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Fluid limits for networks with bandwidth sharing and general document size distributions
 Annals of Applied Probability
, 2009
"... We consider a stochastic model of Internet congestion control, ..."
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Cited by 19 (2 self)
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We consider a stochastic model of Internet congestion control,
Stability of Networks under General File Size Distribution with Alpha Fair Rate Allocation
"... Abstract—Convex optimization has been widely used to model bandwidth allocation policies among TCP flows in the Internet. When the offered load is less than capacity, stochastic stability of networks using such policies has been established for exponentially distributed file sizes. The problem has r ..."
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Cited by 4 (2 self)
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Abstract—Convex optimization has been widely used to model bandwidth allocation policies among TCP flows in the Internet. When the offered load is less than capacity, stochastic stability of networks using such policies has been established for exponentially distributed file sizes. The problem has remained open for general file size distributions, which is very relevant as it is well known that Internet file sizes follow heavytailed distributions. In this paper, building on existing results on the fluid model of the system, we use a partial differential equation to characterize the dynamics. The equation keeps track of residual file size and therefore is suitable to study networks under general file size distributions. For alpha fair bandwidth allocation, with any positive alpha parameter, a Lyapunov function is constructed to prove stability when the offered load does
Network Stability Under Alpha Fair Bandwidth Allocation With General File Size Distribution
"... Abstract—Rate allocation among a fixed set of endtoend connections in the Internet is carried out by congestion control, which has a well established model: it optimizes a concave network utility, a particular case of which is the alphafair bandwidth allocation. This paper studies the slower dyn ..."
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Cited by 3 (0 self)
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Abstract—Rate allocation among a fixed set of endtoend connections in the Internet is carried out by congestion control, which has a well established model: it optimizes a concave network utility, a particular case of which is the alphafair bandwidth allocation. This paper studies the slower dynamics of connections themselves, that arrive randomly in the network and are served at the allocated rate. It has been shown that under the condition that the mean offered load at each link is less than its capacity, the resulting queueing system is stochastically stable, for the case of exponentially distributed filesizes. The conjecture that the result holds for general filesize distributions has remained open, and is very relevant since heavytailed distributions are often the best models of Internet file sizes. In this paper, building on existing fluid models of the system, we use a partial differential equation to characterize the dynamics. The equation keeps track of residual file size and
FLUID LIMITS FOR NETWORKS WITH BANDWIDTH SHARING AND GENERAL DOCUMENT SIZE DISTRIBUTIONS
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1Network Stability under Alpha Fair Bandwidth Allocation with General File Size Distribution
"... Abstract—Rate allocation among a fixed set of endtoend connections in the Internet is carried out by congestion control, which has a well established model: it optimizes a concave network utility, a particular case of which is the alphafair bandwidth allocation. This paper studies the slower dyna ..."
Abstract
 Add to MetaCart
Abstract—Rate allocation among a fixed set of endtoend connections in the Internet is carried out by congestion control, which has a well established model: it optimizes a concave network utility, a particular case of which is the alphafair bandwidth allocation. This paper studies the slower dynamics of connections themselves, that arrive randomly in the network and are served at the allocated rate. It has been shown that under the condition that the mean offered load at each link is less than its capacity, the resulting queueing system is stochastically stable, for the case of exponentially distributed filesizes. The conjecture that the result holds for general filesize distributions has remained open, and is very relevant since heavytailed distributions are often the best models of Internet file sizes. In this paper, building on existing fluid models of the sys