1,062 research outputs found
Fitting procedure for the two-state Batch Markov modulated Poisson process
The Batch Markov Modulated Poisson Process (BMMPP) is a subclass of the versatile Batch Markovian Arrival process (BMAP) which has been proposed for the modeling of dependent events occurring in batches (as group arrivals, failures or risk events). This paper focuses on exploring the possibilities of the \bmmpp for the modeling of real phenomena involving point processes with group arrivals. The first result in this sense is the characterization of the two-state BMMPP with maximum batch size equal to K, the BMMPP2(K), by a set of moments related to the inter-event time and batch size distributions. This characterization leads to a sequential fitting approach via a moments matching method. The performance of the novel fitting approach is illustrated on both simulated and a real teletraffic data set, and compared to that of the EM algorithm. In addition, as an extension of the inference approach, the queue length distributions at departures in the queueing system BMMPP/M/1 is also estimated
Fitting procedure for the two-state Batch Markov modulated Poisson process
The Batch Markov Modulated Poisson Process (BMMPP) is a subclass of the
versatile Batch Markovian Arrival process (BMAP) which has been proposed for
the modeling of dependent events occurring in batches (as group arrivals,
failures or risk events). This paper focuses on exploring the possibilities of
the BMMPP for the modeling of real phenomena involving point processes with
group arrivals. The first result in this sense is the characterization of the
two-state BMMPP with maximum batch size equal to K, the BMMPP2(K), by a set of
moments related to the inter-event time and batch size distributions. This
characterization leads to a sequential fitting approach via a moments matching
method. The performance of the novel fitting approach is illustrated on both
simulated and a real teletraffic data set, and compared to that of the EM
algorithm. In addition, as an extension of the inference approach, the queue
length distributions at departures in the queueing system BMMPP/M/1 is also
estimated
Compact Markov-modulated models for multiclass trace fitting
Markov-modulated Poisson processes (MMPPs) are stochastic models for fitting empirical traces for simulation, workload characterization and queueing analysis purposes. In this paper, we develop the first counting process fitting algorithm for the marked MMPP (M3PP), a generalization of the MMPP for modeling traces with events of multiple types. We initially explain how to fit two-state M3PPs to empirical traces of counts. We then propose a novel form of composition, called interposition, which enables the approximate superposition of several two-state M3PPs without incurring into state space explosion. Compared to exact superposition, where the state space grows exponentially in the number of composed processes, in interposition the state space grows linearly in the number of composed M3PPs. Experimental results indicate that the proposed interposition methodology provides accurate results against artificial and real-world traces, with a significantly smaller state space than superposed processes
A bivariate two-state Markov modulated Poisson process for failure modelling
Motivated by a real failure dataset in a two-dimensional context, this paper
presents an extension of the Markov modulated Poisson process (MMPP) to two
dimensions. The one-dimensional MMPP has been proposed for the modeling of
dependent and non-exponential inter-failure times (in contexts as queuing, risk
or reliability, among others). The novel two-dimensional MMPP allows for
dependence between the two sequences of inter-failure times, while at the same
time preserves the MMPP properties, marginally. The generalization is based on
the Marshall-Olkin exponential distribution. Inference is undertaken for the
new model through a method combining a matching moments approach with an
Approximate Bayesian Computation (ABC) algorithm. The performance of the method
is shown on simulated and real datasets representing times and distances
covered between consecutive failures in a public transport company. For the
real dataset, some quantities of importance associated with the reliability of
the system are estimated as the probabilities and expected number of failures
at different times and distances covered by trains until the occurrence of a
failure
Collaborative Uploading in Heterogeneous Networks: Optimal and Adaptive Strategies
Collaborative uploading describes a type of crowdsourcing scenario in
networked environments where a device utilizes multiple paths over neighboring
devices to upload content to a centralized processing entity such as a cloud
service. Intermediate devices may aggregate and preprocess this data stream.
Such scenarios arise in the composition and aggregation of information, e.g.,
from smartphones or sensors. We use a queuing theoretic description of the
collaborative uploading scenario, capturing the ability to split data into
chunks that are then transmitted over multiple paths, and finally merged at the
destination. We analyze replication and allocation strategies that control the
mapping of data to paths and provide closed-form expressions that pinpoint the
optimal strategy given a description of the paths' service distributions.
Finally, we provide an online path-aware adaptation of the allocation strategy
that uses statistical inference to sequentially minimize the expected waiting
time for the uploaded data. Numerical results show the effectiveness of the
adaptive approach compared to the proportional allocation and a variant of the
join-the-shortest-queue allocation, especially for bursty path conditions.Comment: 15 pages, 11 figures, extended version of a conference paper accepted
for publication in the Proceedings of the IEEE International Conference on
Computer Communications (INFOCOM), 201
Markovian arrivals in stochastic modelling: a survey and some new results
This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs),
which constitute a rich class of point processes used extensively in stochastic modelling. Our
starting point is the versatile process introduced by Neuts (1979) which, under some simplified
notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general
point process can be approximated by appropriate MAPs and, on the other hand, the MAPs
provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian
formalism. While a number of well-known arrival processes are subsumed under a BMAP as
special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous
settings or even spatial arrivals. We survey on the main aspects of the BMAP,
discuss on some of its variants and generalizations, and give a few new results in the context of a
recent state-dependent extension.Peer Reviewe
Findings about the two-state BMMPP for modeling point processes in reliability and queueing systems
The Batch Markov Modulated Poisson Process (BMMPP) is a subclass of the versatile Batch Markovian Arrival process (BMAP) which have been widely used for the modeling of dependent and correlated simultaneous events (as arrivals, failures or risk events, real-time multimedia communications). Both theoretical and applied aspects are examined in this paper. On one hand, the identifiability of the stationary BMMPP2(K) is proven, where K is the maximum batch size. This is a powerful result when inferential tasks related to real data sets are carried out. On the other hand, some findings concerning the correlation and autocorrelation structures are provided.The first and second authors acknowledge financial support from the Spanish Ministry
of Economy and Competitiveness, research project ECO2015-66593-P. The Third author acknowledge
financial support from the Spanish Ministry of Economy and Competitiveness, research project
MTM2015-65915-R; and also from Junta de AndalucÃa, and BBVA Fundation, research project P11-
FQM-7603 and FQM-32
Analysis of an aggregate loss model in a Markov renewal regime
In this article we consider an aggregate loss model with dependent losses. The losses occurrence process is governed by a two-state Markovian arrival process (MAP2), a Markov renewal process process that allows for (1) correlated inter-losses times, (2) non-exponentially distributed inter-losses times and, (3) overdisperse losses counts. Some quantities of interest to measure persistence in the loss occurrence process are obtained. Given a real operational risk database, the aggregate loss model is estimated by fitting separately the inter-losses times and severities. The MAP2 is estimated via direct maximization of the likelihood function, and severities are modeled by the heavy-tailed, double-Pareto Lognormal distribution. In comparison with the fit provided by the Poisson process, the results point out that taking into account the dependence and overdispersion in the inter-losses times distribution leads to higher capital charges
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