Markov Skeleton Processes

Hou,; Zhenting,; Liu, Ming; Zai-ming,; Zou,; Jie-zhong,

doi:10.1007/978-1-4613-0265-0_5

Cited by 13 publications

(21 citation statements)

References 6 publications

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“…The proof which was given by them, can be found in Chapter 1 of [5]. If we denote P x (X(t) ∈ A) by P (x, t, A) for x ∈ E, t ≥ 0 and A ∈ E, then Theorem 2.2 can be rewritten as follows:…”

Section: And There Exists H(x T A)mentioning

confidence: 98%

“…arrival processes) N (t) and the length L(t) of these models are Markov processes only when the models are M/M/1 and M/M/N (see [5]). Also, the waiting time (in the case of N = 1) W (t) is an MP only when the arrival processes are Possion processes [5] . Furthermore, the models MAP/G/1 (MAP means Markov Arrival Process), M + G/M/1, M + G/G/1 (M + G means that the distribution of the arrival time consists of two independent parts: one is determined by a Markov Arrival Process and the other is general), SMAP/G/1 (SMAP means Semi-Markov Arrival Process), M/P H/1, and the queueing network have been investigated recently by a number of researchers.…”

Section: Introductionmentioning

confidence: 99%

“…The input processes (i.e. arrival processes) N (t) and the length L(t) of these models are Markov processes only when the models are M/M/1 and M/M/N (see [5]). Also, the waiting time (in the case of N = 1) W (t) is an MP only when the arrival processes are Possion processes [5] .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Markov Skeleton Processes and Applications to Queueing Systems

Hou

2002

Acta Mathematicae Applicatae Sinica, English Series

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Section: And There Exists H(x T A)mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Markov Skeleton Processes and Applications to Queueing Systems

Hou

2002

Acta Mathematicae Applicatae Sinica, English Series

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“…It has been proposed and studied in probability theory (Hou and Liu 2005;Hou et al 1998) and applied to many fields including queueing theory and reliability engineering.…”

Section: Web Markov Skeleton Processmentioning

confidence: 99%

“…In probability theory, MSPs have been intensively studied and applied to queuing theory, reliability engineering, and other related fields (Hou and Liu 2005;Hou et al 1998). Note that in (Hou and Liu 2005;Hou et al 1998) the definition of MSP is slightly more narrow than ours, where it was required (among others) that for each n C 0, the future development of Z (namely, Zðs n þ ÁÞ) given the information of Z(s n ) should be conditionally independent of the history of Z prior to s n (see e.g.…”

Section: A Rigorous Definition In Mathematicsmentioning

confidence: 99%

Page importance computation based on Markov processes

Gao

Liu

et al. 2011

Inf Retrieval

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This paper is concerned with Markov processes for computing page importance. Page importance is a key factor in Web search. Many algorithms such as PageRank and its variations have been proposed for computing the quantity in different scenarios, using different data sources, and with different assumptions. Then a question arises, as to whether these algorithms can be explained in a unified way, and whether there is a general guideline to design new algorithms for new scenarios. In order to answer these questions, we introduce a General Markov Framework in this paper. Under the framework, a Web Markov Skeleton Process is used to model the random walk conducted by the web surfer on a given graph.average value that the page gives to the surfer in a single visit. These two factors can be computed as the stationary probability distribution of the corresponding embedded Markov chain and the mean staying time on each page of the Web Markov Skeleton Process respectively. We show that this general framework can cover many existing algorithms including PageRank, TrustRank, and BrowseRank as its special cases. We also show that the framework can help us design new algorithms to handle more complex problems, by constructing graphs from new data sources, employing new family members of the Web Markov Skeleton Process, and using new methods to estimate these two factors. In particular, we demonstrate the use of the framework with the exploitation of a new process, named Mirror Semi-Markov Process. In the new process, the staying time on a page, as a random variable, is assumed to be dependent on both the current page and its inlink pages. Our experimental results on both the user browsing graph and the mobile web graph validate that the Mirror Semi-Markov Process is more effective than previous models in several tasks, even when there are web spams and when the assumption on preferential attachment does not hold.

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Threshold dynamics of SAIRS epidemic model with semi‐Markov switching

Ottaviano

2023

Math Methods in App Sciences

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We study the threshold dynamics of a stochastic SAIRS-type model with vaccination, where the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the epidemic dynamics. In the model, the values of the disease transmission rate may switch between different levels under the effect of a semi-Markov process. We provide sufficient conditions ensuring the almost surely epidemic extinction and persistence in time mean. In the case of disease persistence, we investigate the omega-limit set of the system and give sufficient conditions for the existence and uniqueness of an invariant probability measure.

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Markov Skeleton Processes

Cited by 13 publications

References 6 publications

Markov Skeleton Processes and Applications to Queueing Systems

Markov Skeleton Processes and Applications to Queueing Systems

Page importance computation based on Markov processes

Threshold dynamics of SAIRS epidemic model with semi‐Markov switching

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