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- 저자 : S.I. Rabia (검색결과 3 건)
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A discrete time Geo/G/1 retrial queue with general retrial times and balking customers
A. Aboul-Hassan,S.I. Rabia,F.A. Taboly 한국통계학회 2008 Journal of the Korean Statistical Society Vol.37 No.4
In this work, we consider a discrete time Geo/G/1 retrial queue with general retrial times and balking customers. If a new arriving customer finds the server busy, he may join the orbit to retry getting the required service again or depart completely from the system. Using the supplementary variable technique, this queueing system is modelled using a Markov chain. We derive the generating functions of the steady state distribution of this Markov chain. Hence, we establish the generating functions of the orbit size and the system size distributions. This set of generating functions is used to derive various performance measures. We prove a stochastic decomposition law and use it to a derive a measure of the proximity between the distributions of the system size in the present model and the corresponding one without retrials. A set of recursive formulae is built up to facilitate computing the orbit size and the system size distributions. Numerical results are presented with a focus on the effect of balking on the system performance.
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MARKOVIAN EARLY ARRIVAL DISCRETE TIME JACKSON NETWORKS
Aboul-Hassan A.,Rabia S.I. The Korean Statistical Society 2006 Journal of the Korean Statistical Society Vol.35 No.3
In an earlier work, we investigated the problem of using linear programming to bound performance measures in a discrete time Jackson network. There it was assumed that the system evolution is controlled by the early arrival scheme. This assumption implies that the system can't be modelled by a Markov chain. This problem was resolved and performance bounds were calculated. In the present work, we use a modification of the early arrival scheme (without corrupting it) in order to make the system evolves as a Markov chain. This modification enables us to obtain explicit expressions for certain moments that could not be calculated explicitly in the pure early arrival scheme setting. Moreover, this feature implies a reduction in the linear program size as well as the computation time. In addition, we obtained tighter bounds than those appeared before due to the new setting.
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Markovian Early Arrival Discrete Time Jackson Networks
A. Aboul-Hassan,S. I. Rabia 한국통계학회 2006 Journal of the Korean Statistical Society Vol.35 No.3
In an earlier work, we investigated the problem of using linear program-ming to bound performance measures in a discrete time Jackson network.There it was assumed that the system evolution is controlled by the earlyarrival scheme. This assumption implies that the system can’t be modelledby a Markov chain. This problem was resolved and performance boundswere calculated. In the present work, we use a modication of the earlyarrival scheme (without corrupting it) in order to make the system evolvesas a Markov chain. This modication enables us to obtain explicit expres-sions for certain moments that could not be calculated explicitly in the pureearly arrival scheme setting. Moreover, this feature implies a reduction inthe linear program size as well as the computation time. In addition, weobtained tighter bounds than those appeared before due to the new setting.AMS 2000 subject classications.Primary 60K25; Secondary 68M20.Keywords.Discrete time queueing systems, early arrival scheme, performance bounds.1. IntroductionDiscrete time queueing systems received great interest in recent years becausethey are commonly used in the design and analysis of many communicationand computer systems where the time is slotted. These systems include slot-ted ALOHA, slotted Carrier-Sense Multiple-Access (CSMA) and AsynchronousTransfer Mode (ATM) networks (see Atencia and Moreno, 2004; Gelenbe and Pu-jolle, 1997; Li and Yang, 1998; Wodward, 1998). The present work is concernedReceived March 2005; accepted August 2006.
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