Browsing by Subject "Discrete phase type distribution"
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Item Open Access Fitting matrix geometric distributions by model reduction(Taylor and Francis Inc., 2015) Akar, N.A novel algorithmic method is proposed to fit matrix geometric distributions of desired order to empirical data or arbitrary discrete distributions. The proposed method effectively combines two existing approaches from two different disciplines: well-established model reduction methods used in system theory and moment matching methods of applied probability that employ second-order discrete phase-type distributions. The proposed approach is validated with exhaustive numerical examples including well-known statistical data. CopyrightItem Open Access Performance evaluation of slotted optical burst switching systems with quality of service differentiation(Institute of Electrical and Electronics Engineers, 2009) Ozturk, O.; Karasan, E.; Akar, N.Slotted optical burst switching (SOBS) has recently caught the attention of the optical networking community due to performance gains achievable with synchronous infrastructures. In this paper, we study the loss probabilities in a slotted optical burst switching node fed with Poisson burst traffic where the fixed burst size is an integer multiple of the slot length. We develop a discrete-time Markov chain (DTMC) based framework to obtain the loss probabilities in systems with and without quality of service (QoS) differentiation. In particular, we focus on analytical modeling of priority scheduling and offset-based QoS differentiation mechanisms for SOBS networks. The latter problem suffers from the curse of dimensionality which we address by a discrete phase type distribution approximation for the discrete Poisson distribution leading to an accurate approximation for the loss probabilities. A hybrid QoS mechanism which jointly utilizes offset-based differentiation together with priority scheduling is also analyzed. © 2009 IEEE.