A Markov modulated Poisson process model for rainfall increments

2002 ◽  
Vol 45 (2) ◽  
pp. 91-97 ◽  
Author(s):  
C. Onof ◽  
B. Yameundjeu ◽  
J.-P. Paoli ◽  
N. Ramesh
Keyword(s):  
Continuous Time ◽  
Process Model ◽  
Rainfall Intensity ◽  
Arrival Rate ◽  
Rectangular Pulse ◽  
Poisson Processes ◽  
Process Models ◽  
Markov Modulated Poisson Process ◽  
Point Process Models ◽  
Markov Modulated

The problems encountered when using traditional rectangular pulse hierarchical point process models for fine temporal resolution and the growing number of available tip-time records suggest that rainfall increments from tipping-bucket gauges be modelled directly. Poisson processes are used with an arrival rate modulated by a Markov chain in continuous time. The paper shows how, by using two or three states for this chain, much of the structure of the rainfall intensity distribution and the wet/dry sequences can be represented for time-scales as small as 5 minutes.

scholarly journals Multivariate models for rainfall based on Markov modulated Poisson processes

2013 ◽  
Vol 44 (4) ◽  
pp. 631-643 ◽  
Author(s):  
R. Thayakaran ◽  
N. I. Ramesh
Keyword(s):  
Time Series ◽  
Point Process ◽  
Rainfall Intensity ◽  
Likelihood Function ◽  
Process Models ◽  
Rainfall Time Series ◽  
Multivariate Models ◽  
Point Process Models ◽  
Markov Modulated ◽  
Cluster Processes

Point process models for rainfall are constructed generally based on Poisson cluster processes. Most commonly used point process models in the literature were constructed either based on Bartlett–Lewis or Neyman–Scott cluster processes. In this paper, we utilize a class of Cox process models, termed the Markov modulated Poisson process (MMPP), to model rainfall intensity. We use this class of models to analyse rainfall data observed in the form of tip time series from rain gauge tipping buckets in a network of gauges in Somerset, southwest England, recorded by the Hydrological Radar Experiment (HYREX). Univariate and multivariate models are employed to analyse the data recorded at single and multiple sites in the catchment area. As the structure of this proposed class of MMPP models allows us to construct the likelihood function of the observed tip time series, we utilize the maximum likelihood methods in our analysis to make inferences about the rainfall intensity at sub-hourly time scales. The multivariate models are used to analyse rainfall time series jointly at four stations in the region. Properties of the cumulative rainfall in discrete time intervals are studied, and the results of fitting three-state models are presented.

On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions

1996 ◽  
Vol 33 (3) ◽  
pp. 640-653 ◽  
Author(s):  
Tobias Rydén
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Poisson Processes ◽  
Hitting Times ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Minimum Number ◽  
Markov Modulated ◽  
Two Parameters

An aggregated Markov chain is a Markov chain for which some states cannot be distinguished from each other by the observer. In this paper we consider the identifiability problem for such processes in continuous time, i.e. the problem of determining whether two parameters induce identical laws for the observable process or not. We also study the order of a continuous-time aggregated Markov chain, which is the minimum number of states needed to represent it. In particular, we give a lower bound on the order. As a by-product, we obtain results of this kind also for Markov-modulated Poisson processes, i.e. doubly stochastic Poisson processes whose intensities are directed by continuous-time Markov chains, and phase-type distributions, which are hitting times in finite-state Markov chains.

A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

1995 ◽  
Vol 32 (4) ◽  
pp. 1103-1111 ◽  
Author(s):  
Qing Du
Keyword(s):  
Poisson Process ◽  
Arrival Rate ◽  
Loss Probability ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Markov Modulated Poisson Process ◽  
Server Queue ◽  
Monotonicity Result ◽  
Markov Modulated

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i. The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i. In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

scholarly journals A simple multifractal model for self-similar traffic flows in high-speed computer networks

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
High Speed ◽  
Process Models ◽  
Traffic Modeling ◽  
Traffic Flows ◽  
Markov Modulated Poisson Process ◽  
Traffic Trace ◽  
Self Similar ◽  
Markov Modulated ◽  
Speed Computer ◽  
Fitting Model

This paper presents a simple and fast technique of multifractal traffic modeling. It proposes a method of fitting model to a given traffic trace. A comparison of simulation results obtained for an exemplary trace, multifractal model and Markov Modulated Poisson Process models has been performed.

Event and time averages: a review

1992 ◽  
Vol 24 (2) ◽  
pp. 377-411 ◽  
Author(s):  
Pierre Brémaud ◽  
Raghavan Kannurpatti ◽  
Ravi Mazumdar
Keyword(s):  
Continuous Time ◽  
Short Proof ◽  
Sufficient Conditions ◽  
Process Models ◽  
Stationary Case ◽  
Unified Framework ◽  
Martingale Approach ◽  
Point Process Models ◽  
Time Averages ◽  
Necessary And Sufficient

This article reviews results related to event and time averages (EATA) for point process models, including PASTA, ASTA and ANTIPASTA under general hypotheses. In particular, the results for the stationary case relating the Palm and martingale approach are reviewed. The non-stationary case is discussed in the martingale framework where minimal conditions for ASTA generalizing earlier work are presented in a unified framework for the discrete- and continuous-time cases. In addition, necessary and sufficient conditions for ASTA to hold in the stationary case are discussed in the case even when stochastic intensities may not exist and a short proof of the ANTIPASTA results known to date are given.

A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

1995 ◽  
Vol 32 (04) ◽  
pp. 1103-1111 ◽  
Author(s):  
Qing Du
Keyword(s):  
Poisson Process ◽  
Arrival Rate ◽  
Loss Probability ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Markov Modulated Poisson Process ◽  
Server Queue ◽  
Monotonicity Result ◽  
Markov Modulated

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i . The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i . In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

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