| C.S. Chang and J. Cheng, "Computable Exponential Bounds for Intree Networks with Routing", IEEE INFOCOM'95, Boston, pp. 197-204. 21 |
....0 if N X i=1 log( i ( c: 4.2) The quantity c i ( log( i ( is called the effective bandwidth of the process (A i n ) n [14, 24, 29, 32, 39, 29] A similar result was presented by Chang and Cheng in [11, Example 3. 4] but with a different coefficient C( The coefficient in [11], denoted as Gamma( is given by Gamma( max i;j r i ( r j ( where (r 1 ( r K ( T is the (positive) right eigenvector of the matrix F ( associated with its spectral radius ae( In general, the bound in [11] appears to be looser that ours. In particular, Gamma( ....
.... but with a different coefficient C( The coefficient in [11] denoted as Gamma( is given by Gamma( max i;j r i ( r j ( where (r 1 ( r K ( T is the (positive) right eigenvector of the matrix F ( associated with its spectral radius ae( In general, the bound in [11] appears to be looser that ours. In particular, Gamma( is always larger than 1 for 0 unlike C( which maybe smaller than 1 (see Section 4.1.1) Example 4.1 (Computation of C( for discrete time on off sources) Consider the case when (A n ) n is the superposition of N independent and ....
C.-S. Chang and J. Cheng, "Computable Exponential Bounds for Intree Networks with Routing ". Proc. INFOCOM'95, pp. ***, 1995.
....guarantees, one is usually interested in bounding the mean delay of the packets through the network or the probability that the delay exceeds a certain value. For this reason, the concept of Exponentially Bounded Burstiness (EBB) was introduced in [YaS93] see also the closely related works [Kur92, ChC95]) A continuous traffic stream with instantaneous rate R(t) is EBB with upper rate ae and bounding function Ae Gammaffoe if for all oe 0 and t s 0 Pr aeZ t s R(u)du ae(t Gamma s) oe oe Ae Gammaffoe ; 1) where ae; A; ff 0. The EBB calculus is based on an appropriate EBB ....
....work leaves several issues open for further research. For instance, the problem of handling processes with a bounding function f(oe) 1=oe ff for some ff 0: In such a case, the calculus developed here can t be used for feedforward networks of arbitrary size since f 62 F (see Definition 1) In [ChC95], an efficient methodology for deriving tight exponential bounds for intree networks is developed. The extension of that approach to sums of exponentials and general bounding functions would be especially useful. Acknowledgement The authors would like to thank Prof. Ofer Zeitouni for fruitful ....
C.S. Chang and J. Cheng, "Computable Exponential Bounds for Intree Networks with Routing," in the proceedings of INFOCOM '95, pp.197-204.
....tail distribution of the workload, queue length, and delay in a queue in isolation. Bounds of this type have proved to be helpful for analyzing ATM multiplexers fed by different classes of traffic such as data, voice, video, etc. see e.g. 12] This paper is one of the first attempts (see also [4, 5, 8, 17, 22] for related work) to derive bounds for more general structures, including acyclic queueing networks. Bounding quantities such as the probability distribution of the end to end delay seen by individual sessions along their route in the network will allow network designers to get a better ....
C.-S. Chang and J. Cheng, "Computable Exponential Bounds for Intree Networks with Routing". Preprint, Jul. 1994.
.... traffic load) as an optimization problem [42] In both cases, the ATM network is approximated by a circuit switched network (i.e. a network that does not take advantage of statistical multiplexing gains to admit more connections) Currently, end to end performance evaluation (see, e.g. [9, 49, 4]) and statistical multiplexing (see, e.g. 40, 2, are very active areas of study. Whenever possible, the most recent results on performance evaluation should, of course, be applied to the problems described in x2 before a simulation study is initiated. 4.3 Importance Sampling for Estimating ....
C.-S. Chang and J. Cheng. Computable exponential bounds for intree networks with routing. to appear in Proc. IEEE INFOCOM'95, 1995.
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C.S. Chang and J. Cheng, "Computable Exponential Bounds for Intree Networks with Routing", IEEE INFOCOM'95, Boston, pp. 197-204. 21
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