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BROWNIAN APPROXIMATIONS TO FIRST PASSAGE PROBABILITIES BY
, 1980
"... N00014-77-C-0306 ' (NR-042-373) ..."
Fluid and Brownian Approximations for an Internet Congestion Control Model
- Proceedings of the 43rd IEEE Conference on Decision and Control, December 2004
, 2004
"... We consider a stochastic model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is shared fairly amongst elastic document transfers. We focus on the heavy traffic regime in which the average load placed on each resource is appr ..."
Abstract
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Cited by 16 (1 self)
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scale the flow count process can be approximately recovered as a continuous lifting of the workload process. Under proportional fair sharing of bandwidth and a mild condition, we show how state space collapse can be combined with a new invariance principle to establish a Brownian model as a diffusion
Brownian Approximations of Multiclass Open Queueing Networks
- Operations Research
, 2001
"... We study a multiclass open queueing network with a set of single-server stations that operate under a combination of FIFO (first-in-first-out) and priority service disciplines, and are subject to random breakdowns. Assuming that the primitive processes -- in particular, external arrivals, service ..."
Abstract
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Cited by 2 (0 self)
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, service requirements, service capacities (up and down times) and the routing mechanism -- follow two-moment approximations (based on functional central limit theorems), we develop a semi-martingale reflected Brownian motion (SRBM) approx- imation for the performance processes such as workload, queue
BROWNIAN APPROXIMATION TO COUNTING GRAPHS SOUMIK PAL
"... Abstract. Let C(n, k) denote the number of connected graphs with n labeled vertices and n+ k − 1 edges. For any sequence (kn), the limit of C(n, kn) as n tends to infinity is known. It has been observed that, if kn = o( n), this limit is asymptotically equal to the knth moment of the area under the ..."
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the standard Brownian excursion. These moments have been computed in the literature via independent methods. In this article we show why this is true for kn = o ( 3 n) starting from an observation made by Joel Spencer. The elementary argument uses a result about strong embedding of the Uniform empirical
L.: Stein’s method for Brownian approximations
- Commun. Stoch. Anal
, 2013
"... HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
Abstract
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Cited by 2 (0 self)
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HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
A Brownian approximation of a production-inventory system with a manufacturer that subcontracts
- Operations Research
"... This paper considers a production-inventory problem where a manufacturer fulfills stochastic, stationary demand for a single product from a finished goods inventory. The inventory can be replenished by two production resources, in-house production and a subcontractor, which both have finite capacity ..."
Abstract
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Cited by 10 (0 self)
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capacity. We construct a Brownian ap-proximation of the optimal control problem assuming that the manufacturer uses a ‘dual base-stock ’ policy to control replenishment from the two sources and her objec-tive is to minimize average cost. A closed-form expression is obtained for one optimal base
Self-Similarity Through High-Variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level
- IEEE/ACM TRANSACTIONS ON NETWORKING
, 1997
"... A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is self-similar or long-range dependent in nature (i.e., bursty over a wide range of time scales) -- in sharp contrast to commonly made tr ..."
Abstract
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Cited by 740 (24 self)
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A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is self-similar or long-range dependent in nature (i.e., bursty over a wide range of time scales) -- in sharp contrast to commonly made traffic modeling assumptions. In this paper, we provide a plausible physical explanation for the occurrence of self-similarity in LAN traffic. Our explanation is based on new convergence results for processes that exhibit high variability (i.e., infinite variance) and is supported by detailed statistical analyses of real-time traffic measurements from Ethernet LAN's at the level of individual sources. This paper is an extended version of [53] and differs from it in significant ways. In particular, we develop here the mathematical results concerning the superposition of strictly alternating ON/OFF sources. Our key mathematical result states that the superposition of many ON/OFF sources (also k...
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