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33
Fluid models and solutions for largescale ip networks
 In Proc. of ACM SIGMETRICS
, 2003
"... In this paper we present a scalable model of a network of Active Queue Management (AQM) routers serving a large population of TCP flows. We present efficient solution techniques that allow one to obtain the transient behavior of the average queue lengths, packet loss probabilities, and average endt ..."
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Cited by 39 (1 self)
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In this paper we present a scalable model of a network of Active Queue Management (AQM) routers serving a large population of TCP flows. We present efficient solution techniques that allow one to obtain the transient behavior of the average queue lengths, packet loss probabilities, and average endtoend latencies. We model different versions of TCP as well as different versions of RED, the most popular AQM scheme currently in use. Comparisons between our models andns simulation show our models to be quite accurate while at the same time requiring substantially less time to solve, especially when workloads and bandwidths are high. Categories and Subject Descriptors
RateBased versus QueueBased Models of Congestion Control
 in Proceedings of ACM SIGMETRICS
, 2004
"... Mathematical models of congestion control capture the congestion indication mechanism at the router in two different ways: ratebased models, where the queuelength at the router does not explicitly appear in the model, and queuebased models, where the queue length at the router is explicitly a p ..."
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Cited by 26 (3 self)
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Mathematical models of congestion control capture the congestion indication mechanism at the router in two different ways: ratebased models, where the queuelength at the router does not explicitly appear in the model, and queuebased models, where the queue length at the router is explicitly a part of the model. Even though most congestion indication mechanisms use the queue length to compute the packet marking or dropping probability to indicate congestion, we argue that, depending upon the choice of the parameters of the AQM scheme, one would obtain a ratebased model or a rateandqueuebased model as the deterministic limit of a stochastic system with a large number of users.
Nonlinear instabilities in TCPRED
 IEEE/ACM Transactions on Networking
, 2002
"... Abstract—This work develops a discretetime dynamical feedback system model for a simplified TCP network with RED control and provides a nonlinear analysis that can help in understanding observed parametric sensitivities. The model describes network dynamics over large parameter variations. The dyna ..."
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Cited by 20 (4 self)
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Abstract—This work develops a discretetime dynamical feedback system model for a simplified TCP network with RED control and provides a nonlinear analysis that can help in understanding observed parametric sensitivities. The model describes network dynamics over large parameter variations. The dynamical model is used to analyze the TCPRED operating point and its stability with respect to various RED controller and system parameters. Bifurcations are shown to occur as system parameters are varied. These bifurcations, which involve the emergence of oscillatory and/or chaotic behavior, shed light on the parametric sensitivity observed in practice. The bifurcations arise due to the presence of a nonlinearity in the TCP throughput characteristic as a function of drop probability at the gateway. Among the bifurcations observed in the system are period doubling and border collision bifurcations. The bifurcations are studied analytically, numerically, and experimentally. Index Terms—Congestion control, nonlinear instability, RED, TCP.
A Generic Mean Field Convergence Result for Systems of Interacting Objects
"... We consider a model for interacting objects, where the evolution of each object is given by a finite state Markov chain, whose transition matrix depends on the present and the past of the distribution of states of all objects. This is a general model of wide applicability; we mention as examples: TC ..."
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Cited by 17 (4 self)
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We consider a model for interacting objects, where the evolution of each object is given by a finite state Markov chain, whose transition matrix depends on the present and the past of the distribution of states of all objects. This is a general model of wide applicability; we mention as examples: TCP connections, HTTP flows, robot swarms, reputation systems. We show that when the number of objects is large, the occupancy measure of the system converges to a deterministic dynamical system (the “mean field”) with dimension the number of states of an individual object. We also prove a fast simulation result, which allows to simulate the evolution of a few particular objects imbedded in a large system. We illustrate how this can be used to model the determination of reputation in large populations, with various liar strategies. 1
Using Partial Differential Equations to Model TCP Mice and Elephants in Large IP Networks
 IEEE/ACM Transactions on Networking
, 2004
"... Fluid models of IP networks have been recently proposed as a way to break the scalability barrier of traditional discrete statespace models, both simulative (e.g., ns2) and analytical (e.g., queues and Markov chains). Fluid models adopt... ..."
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Cited by 14 (1 self)
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Fluid models of IP networks have been recently proposed as a way to break the scalability barrier of traditional discrete statespace models, both simulative (e.g., ns2) and analytical (e.g., queues and Markov chains). Fluid models adopt...
Meanfield analysis for the evaluation of gossip protocols
 SIGMETRICS Perform. Eval. Rev
, 2008
"... Abstract—Gossip protocols are designed to operate in very large, decentralised networks. A node in such a network bases its decision to interact (gossip) with another node on its partial view of the global system. Because of the size of these networks, analysis of gossip protocols is mostly done usi ..."
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Cited by 12 (5 self)
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Abstract—Gossip protocols are designed to operate in very large, decentralised networks. A node in such a network bases its decision to interact (gossip) with another node on its partial view of the global system. Because of the size of these networks, analysis of gossip protocols is mostly done using simulations, that tend to be expensive in computation time and memory consumption. We employ meanfield approximation for an analytical evaluation of gossip protocols. Nodes in the network are represented by small identical stochastic models. Joining all nodes would result in an enormous stochastic process. If the number of nodes goes to infinity, however, meanfield analysis allows us to replace this intractably large stochastic process by a small deterministic process. This process approximates the behaviour of very large gossip networks, and can be evaluated using simple matrixvector multiplications. I.
SHRiNK: Enabling scaleable performance prediction and efficient simulation of networks
 IEEE/ACM Transactions on Networking
, 2005
"... Abstract — As the Internet grows, it is becoming increasingly difficult to collect performance measurements of a network or a webserver farm, to monitor its state, and to perform simulations efficiently. Besides, the heterogeneity of the Internet makes it timeconsuming and difficult to devise traff ..."
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Cited by 7 (4 self)
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Abstract — As the Internet grows, it is becoming increasingly difficult to collect performance measurements of a network or a webserver farm, to monitor its state, and to perform simulations efficiently. Besides, the heterogeneity of the Internet makes it timeconsuming and difficult to devise traffic models and analytic tools which would allow us to work with summary statistics. We explore a method to sidestep these problems by combining sampling, modeling and simulation. Our hypothesis is this: if we take a sample of the input traffic, and feed it into a suitably scaled version of the system, we can extrapolate from the performance of the scaled system to that of the original. Our main findings are: When we scale an IP network which is shared by short and longlived TCPlike and UDP flows; and which is controlled by a variety of active queue management schemes, then performance measures such as queueing delay and drop probability are left virtually unchanged. We show this in theory and in simulations. This makes it possible to capture the performance of large networks quite faithfully using smaller scale replicas. I.
Characterization of General TCP Traffic under a Large Number of Flows Regime
 In IEEE INFOCOM 2003
, 2003
"... Shortlived TCP traffic (e.g., web mice) composes the majority of the current Internet traffic. Accurate traffic modeling of a large number of shortlived TCP flows is extremely difficult due to (i) the interaction between session, transport, and network layers; and (ii) the explosion of the size of ..."
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Cited by 5 (4 self)
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Shortlived TCP traffic (e.g., web mice) composes the majority of the current Internet traffic. Accurate traffic modeling of a large number of shortlived TCP flows is extremely difficult due to (i) the interaction between session, transport, and network layers; and (ii) the explosion of the size of state space when the number of flows is large. Typically, adhoc assumptions are required for the analysis to be tractable under a certain regime.
Asymptotic behavior of heterogeneous TCP flows and RED gateway
 IEEE/ACM Transactions on Networking
, 2006
"... Abstract—We introduce a stochastic model of a bottleneck ECN/RED gateway under a large number of heterogeneous TCP flows, i.e., flows with diverse roundtrip delays and session dynamics. We investigate the asymptotic behavior of the system and show that as the number of flows becomes large, the buff ..."
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Cited by 5 (1 self)
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Abstract—We introduce a stochastic model of a bottleneck ECN/RED gateway under a large number of heterogeneous TCP flows, i.e., flows with diverse roundtrip delays and session dynamics. We investigate the asymptotic behavior of the system and show that as the number of flows becomes large, the buffer dynamics and aggregate traffic simplify and can be accurately described by simple stochastic recursions independent of the number of flows, resulting in a scalable model. Based on the Central Limit analysis in the paper, we identify the sources of fluctuations in queue size and describe the relationship between the system parameters such as the marking function and variance of queue size. A closedform approximation for the mean queue size as a function of system parameters is provided from a simple steadystate analysis. Numerical examples are provided to validate our results. Index Terms—Congestion control, modeling, stochastic systems. I.
SHRiNK: A Method for Enabling Scaleable Performance Prediction and Efficient Network Simulation
 IEEE/ACM Transactions on Networking
, 2005
"... Abstract—As the Internet grows, it is becoming increasingly difficult to collect performance measurements, to monitor its state, and to perform simulations efficiently. This is because the size and the heterogeneity of the Internet makes it timeconsuming and difficult to devise traffic models and a ..."
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Cited by 5 (0 self)
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Abstract—As the Internet grows, it is becoming increasingly difficult to collect performance measurements, to monitor its state, and to perform simulations efficiently. This is because the size and the heterogeneity of the Internet makes it timeconsuming and difficult to devise traffic models and analytic tools which would allow us to work with summary statistics. We explore a method to side step these problems by combining sampling, modeling, and simulation. Our hypothesis is this: if we take a sample of the input traffic and feed it into a suitably scaled version of the system, we can extrapolate from the performance of the scaled system to that of the original. Our main findings are as follows. When we scale an IP network which is shared by short and longlived TCPlike and UDP flows and which is controlled by a variety of active queue management schemes, then performance measures such as queueing delay and drop probability are left virtually unchanged. We show this in theory and in simulations. This makes it possible to capture the performance of large networks quite faithfully using smaller scale replicas. Index Terms—Network downscaling, performance extrapolation, smallscale network replica, traffic sampling. I.