Siegmund Duality for Continuous Time Markov Chains on Z_+~d

For the continuous time Markov chain with transition function P（t） on Z d ＋ , we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P - （t）. If Q, the q-matrix of P（t）, is uniformly bounded, we show that the Siegmund dual relation can be expressed directly in terms of q-matrices, and a sufficient condition under which the Q-function is the Siegnmnd dual of some Q-function is also given.

Analyzing Effect of Demand Rate on Safety of Systems with Periodic Proof-tests

Quantitative safety assessment of safety systems plays an important role in decision making at all stages of system lifecycle, i.e., design, deployment and phase out. Most safety assessment methods consider only system parameters, such as configuration, hazard rate, coverage, repair rate, etc. along with periodic proof-tests （or inspection）. Not considering demand rate will give a pessimistic safety estimate for an application with low demand rate such as nuclear power plants, chemical plants, etc. In this paper, a basic model of IEC 61508 is used. The basic model is extended to incorporate process demand and behavior of electronic- and/or computer-based system following diagnosis or proof-test. A new safety index, probability of failure on actual demand （PFAD） based on extended model and demand rate is proposed. Periodic proof-test makes the model semi-Markovian, so a piece-wise continuous time Markov chain （CTMC） based method is used to derive mean state probabilities of elementary or aggregated state. Method to determine probability of failure on demand （PFD） （IEC 61508） and PFAD based on these state probabilities are described. In example, safety indices of PFD and PFAD are compared.

Formal management-specifying approach for model-based safety assessment

In the field of model-based system assessment,mathematical models are used to interpret the system behaviors.However,the industrial systems in this intelligent era will be more manageable.Various management operations will be dynamically set,and the system will be no longer static as it is initially designed.Thus,the static model generated by the traditional model-based safety assessment(MBSA)approach cannot be used to accurately assess the dependability.There mainly exists three problems.Complex:huge and complex behaviors make the modeling to be trivial manual;Dynamic:though there are thousands of states and transitions,the previous model must be resubmitted to assess whenever new management arrives;Unreusable:as for different systems,the model must be resubmitted by reconsidering both the management and the system itself at the same time though the management is the same.Motivated by solving the above problems,this research studies a formal management specifying approach with the advantages of agility modeling,dynamic modeling,and specification design that can be re-suable.Finally,three typical managements are specified in a series-parallel system as a demonstration to show the potential.

Reliability Analysis of Satellite Turntable System under Multiple Operation Modes Based on Multi-Valued Decision Diagrams

As a payload support system deployed on satellites,the turntable system is often switched among different working modes during the on-orbit operation,which can experience great state changes.In each mode,the missions to be completed are different,consecutive and non-over-lapping,from which the turntable system can be considered to be a phased-mission system(PMS).Reliability analysis for PMS has been widely studied.However,the system mode cycle characteristic has not been taken into account before.In this paper,reliability analysis method of the satellite turntable system is proposed considering its multiple operation modes and mode cycle characteristic.Firstly,the multi-valued decision diagrams(MDD)manipulation rules between two adjacent mission cycles are proposed.On this basis,MDD models for the turntable system in different states are established and the reliability is calculated using the continuous time Markov chains(CTMC)method.Finally,the comparative study is carried out to show the effectiveness of our proposed method.

AVAILABILITY MODEL FOR SELF TEST AND REPAIR IN FAULT TOLERANT FPGA-BASED SYSTEMS

Dynamically reconfigurable Field Programmable Gate Array(dr-FPGA) based electronic systems on board mission-critical systems are highly susceptible to radiation induced hazards that may lead to faults in the logic or in the configuration memory. The aim of our research is to characterize self-test and repair processes in Fault Tolerant(FT) dr-FPGA systems in the presence of environmental faults and explore their interrelationships. We develop a Continuous Time Markov Chain(CTMC) model that captures the high level fail-repair processes on a dr-FPGA with periodic online Built-In Self-Test(BIST) and scrubbing to detect and repair faults with minimum latency. Simulation results reveal that given an average fault interval of 36 s, an optimum self-test interval of 48.3 s drives the system to spend 13% of its time in self-tests, remain in safe working states for 76% of its time and face risky fault-prone states for only 7% of its time. Further, we demonstrate that a well-tuned repair strategy boosts overall system availability, minimizes the occurrence of unsafe states, and accommodates a larger range of fault rates within which the system availability remains stable within 10% of its maximum level.

A Stochastic SIVS Epidemic Model Based on Birth and Death Process

A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.

Probabilistic Modelling of COVID-19 Dynamic in the Context of Madagascar

We propose a probabilistic approach to modelling the propagation of the coronavirus disease 2019 (COVID-19) in Madagascar, with all its specificities. With the strategy of the Malagasy state, which consists of isolating all suspected cases and hospitalized confirmed case, we get an epidemic model with seven compartments: susceptible (S), Exposed (E), Infected (I), Asymptomatic (A), Hospitalized (H), Cured (C) and Death (D). In addition to the classical deterministic models used in epidemiology, the stochastic model offers a natural representation of the evolution of the COVID-19 epidemic. We inferred the models with the official data provided by the COVID-19 Command Center (CCO) of Madagascar, between March and August 2020. The basic reproduction number R0 and the other parameters were estimated with a Bayesian approach. We developed an algorithm that allows having a temporal estimate of this number with confidence intervals. The estimated values are slightly lower than the international references. Generally, we were able to obtain a simple but effective model to describe the spread of the disease.

Simplified Markov Model for Reliability Analysis of Phased-Mission System Using States Merging Method

This paper presents a simplified Markov model to evaluate the reliability of phased-mission system(PMS). The time cost and storage requirement are very huge for traditional Markov model to analyze the PMS reliability as the number of components increases to a large scale. The states merging method proposed in this paper can account for the PMS with subsystems consisting of identical components, and similar PMSs are common in real-world systems. The simplified Markov model by states merging has smaller number of system states, compared with the traditional one. Furthermore, for the above subsystems, the size of our model increases only linearly as the number of components increases, while the size of the traditional model exponentially increases.Finally, the effectiveness and correctness of our approach are analyzed by comparing with the traditional Markov method.

Survivability Evaluation in Large-Scale Mobile Ad-Hoc Networks

Survivability refers to the ability of a network system to fulfill critical services in a timely manner to end users in the presence of failures and/or attacks. In order to establish a highly survivable system, it is necessary to measure its survivability to evaluate the performance of the system＇s services under adverse conditions. According to survivability requirements of large-scale mobile ad-hoc networks （MANETs）, we propose a novel model for quantitative evaluation on survivability. The proposed model considers various types of faults and connection states of mobile hosts, and uses the continuous time Markov chain （CTMC） to describe the survivability of MANETs in a precise manner. We introduce the reliability theory to perform quantitative analysis and survivability evaluation of segment-by-segment routing （SSR）, multipath-based segment-by-segment routing （MP-SSR）, and segment-by-segment-based multipath routing （SS-MPR） in large-scale MANETs. The proposed model can be used to analyze the network performance much more easily than a simulation-based approach. Numerical validation shows that the proposed model can be used to obtain a better evaluation result on the survivability of large-scale MANETs.

Disjoint-Path Routing Mechanism in Mobile Opportunistic Networks

The prevalent multi-copy routing algorithms in mobile opportunistic networks(MONs)easily cause network congestion.This paper introduces a disjoint-path(DP)routing algorithm,where each node can only transmit packets once except the source node,to effectively control the number of packet copies in the network.The discrete continuous time Markov chain(CTMC)was utilized to analyze the state transition between nodes,and the copy numbers of packets with the DP routing algorithm were calculated.Simulation results indicate that DP has a great improvement in terms of packet delivery ratio,average delivery delay,average network overhead,energy and average hop count.