped Markovian bulk-arrival and bulk-service queues

2021 ◽  
Author(s):  
Anyue Chen ◽  
Junping Li ◽  
Xiaohan Wu ◽  
Jing Zhang
Keyword(s):  
Decay Parameter ◽  
Bulk Service ◽  
Bulk Arrival

eMap: A Web Application for Identifying and Visualizing Electron or Hole Hopping Pathways in Proteins

2019 ◽  
Author(s):  
Ruslan N. Tazhigulov ◽  
James R. Gayvert ◽  
Melissa Wei ◽  
Ksenia B. Bravaya
Keyword(s):  
Web Application ◽  
Shortest Paths ◽  
Coarse Grained ◽  
Decay Parameter ◽  
Electron Hole ◽  
Web Based ◽  
Aromatic Amino Acid Residue ◽  
Pathways Model ◽  
Visualization Tools ◽  
Effective Decay

<p>eMap is a web-based platform for identifying and visualizing electron or hole transfer pathways in proteins based on their crystal structures. The underlying model can be viewed as a coarse-grained version of the Pathways model, where each tunneling step between hopping sites represented by electron transfer active (ETA) moieties is described with one effective decay parameter that describes protein-mediated tunneling. ETA moieties include aromatic amino acid residue side chains and aromatic fragments of cofactors that are automatically detected, and, in addition, electron/hole residing sites that can be specified by the users. The software searches for the shortest paths connecting the user-specified electron/hole source to either all surface-exposed ETA residues or to the user-specified target. The identified pathways are ranked based on their length. The pathways are visualized in 2D as a graph, in which each node represents an ETA site, and in 3D using available protein visualization tools. Here, we present the capability and user interface of eMap 1.0, which is available at https://emap.bu.edu.</p>

Extending Quasi-Invariant Measures by Using Subgroups of a Given Group

2003 ◽  
Vol 10 (2) ◽  
pp. 247-255
Author(s):  
A. Kharazishvili
Keyword(s):  
Invariant Measures ◽  
Uncountable Group

Abstract A method of extending σ-finite quasi-invariant measures given on an uncountable group, by using a certain family of its subgroups, is investigated.

scholarly journals Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 80
Author(s):  
Sergey Kryzhevich ◽  
Viktor Avrutin ◽  
Nikita Begun ◽  
Dmitrii Rachinskii ◽  
Khosro Tajbakhsh
Keyword(s):  
Risk Management ◽  
Invariant Measure ◽  
Invariant Measures ◽  
Interval Exchange ◽  
Management Model ◽  
Closing Lemma ◽  
Symbolic Model ◽  
Metric Properties ◽  
Ergodic Measures ◽  
Maximal Invariant

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the number of ergodic measures and the minimality of the symbolic model) to ITMs. Further, we proved a version of the closing lemma and studied how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally.

Sign in / Sign up

Export Citation Format

Share Document