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We derive several algorithms for the busy period distribution of the canonical Markovian fluid flow model. One of them is similar to the Latouche–Ramaswami algorithm for quasi-birth–death models and is shown to be quadratically convergent. These algorithms significantly increase the efficiency of the matrix-geometric procedures developed earlier by the(More)
We establish in a direct manner that the steady state distribution of Markovian fluid flow models can be obtained from a quasi birth and death queue. This is accomplished through the construction of the processes on a common probability space and the demonstration of a distributional coupling relation between them. The results here provide an interpretation(More)
The Markov modulated fluid model with finite buffer of size β is analyzed using a stochastic discretization yielding a sequence of finite waiting room queueing models with iid amounts of work distributed as exp(nλ). The n-th approximating queue’s system size is bounded at a value qn such that the corresponding expected amount of work qn/(nλ) → β as n → ∞.(More)
Based on the matrix-analytic approach to fluid flows initiated by Ramaswami, we develop an efficient time dependent analysis for a general Markov modulated fluid flow model with a finite buffer and an arbitrary initial fluid level at time 0. We also apply this to an insurance risk model with a dividend barrier and a general Markovian arrival process of(More)
In this paper, we propose a queueing model based on an integer-valued rst-order autoregressive(INAR(1)) process. We derive the queue length distribution and its asymptotic decay rate of the proposed model. Also, our numerical study shows that the new model can be considered as an alternative approach to the well-known MMPP=D=1 queue in terms of performance(More)
In this work, we develop a stochastic model, GOP ARIMA (autoregressive integrated moving average for a group of pictures) for VBR processes with a regular GOP pattern. It explicitly incorporates the deterministic time-dependent behavior of frame-level VBR traffic. The GOP ARIMA model elaborately represents the inter- and intra-GOP sample autocorrelation(More)
Telephone availability is critical, particularly in emergency situations when people need immediate help. We used statistical data analysis and queueing models to identify the root cause of dial-tone unavailability in parts of the AT&T network and to develop remedies. Our solutions restored quality service, protecting the AT&T brand name and ensuring the(More)
This paper proposes a simple factorization principle that can be used efficiently and effectively to derive the vector generating function of the queue length at an arbitrary time of the BMAP/G/1/ queueing systems under variable service speed. We first prove the factorization property. Then we provide moments formula. Lastly we present some applications of(More)
Long been observed characteristics of empirical VBR process is its slowly decaying sample autocorrelations. In this work, we explain slowly decaying sample autocorrelations of the empirical VBR using the non-stationary model, which well reflects the stochastic characteristics of VBR process. Our model generates the synthetic sequence which has the same(More)