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25th IEEE/ACM International Symposium on Quality of Service (IWQoS)

作者： Dong, Fang Wu, Kui Srinivasan, Venkatesh Univ Victoria Dept Comp Sci Victoria BC V8W 3P6 Canada

ISBN: (纸本)9781538627044

markov-modulated poisson process (MMPP) has been extensively studied in random process theory and widely used as a network traffic model. Most methods for estimating MMPP parameters are based on the exact arrival times. Nevertheless, in many applications it is costly to record the exact time of each arrival. Instead, we only record the number of arrivals in fixed-length time slots, which is called arrival count. Since arrival count data does not maintain detailed arrival times, it is non trivial to develop effective methods for MMPP parameter estimation with arrival counts only. Very few existing works deal with this challenge. This paper tackles the above challenge with copula analysis. The theoretical marginal distribution and copula of arrival counts in MMPP are applied to develop a new estimation method, Mar-Cpa, which is a two-step estimation method involving marginal matching followed by copula matching. Our evaluation results demonstrate that the proposed method is fast and accurate.

关键词： markov-modulated poisson process Arrival Counts Copula Parameter Estimation

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Estimating the parameters of a seasonal markov-modulated poisson process

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STATISTICAL METHODOLOGY 2015年 26卷 103-123页

作者： Guillou, Armelle Loisel, Stephane Stupfler, Gilles Univ Strasbourg F-67084 Strasbourg France CNRS IRMA UMR 7501 F-67084 Strasbourg France Univ Lyon 1 Inst Sci Financiere & Assurances F-69007 Lyon France Aix Marseille Univ CNRS EHESS GREQAM UMR 7316Cent Marseille F-13002 Marseille France

Motivated by seasonality and regime-switching features of some insurance claim counting processes, we study the statistical analysis of a markov-modulated poisson process featuring seasonality. We prove the strong consistency and the asymptotic normality of a maximum split-time likelihood estimator of the parameters of this model, and present an algorithm to compute it in practice. The method is illustrated on a small simulation study and a real data analysis. (C) 2015 Elsevier B.V. All rights reserved.

关键词： markov-modulated poisson process Seasonality Split-time likelihood Strong consistency Asymptotic normality

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Hawkes process Modelling for Chemical Reaction Networks in a Random

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SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 2024年第3期23卷 2444-2488页

作者： Sinzger-D'Angelo, Mark Hasenauer, Jan Koeppl, Heinz Tech Univ Darmstadt Dept Elect Engn & Informat Technol Darmstadt Germany Univ Bonn Interdisciplinary Res Unit Math & Life Sci Bonn Germany Tech Univ Darmstadt Dept Elect Engn & Informat Technol Darmstadt Germany Tech Univ Darmstadt Ctr Synthet Biol Darmstadt Germany

Cellular processes are open systems, situated in a heterogeneous context, rather than operating in isolation. Chemical reaction networks (CRNs) whose reaction rates are modelled as external stochastic processes account for the heterogeneous environment when describing the embedded process. A marginal description of the embedded process is of interest for (i) marginal simulations that bypass the co-simulation of the environment, (ii) obtaining new process equations from which moment equations can be derived, (iii) the computation of information-theoretic quantities, and (iv) state estimation. It is known since Snyder's and related works that marginalization over a stochastic intensity turns point processes into self-exciting ones. While the Snyder filter specifies the exact history-dependent propensities in the framework of CRNs in a markov environment, it was recently suggested to use approximate filters for the marginal description. By regarding the chemical reactions as events, we establish a link between CRNs in a linear random environment and Hawkes processes, a class of self-exciting counting processes widely used in event analysis. The Hawkes approximation can be obtained via a moment closure scheme or as the optimal linear approximation under the quadratic criterion. We show the equivalence of both approaches. Furthermore, we use martingale techniques to provide results on the agreement of the Hawkes process and the exact marginal process in their second-order statistics, i.e., covariance, auto/cross-correlation. We introduce an approximate marginal simulation algorithm and illustrate it in case studies.

关键词： markov-modulated poisson process chemical reaction networks random environment marginal simulation spectral analysis Hawkes process

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Asymptotic Analysis of the Output process in Retrial Queue with markov-modulated poisson Input Under Low Rate of Retrials Condition 22nd

Asymptotic Analysis of the Output Process in Retrial Queue w...

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22nd International Conference on Distributed Computer and Communication Networks (DCCN)

作者： Lapatin, Ivan Nazarov, Anatoly Natl Res Tomsk State Univ Inst Appl Math & Comp Sci 36 Lenina Ave Tomsk 634050 Russia

ISBN: (纸本)9783030366254;9783030366247

We consider retrial queue with markov-modulated poisson input process and exponential probability distribution of service durations. The object of our research is output flow of the system. We use asymptotic analysis method under low rate of retrials limit condition to obtain probability distribution of the number of served customers at the moment t. The obtained formulae has explicit expression and contains matrix exponential. Furthermore, we show that the output belongs to the class of markovian arrival processes.

关键词： Output process Retrial queue markov-modulated poisson process markovian arrival process Queueing system Asymptotic analysis method

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Cloud Firewall Under Bursty and Correlated Data Traffic: A Theoretical Analysis

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IEEE TRANSACTIONS ON CLOUD COMPUTING 2022年第3期10卷 1620-1633页

作者： Carvalho, Glaucio H. S. Woungang, Isaac Anpalagan, Alagan Ryerson Univ Dept Comp Sci 350 Victoria St Toronto ON M5B 2K3 Canada Ryerson Univ Dept Elect & Comp Engn Toronto ON M5B 2K3 Canada

Cloud firewalls stand as one of the major building blocks of the cloud security framework protecting the Virtual Private Infrastructure against attacks such as the Distributed Denial of Service (DDoS). In order to fully characterize the cloud firewall operation and gain actionable insights on the design of cloud security, performance models for the cloud firewall become imperative. In this article, we propose a multi-dimensional Continuous-Time markov Chain model for the cloud firewall that takes into account the burstiness and correlation features of the legitimate and malicious data traffic. By adopting the markov-modulated poisson process (MMPP) and the Interrupted poisson process (IPP), we identify the workload conditions under which the cloud firewall might be subject to a loss of availability. Furthermore, by comparing the IPP and poisson attacks, we numerically verify that the cloud firewall is inherently vulnerable to a burstiness-aware attack which might seriously compromise its operation. Additionally, we characterize the joint harmful impact of burstiness and correlation on the cloud firewall that might lead to performance degradation. Finally, we design an elastic doud firewall by proposing a MMPP-driven load balancing procedure that provisions virtual firewalls dynamically while fulfilling a Service Level Agreement (SLA) latency specification.

关键词： Cloud security DDoS markov process firewall markov-modulated poisson process

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Optimal liquidation problem in illiquid markets

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第3期296卷 1050-1066页

作者： Sadoghi, Amirhossein Vecer, Jan Rennes Sch Business Dept Finance & Accounting 2 Rue Robert dArbrissel F-35065 Rennes France Charles Univ Prague Dept Probabil & Math Stat Sokolovska 83 Prague 18675 8 Czech Republic Frankfurt Sch Finance & Management Dept Finance Adickesalle 32-34 D-60322 Frankfurt Germany

In this research, we develop a trading strategy for the optimal liquidation problem of large-order trading, with different market microstructures, in an illiquid market. We formulate the liquidation problem as a discrete-time markov decision process. In this market, the flow of liquidity events can be viewed as a point process with stochastic intensity. Based on this fact, we model the price impact as a linear func-tion of a self-exciting dynamic process. Our trading algorithm is designed in such a way that when no favourite orders arrive in the Limit Order Book (LOB), the optimal solution takes offers from the lower levels of the LOB. This solution might contradict conventional optimal execution methods, which only trade with the best available limit orders;however, our findings show that the proposed strategy may reduce final inventory costs by preventing orders not being filled at earlier trading times. Furthermore, the results indicate that an optimal trading strategy is dependent on characteristics of the market mi-crostructure. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Finance Optimal liquidation problem Illiquid market markov-modulated poisson process Hawkes processes

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STATIONARY markovIAN ARRIVAL processES: RESULTS AND OPEN PROBLEMS

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ANZIAM JOURNAL 2022年第1期64卷 54-68页

作者： Asanjarani, Azam Nazarathy, Yoni Univ Auckland Dept Math Auckland 1142 New Zealand Univ Queensland Sch Math & Phys St Lucia Qld Australia

We consider two classes of irreducible markovian arrival processes specified by the matrices C and D: the markov-modulated poisson process (MMPP) and the markov-switched poisson process (MSPP). The former exhibits a diagonal matrix D while the latter exhibits a diagonal matrix C. For these two classes we consider the following four statements: (I) the counting process is overdispersed;(II) the hazard rate of the event-stationary interarrival time is nonincreasing;(III) the squared coefficient of variation of the event-stationary process is greater than or equal to one;(IV) there is a stochastic order showing that the time-stationary interarrival time dominates the event-stationary interarrival time. For general MSPPs and order two MMPPs, we show that (I)-(IV) hold. Then for general MMPPs, it is easy to establish (I), while (II) is shown to be false by a counter-example. For general simple point processes, (III) follows from (IV). For MMPPs, we conjecture that (IV) and thus (III) hold. We also carry out some numerical experiments that fail to disprove this conjecture. Importantly, modelling folklore has often treated MMPPs as "bursty", and implicitly assumed that (III) holds. However, to the best of our knowledge, proving this is still an open problem.

关键词： markovian arrival process markov-modulated poisson process markov-switched poisson process over-dispersion hazard rate squared coefficient of variation interarrival times stationary process bursty

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Stochastic Evolution Under markov-modulated poisson Perturbation in the Diffusion Approximation Scheme

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CYBERNETICS AND SYSTEMS ANALYSIS 2025年

作者： Chabanyuk, Ya. M. Semenyuk, S. A. Khimka, U. T. Chypurko, R. A. Ivan Franko Natl Univ Lviv Lvov Ukraine Lublin Univ Technol Lublin Poland Lviv Polytech Natl Univ Lvov Ukraine

The authors studied the asymptotic behavior of stochastic evolutionary systems with markov-modulated poisson perturbation in the diffusion approximation scheme. They considered combining the poisson process with the markov process, which enables describing random transitions between different modes of evolution. The authors presented the ergodic properties of the markov-modulated poisson process that ensure the stable system's behavior on average. They also constructed limit generators for the original system of stochastic differential equations. The results allow for studying stochastic optimization and optimal control problems.

关键词： stochastic evolution markov-modulated poisson process diffusion approximation scheme

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markov-modulated poisson processes as a new framework for analysing capture-recapture data

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METHODS IN ECOLOGY AND EVOLUTION 2018年第4期9卷 929-935页

作者： Choquet, Remi Paul Valery Montpellier 3 Univ Univ Montpellier CNRS CEFE Montpellier 5 France

1. Opportunistic capture-recapture data consists of observations over non-constant time intervals and so fails to satisfy the basic assumptions of traditional capture-recapture models. Analysing opportunistic capture-recapture data is often done by discretizing time intervals or summarizing data, but without taking into account the continuous time process of the state and/or the capture. 2. To deal with non-constant time-intervals, continuous time closed capture-recapture models have been proposed by Yip, Huggins, and Lin (1996), Hwang and Chao (2002), Schofield, Barker, and Gelling (2017) for estimating population size. More recently, a continuous time Cormack-Jolly-Seber model has been proposed by Fouchet, Santin-Janin, Sauvage, Yoccoz, and Pontier (2016) to reduce bias in survival rates, and a two-state process has been proposed by Choquet, Garnier, Awuve, and Besnard (2017) to estimate reproduction rates and survival rates of young within a season. 3. The aim of the current study is to demonstrate how an approach based on a markov-modulated poisson process (MMPP) (Freed & Shepp, 1982) allows, in a similar way to a multistate model, to model opportunistic data, using several states. To this end, several multistate models were rewritten as MMPP models, showing, the potential for this approach to address the ecological questions as multistate models, but using an extended data framework. In particular, it is a useful framework for dealing with data that has unordered levels of uncertainty. 4. The methods were illustrated using simulations and analysis of data on the Alpine ibex (Capra ibex).

关键词： capture-recapture likelihood markov-modulated poisson process non-constant time interval uncertainty

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Traffic model of machine-type communication for railway signal equipment based on MMPP

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IET MICROWAVES ANTENNAS & PROPAGATION 2019年第8期13卷 1072-1079页

作者： Lin, Junting Hu, Xueyang Dang, Jianwu Wu, Zhongqing Lanzhou Jiaotong Univ Sch Automat & Elect Engn Lanzhou Gansu Peoples R China Lanzhou Jiaotong Univ Sch Elect & Informat Engn Lanzhou Gansu Peoples R China

Machine-to-machine communication can realise considerably better information cognition of fixed and mobile equipment during rail transit. To assess the network access performance of the machine-type communication (MTC) of railway signal equipment for next-generation intelligent transportation system, the forecasting model of the machine communication traffic of railway signal equipment was divided into station indoor model, station outdoor model, and section movement model on the basis of cell units, and the traffic quantity and signaling overhead of the three models were calculated respectively. Based on poisson's distribution and the markov update process, an improved markov-modulated poisson process (IMMPP) of the source traffic model was designed. Compared with the 3GPP traffic model, the IMMPP model maintains a good balance between the complexity and the relatively high accuracy of the signal equipment in the station outdoor and section scenarios. The simulation experiments showed that the IMMPP consumed 0.44 s more than 3GPP model 2 in the section scenario and 1.99 s in the station outdoor scenario, and the simulation equipment was in accordance with the actual railway signal equipment. The research result can provide a reference for the description of MTC traffic of other specialised equipment in the railway environment.

关键词： telecommunication traffic cellular radio markov processes machine-to-machine communication railway communication intelligent transportation systems poisson distribution machine-type communication machine-to-machine communication mobile equipment railway environment forecasting model machine communication traffic railway-signalling equipment station indoor model station outdoor model section movement model source traffic model massive MTC equipment 3rd Generation Partnership Project traffic model 3GPP model 2 MTC traffic markov-modulated poisson process markov update process railway signal equipment improved MMPP model

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