USING SINGULARITY ANALYSIS TO APPROXIMATE TRANSIENT CHARACTERISTICS IN QUEUEING SYSTEMS
نویسندگان
چکیده
منابع مشابه
Using singularity analysis to approximate transient characteristics in queueing systems
In this paper, we develop a simple method to approximate the transient behavior of queueing systems. In particular, it is shown how singularity analysis of a known generating function of a transient sequence of some performance measure leads to an approximation of this sequence. To illustrate our approach, several specific transient sequences are investigated in detail. By means of some numeric...
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T exact distribution of the nth customer’s sojourn time in an M/M/s queue with k customers initially present is derived. Algorithms for computing the covariance between sojourn times for an M/M/1 queue with k customers present at time 0 are also developed. Maple computer code is developed for practical application of transient queue analysis for many system measures of performance without regar...
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Characterization of the stability boundary of differential-algebraic (DAE) systems is more complicated than for systems described by ordinary differential equations (ODEs). In addition to unstable equilibria and periodic orbits, algebraic singularity plays an important role in defining the stability boundary. This paper presents a Lyapunov-based method for direct assessment of transient singula...
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Markov models of the queueing theory described by birth-death processes (BDP) have been investigated and applied for a long time (see, e.g., [1, 2]). At the same time, creation of new methods to study BDP and enlargement of the range of the solved problems invoked appearance of a new series of works [3–11]. More realistic models of queueing systems described by nonstationary Markov chains are a...
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ژورنال
عنوان ژورنال: Probability in the Engineering and Informational Sciences
سال: 2009
ISSN: 0269-9648,1469-8951
DOI: 10.1017/s0269964809000199