A Stochastic Hybrid Systems framework for analysis of Markov reward models

Dhople, Sairaj V.; DeVille, Lee; Domínguez-García, Alejandro D.

doi:10.1016/j.ress.2013.10.011

Cited by 25 publications

(24 citation statements)

References 62 publications

(102 reference statements)

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“…For the SGN, in Theorem 1, there exists at least one mixed strategy NE. Through the work of Filar and Vrieze , an NE of a discounted stochastic game can be found by solving a nonlinear programming problem as follows.

\min_{u^{1}, u^{2}, σ^{1}, σ^{2}} ({}, 1^{T} ([], u^{k} - R^{k} ((),, π^{1}, π^{2}) - δ P ((),, π^{1}, π^{2}) u^{k})), k = 1, 2 R^{1} ((), p_{i}) π^{2} ((), p_{i}) + δ T ((),, p_{i}, u^{1}) π^{2} ((), p_{i}) \leq u^{1} ((), p_{i}) 1, i = 1, \dots, (||, P) T ((),, p, u^{k}) = {[{([], p ((), p_{1} true| p, t^{1}, t^{2}), \dots, p ((), p_{|P|} true| p, t^{1}, t^{2}))}^{T} u^{k}]}_{t^{1} \in T^{1}, t^{2} \in T^{2}}, p_{i} \in P, u^{k} \in ℜ^{|P|}

are variables for value vectors,

π^{k} \in Ω^{|T^{k}|}

and

true \underset{t_{i} \in t_{p}^{k}}{true\sum} π ((), t_{italicpi}^{k}) = 1

; 1 is a unit vector with appropriate dimensions, R k ( π 1 , π 2 ) is the vector [ π 1 ( p 1 ) T R k ( p 1 ) π 2 ( p 1 ), …, π 1 ( p | P | ) T R k ( p | P | ) π 2 ( p | P | )], and the state transition probability matrix P ( π 1 , π 2 ) induced by the strategy pair ( π 1 , π 2 ) is

[π^{1} {((), p)}^{T} ([], P ((), p^{'} | p, t^{1}, t^{<...>}))]

…”

Section: Security Model Of Digital Goods Businessmentioning

confidence: 99%

“…For the SGN, in Theorem 1, there exists at least one mixed strategy NE. Through the work of Filar and Vrieze Online digital goods business security analysis J. Lv and C. Zhao [11,20], an NE of a discounted stochastic game can be found by solving a nonlinear programming problem as follows. min…”

Section: Parametermentioning

confidence: 99%

“…Therefore, in this work, a mathematic and graphical modeling framework, based on stochastic game nets (SGN), is presented to model and analyze game issues [11,12]. This approach is appropriate to investigate complex and dynamic game issues and to compute the NE and best-response strategies in digital goods business.…”

Section: Introductionmentioning

confidence: 99%

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Security analysis of online digital goods business based on stochastic game net model

Liu

Zhao

2015

Security Comm Networks

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Digital goods business as a new mode of e‐commerce develops distinct features while it faces new threats. The aim of this paper is to show how a stochastic game nets (SGN) framework can be used to model and analyze digital goods business that is subject to various attacks. We illustrate our work in the following steps. A scenario of digital goods business security is built to identify action procedures of participants in the scene and to investigate the risk factors. Next, the interactive processes in digital goods business scenario is used for designing, establishing, and simulating an extensible graphically SGN model. The developed SGN model provides an efficient environment for defining uncertainties in digital goods business with proposed indicators. The findings of the study show that business security can be improved by using risk management actions, and the overall system costs can be reduced. Copyright © 2015 John Wiley & Sons, Ltd.

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\min_{u^{1}, u^{2}, σ^{1}, σ^{2}} ({}, 1^{T} ([], u^{k} - R^{k} ((),, π^{1}, π^{2}) - δ P ((),, π^{1}, π^{2}) u^{k})), k = 1, 2 R^{1} ((), p_{i}) π^{2} ((), p_{i}) + δ T ((),, p_{i}, u^{1}) π^{2} ((), p_{i}) \leq u^{1} ((), p_{i}) 1, i = 1, \dots, (||, P) T ((),, p, u^{k}) = {[{([], p ((), p_{1} true| p, t^{1}, t^{2}), \dots, p ((), p_{|P|} true| p, t^{1}, t^{2}))}^{T} u^{k}]}_{t^{1} \in T^{1}, t^{2} \in T^{2}}, p_{i} \in P, u^{k} \in ℜ^{|P|}

are variables for value vectors,

π^{k} \in Ω^{|T^{k}|}

and

true \underset{t_{i} \in t_{p}^{k}}{true\sum} π ((), t_{italicpi}^{k}) = 1

[π^{1} {((), p)}^{T} ([], P ((), p^{'} | p, t^{1}, t^{<...>}))]

…”

Section: Security Model Of Digital Goods Businessmentioning

confidence: 99%

Section: Parametermentioning

confidence: 99%

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Security analysis of online digital goods business based on stochastic game net model

Liu

Zhao

2015

Security Comm Networks

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“…Garg (2015b) used RAM-index for analyzing the effect of individual components on performance of bleaching unit of paper industry and computed results are compared with LambdaTau and fuzzy methodologies. Dhople et al (2014) proposed a framework to analyze Markov reward models, which are commonly used in system performability analysis. Sharma and Khanduja (2013) discussed the performance evaluation of refining system of sugar plant.…”

Section: Introductionmentioning

confidence: 99%

Performance modeling of the serial processes in refining system of a sugar plant using RAMD analysis

Aggarwal

Kumar

Singh

2016

Int J Syst Assur Eng Manag

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The main objective of this paper is to present a method to identify the critical component of the system. As traditionally, any one parameter among availability, reliability and maintainability parameters is computed to identify the critical component and its effect on performance of the system. In this paper, reliability, availability, maintainability and dependability (RAMD) parameters or indices are computed to identify the critical component of the system. Mathematical modeling of the system based on Markov birth-death process is carried out to derive Chapman-Kolmogorov differential equations. These equations are further solved and RAMD parameters are computed with mean time between failures (MTBF), mean time to repair (MTTR) and dependability ratio parameters for each component of the system. Sensitivity analysis has been conducted for finding the most critical component of the system by varying the failure and repair rates of each subsystem of the system. To show the application of the proposed method, a case of the refining system, a repairable industrial system of sugar plant has been taken for evaluating RAMD indices of the system.

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“…Additionally, metastability and large deviations in SHS were studied in [7] using path-integral methods, and limit theorems for PDMP are presented in [37]. SHS represent a powerful formalism that has been applied to many fields, including: networked control systems [1], power systems [15], system reliability theory [16], and chemical reaction dynamics [42]. A recent and comprehensive review of the state of the art of such systems, that also contains an extensive history, bibliography, and list of applications of SHS, is [45].…”

mentioning

confidence: 99%

Moment Closure and Finite-Time Blowup for Piecewise Deterministic Markov Processes

DeVille

Dhople

Domínguez-García³

et al. 2016

SIAM J. Appl. Dyn. Syst.

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We present a variety of results analyzing the behavior of a class of stochastic processes-referred to as Piecewise Deterministic Markov Processes (PDMPs)-on the infinite time interval, and determine general conditions on when the moments of such processes will, or will not, be wellbehaved. We also characterize the types of finite-time blowups that are possible for these processes, and obtain bounds on their probabilities.

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A Stochastic Hybrid Systems framework for analysis of Markov reward models

Cited by 25 publications

References 62 publications

Security analysis of online digital goods business based on stochastic game net model

Security analysis of online digital goods business based on stochastic game net model

Performance modeling of the serial processes in refining system of a sugar plant using RAMD analysis

Moment Closure and Finite-Time Blowup for Piecewise Deterministic Markov Processes

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