N. Duffield. Conditioned asymptotics for tail probabilities in large multiplexers. Performance Evaluation, 31: 281 -- 300, 1998. Home/Search Document Details and Download
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An Analysis of the Phase Transition Phenomenon in Packet Networks - Mandies, Kim (2000) (Correct)
....which indicates that the overflow probability decays exponentially in the buffer size. Our proof of this result is based on the decomposition into packet and burst effects as given in Theorem 3.1. Then we apply a variant of the burst level asymptotic that was derived in Theorem 1 of Duffield [7]. 12 Before we start to give Theorem 1 of [7] and the linear asymptote, we first introduce some notation. Suppose there is a 0 which is the unique positive solution to lim 1 loglF, exp(OA(t) cO. 11) t oo t Suppose furthermore that for i = 0, 1, ai(O) lira logIF, eOA(t) X(O) i) cot ....
....decays exponentially in the buffer size. Our proof of this result is based on the decomposition into packet and burst effects as given in Theorem 3.1. Then we apply a variant of the burst level asymptotic that was derived in Theorem 1 of Duffield [7] 12 Before we start to give Theorem 1 of [7] and the linear asymptote, we first introduce some notation. Suppose there is a 0 which is the unique positive solution to lim 1 loglF, exp(OA(t) cO. 11) t oo t Suppose furthermore that for i = 0, 1, ai(O) lira logIF, eOA(t) X(O) i) cot = lira log lF, i eOA(t) cot. In order for ....
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N. DUFFIELD. Conditioned asymptotics for tail probabilities in large multiplexers. Performance Evaluation, 31:281-300, 1998.
Simple Models of Network Access, with Applications to.. - Mandjes, Mitra.. (2002) (Correct)
....given by IP (WN Nx) I(x) J(x) I(0) with J(x) equal to inf t 0s # #(x ct) 12) Proof. Evidently,IP ( WN Nx) equals ( WN Nx WN 0) IP (WN 0) As shown in Section II C, WN Nx WN 0) IP (V N Nx VN 0) Immediately from Theorem 1 of Duffield [8], we have log IP (V N Nx VN 0) J(x) Together with Lemma IV.1 this proves the stated. # The variational problem in (12) cannot be solved analytically; numerical methods have to be applied. Fortunately, for large x asymptotics are available. Simple approximations for large buffers. Let ....
....cannot be solved analytically; numerical methods have to be applied. Fortunately, for large x asymptotics are available. Simple approximations for large buffers. Let # the equation lim t## t 1 log IEe = c#. Define, for i =0, 1, a i : lim log IE i e A(t) c# t. In Duffield [8] it is proven that, for x ##, J(x) # x r a 1 a 0 o(x) Following the Chernoff Dominant Eigenvalue method of [9] we propose an even simpler approximation: IP x I(0) 13) Here # = r (r c) # c, and I(0) is given in Lemma IV.1. In [9] it is shown that this ....
N. Duffield. Conditioned asymptotics for tail probabilities in large multiplexers. Performance Evaluation, 31: 281 -- 300, 1998.
Transient Analysis of Traffic generated by Bursty Sources.. - Mandjes, van Uitert (2000) (Correct)
....we restricted ourselves to the case where the sojourn times in the states of the flow had an exponential distribution; the analysis provided here holds for generally distributed sojourn times. We present results for a variety of measurement procedures. The results are related to those of Duffield [9] who considers the situation with a non negligible queue, and with Duffield and Whitt [11] who develop procedures to approximate future aggregate input (with techniques related to the ones we use in the present paper, like inversion of Laplace transforms) Where 4 several previous studies on ....
N. Duffield. Conditioned asymptotics for tail probabilities in large multiplexers. Performance Evaluation, 31: 281 -- 300, 1998. 23
A large deviations analysis of the transient of a queue with.. - Mandjes, Ridder (2000) (Correct)
....any insight into the system s behavior. For instance, we would like to know what the influence is of the initial queue length, or whether the system essentially returns to equilibrium before attaining the extreme value of bu#er overflow at time t. A novel study on transient behavior is by Du#eld [10]. He only conditions on the states of the modulating chains and does not take into account the amount of tra#c in the bu#er. This paper aims at finding manageable and accurate asymptotics of the transient probability. The contribution of our study is twofold. In the first place, by using the ....
N. Duffield. Conditioned asymptotics for tail probabilities in large multiplexers. Performance Evaluation, 31: 281 -- 300, 1998.
Simple Models of Network Access, with Applications to.. - Mandjes, Mitra.. (Correct)
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N. Duffield. Conditioned asymptotics for tail probabilities in large multiplexers. Performance Evaluation, 31: 281 -- 300, 1998.
Classification of Recent Publications on Self-Similar Traffic.. - Greiner (1997) (Correct)
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Duffield, N. G. (1997). Conditioned Asymptotics for Tail Probabilities in Large Multiplexers. Technical report, AT&T Laboratories, 600 Mountain Avenue, Murray Hill, NJ, 07974, USA. To appear in Performance Evaluation.
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