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Markovian Arrival Process Parameter Estimation With Group Data
IEEE/ACM Transactions on Networking, 2009This paper addresses a parameter estimation problem of Markovian arrival process (MAP). In network traffic measurement experiments, one often encounters the group data where arrival times for a group are collected as one bin. Although the group data are observed in many situations, nearly all existing estimation methods for MAP are based on nongroup ...
Hiroyuki Okamura +2 more
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Multi-class Markovian arrival processes and their parameter fitting
Performance Evaluation, 2010Markovian arrival processes are a powerful class of stochastic processes to represent stochastic workloads that include autocorrelation in performance or dependability modeling. However, fitting the parameters of a Markovian arrival process to given measurement data is non-trivial and most known methods focus on a single class case, where all events ...
Peter Buchholz +2 more
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The first two moment matrices of the counts for the markovian arrival process
Stochastic Models, 1992Summary: Analytic, asymptotic and algorithmic properties of the first two moment matrices of the counts during an interval \((0,t]\) in the Markovian arrival process (MAP) are discussed. These properties are useful in the computation of Palm densities and dispersion functions with arbitrary initial conditions. These descriptors, in turn, are helpful in
Marcel F Neuts
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A discrete queue with the markovian arrival process and phase type primary and secondary services
Stochastic Models, 1994 A discrete time queueing model with Markovian arrival process in which jobs require primary and possibly secondary service, is analysed. Under the assumptions of infinite waiting room for the primary queue and no waiting room for the secondary queue we ...
Attahiru S Alfa, S Chakravarthy
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Markovian Arrival Processes in Multi-dimensions
2020Phase Type Distributions (PHDs) and Markovian Arrival Processes (MAPs) are established models in computational probability to describe random processes in stochastic models. In this paper we extend MAPs to Multi-Dimensional MAPs (MDMAPs) which are a model for random vectors that may be correlated in different dimensions.
Andreas Blume +2 more
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Descriptors of arrival-process burstiness with application to the discrete Markovian arrival process
Queueing Systems, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mary A. Johnson, Surya Narayana
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The Batch Markovian Arrival Process Subject to Renewal Generated Geometric Catastrophes
Stochastic Models, 2007 We deal with a population of individuals that grows stochastically according to a batch Markovian arrival process and is subject to renewal generated geometric catastrophes.
Antonis Economou, A Gómez-Corral
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2014
PHDs can be extended to describe correlated inter-event times. The resulting models are denoted as Markovian Arrival Processes (MAPs) and have been introduced in the pioneering work of Neuts [124]. MAPs are a very flexible and general class of stochastic processes. In this chapter we first introduce the general model and its analysis, then the specific
Peter Buchholz, Jan Kriege, Iryna Felko
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PHDs can be extended to describe correlated inter-event times. The resulting models are denoted as Markovian Arrival Processes (MAPs) and have been introduced in the pioneering work of Neuts [124]. MAPs are a very flexible and general class of stochastic processes. In this chapter we first introduce the general model and its analysis, then the specific
Peter Buchholz, Jan Kriege, Iryna Felko
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Counter-examples involving markovian arrival processes
Communications in Statistics. Stochastic Models, 1991Summary: By considering simple two-state Markovian arrival processes, a number of examples are given which show the limitations of the information conveyed by the distributions of the counting random variables. Some of these are intended to lay some conjectures on point processes to rest, while others have primarily didactic value.
Liu, Dan, Neuts, Marcel F.
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Parallelization of EM-Algorithms for Markovian Arrival Processes
2020Markovian Arrival Processes (MAPs) are widely used stochastic models to describe correlated events. For the parameter fitting of MAPs according to measured data, the expectation-maximization (EM) algorithm is commonly seen as the best approach. Unfortunately, EM algorithms require a huge computational effort if the number of data points is large or the
Andreas Blume +2 more
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