COHERENCE OF DEMPSTER'S CONDITIONING RULE IN DISCRETE POSSIBILISTIC MARKOV MODELS

2000 ◽  
Vol 08 (03) ◽  
pp. 241-252 ◽  
Author(s):  
HUGO J. JANSSEN ◽  
GERT DE COOMAN ◽  
ETIENNE E. KERRE
Keyword(s):  
Markov Models ◽  
Markov Condition ◽  
Selection Of Variables ◽  
One Step ◽  
Step Transition ◽  
The One ◽  
Available Information ◽  
Selection Of

We consider discrete possibilistic systems for which the available information is given by one-step transition possibilities and initial possibilities. These systems can be represented, or modelled, by a collection of variables satisfying a possibilistic counterpart of the Markov condition. This means that, given the values assumed by a selection of variables, the possibility that a subsequent variable assumes some value only depends on the value taken by the most recent variable of the selection. The one-step transition possibilities are recovered by computing the conditional possibility of any two consecutive variables. Under the behavioural interpretation as marginal betting rates against events these 'conditional' possibilities and the initial possibilities should satisfy the rationality criteria of 'avoiding sure loss' and 'coherence'. We show that this is indeed the case when the conditional possibilities are defined using Dempster's conditioning rule.

Perturbation theory for unbounded Markov reward processes with applications to queueing

1988 ◽  
Vol 20 (01) ◽  
pp. 99-111 ◽  
Author(s):  
Nico M. Van Dijk
Keyword(s):  
Transition Probabilities ◽  
Arrival Rate ◽  
Average Reward ◽  
Reward Function ◽  
One Step ◽  
Reward Process ◽  
Markov Reward ◽  
Step Transition ◽  
The One ◽  
Queueing Processes

Consider a perturbation in the one-step transition probabilities and rewards of a discrete-time Markov reward process with an unbounded one-step reward function. A perturbation estimate is derived for the finite horizon and average reward function. Results from [3] are hereby extended to the unbounded case. The analysis is illustrated for one- and two-dimensional queueing processes by an M/M/1-queue and an overflow queueing model with an error bound in the arrival rate.

Stabilité de la récurrence nulle pour certaines chaines de Markov perturbées

1983 ◽  
Vol 20 (3) ◽  
pp. 482-504 ◽  
Author(s):  
C. Cocozza-Thivent ◽  
C. Kipnis ◽  
M. Roussignol
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Transition Probability ◽  
The Other ◽  
Barrier Functions ◽  
One Step ◽  
Null Recurrence ◽  
Step Transition ◽  
The One ◽  
Taylor's Formula

We investigate how the property of null-recurrence is preserved for Markov chains under a perturbation of the transition probability. After recalling some useful criteria in terms of the one-step transition nucleus we present two methods to determine barrier functions, one in terms of taboo potentials for the unperturbed Markov chain, and the other based on Taylor's formula.

scholarly journals Transient analysis of a queue with queue-length dependent MAP and its application to SS7 network

1999 ◽  
Vol 12 (4) ◽  
pp. 371-392
Author(s):  
Bong Dae Choi ◽  
Sung Ho Choi ◽  
Dan Keun Sung ◽  
Tae-Hee Lee ◽  
Kyu-Seog Song
Keyword(s):  
Congestion Control ◽  
Queue Length ◽  
Transient Analysis ◽  
Transition Probabilities ◽  
Transient Behavior ◽  
Complex Model ◽  
Arrival Process ◽  
One Step ◽  
Step Transition ◽  
The One

We analyze the transient behavior of a Markovian arrival queue with congestion control based on a double of thresholds, where the arrival process is a queue-length dependent Markovian arrival process. We consider Markov chain embedded at arrival epochs and derive the one-step transition probabilities. From these results, we obtain the mean delay and the loss probability of the nth arrival packet. Before we study this complex model, first we give a transient analysis of an MAP/M/1 queueing system without congestion control at arrival epochs. We apply our result to a signaling system No. 7 network with a congestion control based on thresholds.

The Reliability Analysis of Mechanical Leg (2UPS+UP) Based on a Discrete Time Repairable Markov Model

2015 ◽  
Vol 713-715 ◽  
pp. 760-763
Author(s):  
Jia Lei Zhang ◽  
Zhen Lin Jin ◽  
Dong Mei Zhao
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Transition Probability ◽  
Continuous Model ◽  
Transition Probability Matrix ◽  
State Equations ◽  
One Step ◽  
The Difference ◽  
Step Transition ◽  
The One

We have analyzed some reliability problems of the 2UPS+UP mechanism using continuous Markov repairable model in our previous work. According to the check and repair of the robot is periodic, the discrete time Markov repairable model should be more appropriate. Firstly we built up the discrete time repairable model and got the one step transition probability matrix. Secondly solved the steady state equations and got the steady state availability of the mechanical leg, by the solution of the difference equations the reliability and the mean time to first failure were obtained. In the end we compared the reliability indexes with the continuous model.

The departure process from the GI/G/1 Queue

1969 ◽  
Vol 6 (3) ◽  
pp. 704-707 ◽  
Author(s):  
Thomas L. Vlach ◽  
Ralph L. Disney
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Transition Probabilities ◽  
Two Dimensional ◽  
Departure Process ◽  
Dimensional State Space ◽  
Semi Markov Process ◽  
One Step ◽  
Step Transition ◽  
The One

The departure process from the GI/G/1 queue is shown to be a semi-Markov process imbedded at departure points with a two-dimensional state space. Transition probabilities for this process are defined and derived from the distributions of the arrival and service processes. The one step transition probabilities and a stationary distribution are obtained for the imbedded two-dimensional Markov chain.

A Nonuniform Cell Partition for the Analysis of Nonlinear Stochastic Systems

1998 ◽  
Vol 65 (4) ◽  
pp. 867-869 ◽  
Author(s):  
J. Q. Sun
Keyword(s):  
Ad Hoc ◽  
Stochastic Systems ◽  
Transition Probability ◽  
Nonlinear Stochastic Systems ◽  
Transition Probability Density ◽  
Generalized Cell Mapping ◽  
One Step ◽  
Step Transition ◽  
The One ◽  
Cell Partition

This paper presents a study of nonuniform cell partition for analyzing the response of nonlinear stochastic systems by using the generalized cell mapping (GCM) method. The necessity of nonuniform cell partition for nonlinear systems is discussed first. An ad hoc scheme is then presented for determining optimal cell sizes based on the statistical analysis of the GCM method. The proposed nonuniform cell partition provides a roughly uniform accuracy for the estimate of the one-step transition probability density function over a large region in the state space where the system varies significantly from being linear to being strongly nonlinear. The nonuniform cell partition is shown to lead to more accurate steady-state solutions and enhance the computational efficiency of the GCM method.

Perturbation theory for unbounded Markov reward processes with applications to queueing

1988 ◽  
Vol 20 (1) ◽  
pp. 99-111 ◽  
Author(s):  
Nico M. Van Dijk
Keyword(s):  
Transition Probabilities ◽  
Arrival Rate ◽  
Average Reward ◽  
Reward Function ◽  
One Step ◽  
Reward Process ◽  
Markov Reward ◽  
Step Transition ◽  
The One ◽  
Queueing Processes

Consider a perturbation in the one-step transition probabilities and rewards of a discrete-time Markov reward process with an unbounded one-step reward function. A perturbation estimate is derived for the finite horizon and average reward function. Results from [3] are hereby extended to the unbounded case. The analysis is illustrated for one- and two-dimensional queueing processes by an M/M/1-queue and an overflow queueing model with an error bound in the arrival rate.

scholarly journals Imaging the emergence of bacterial turbulence: Phase diagram and transition kinetics

2021 ◽  
Vol 7 (17) ◽  
pp. eabd1240
Author(s):  
Yi Peng ◽  
Zhengyang Liu ◽  
Xiang Cheng
Keyword(s):  
Phase Diagram ◽  
Swimming Speed ◽  
Dominant Role ◽  
Quantitative Agreement ◽  
Interparticle Interactions ◽  
Long Wavelength ◽  
One Step ◽  
Quantitative Verification ◽  
Step Transition ◽  
The One

We experimentally study the emergence of collective bacterial swimming, a phenomenon often referred to as bacterial turbulence. A phase diagram of the flow of 3D Escherichia coli suspensions spanned by bacterial concentration, the swimming speed of bacteria, and the number fraction of active swimmers is systematically mapped, which shows quantitative agreement with kinetic theories and demonstrates the dominant role of hydrodynamic interactions in bacterial collective swimming. We trigger bacterial turbulence by suddenly increasing the swimming speed of light-powered bacteria and image the transition to the turbulence in real time. Our experiments identify two unusual kinetic pathways, i.e., the one-step transition with long incubation periods near the phase boundary and the two-step transition driven by long-wavelength instabilities deep inside the turbulent phase. Our study provides not only a quantitative verification of existing theories but also insights into interparticle interactions and transition kinetics of bacterial turbulence.

Ideal‐Filter Capillary Electrophoresis (IFCE) Facilitates the One‐Step Selection of Aptamers

2019 ◽  
Vol 131 (9) ◽  
pp. 2765-2769 ◽  
Author(s):  
An T. H. Le ◽  
Svetlana M. Krylova ◽  
Mirzo Kanoatov ◽  
Shrey Desai ◽  
Sergey N. Krylov
Keyword(s):  
Capillary Electrophoresis ◽  
One Step ◽  
Ideal Filter ◽  
The One ◽  
Step Selection ◽  
Selection Of

On a characterization property of finite irreducible Markov chains

1970 ◽  
Vol 7 (3) ◽  
pp. 771-775
Author(s):  
I. V. Basawa
Keyword(s):  
Transition Matrix ◽  
Transition Probabilities ◽  
Homogeneous Markov Chain ◽  
Finite State ◽  
One Step ◽  
Characterization Property ◽  
Step Transition ◽  
The One ◽  
Image Position ◽  
Finite State Space

Let {Xk}, k = 1, 2, ··· be a sequence of random variables forming a homogeneous Markov chain on a finite state-space, S = {1, 2, ···, s}. Xk could be thought of as the state at time k of some physical system for which are the (one-step) transition probabilities. It is assumed that all the states are inter-communicating, so that the transition matrix P = ((pij)) is irreducible.

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