## Statistical bandwidth sharing: a study of congestion at flow level (2001)

Citations: | 178 - 18 self |

### BibTeX

@INPROCEEDINGS{Fredj01statisticalbandwidth,

author = {S. Ben Fredj and T. Bonald and A. Proutiere and G. Régnié and J. W. Roberts},

title = {Statistical bandwidth sharing: a study of congestion at flow level},

booktitle = {},

year = {2001},

pages = {111--122}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we study the statistics of the realized throughput of elastic document transfers, accounting for the way network bandwidth is shared dynamically between the randomly varying number of concurrent flows. We first discuss the way TCP realizes statistical bandwidth sharing, illustrating essential properties by means of packet level simulations. Mathematical flow level models based on the theory of stochastic networks are then proposed to explain the observed behavior. A notable result is that first order performance (e.g., mean throughput) is insensitive with respect both to the flow size distribution and the flow arrival process, as long as “sessions ” arrive according to a Poisson process. Perceived performance is shown to depend most significantly on whether demand at flow level is less than or greater than available capacity. The models provide a key to understanding the effectiveness of techniques for congestion management and service differentiation. 1.

### Citations

1804 |
Data Networks
- Bertsekas, Gallagher
- 1992
(Show Context)
Citation Context ...ositive constant and the wr are weights. This may be considered as a utility maximization problem with particular interpretations for the utility of individual allocations. Classical max-min fairness =-=[5]-=- arises in the limit α →∞with weights wr ≡ 1, while weighted proportional fairness as discussed in [20] occurs as α → 1. As α decreases from ∞ towards 0, the different allocations give relatively less... |

1421 | Wide Area Traffic: The Failure of Poisson Modeling
- Paxson, Floyed
- 1995
(Show Context)
Citation Context ...RTT) or other external factors affecting the bandwidth it obtains on a shared link. Measurements of the size of documents such as Web pages and FTP files show that their distribution has a heavy tail =-=[10, 28]-=-. The precise distribution clearly depends on the type of document considered. A reasonable fit to the form of the heavy tail is provided by the Pareto distribution: Pr[size ≤ x] =1− k , for x ≥ k, (1... |

1378 |
Rate control in communication networks: shadow prices, proportional fairness and stability
- Kelly, Mauloo, et al.
- 1998
(Show Context)
Citation Context ...of these flows. The Br must satisfy the capacity constraints: � xrBr ≤ Cl, for l ∈L. (11) r∋l The issue of what constitutes a fair bandwidth allocation has been discussed in a number of recent papers =-=[20, 26, 24]-=-. A significant range of fairness notions can be expressed as the solution to the following optimization problem [26]: Maximize � B 1−α r wrxr , subject to constraints (11), 1 − α r (12) where α �= 1 ... |

1136 | BESTAVROS: “Self-similarity in World Wide Web traffic: evidence and possible causes
- CROVELLA, A
- 1997
(Show Context)
Citation Context ...RTT) or other external factors affecting the bandwidth it obtains on a shared link. Measurements of the size of documents such as Web pages and FTP files show that their distribution has a heavy tail =-=[10, 28]-=-. The precise distribution clearly depends on the type of document considered. A reasonable fit to the form of the heavy tail is provided by the Pareto distribution: Pr[size ≤ x] =1− k , for x ≥ k, (1... |

553 |
Reversibility and stochastic networks
- Kelly
- 1979
(Show Context)
Citation Context ...work The succession of document transfers and think-times constituting a session may be represented as a customer visiting two stations in a stochastic network of the kind considered notably by Kelly =-=[19]-=- 3 (see Figure 8). The first and last station to be visited is the link, and successive visits to the link are separated by a visit to a think-time station. Outside arrivals are Poisson and every cust... |

466 | Fair end-to-end window-based congestion control
- Mo, Walrand
- 2000
(Show Context)
Citation Context ...of these flows. The Br must satisfy the capacity constraints: � xrBr ≤ Cl, for l ∈L. (11) r∋l The issue of what constitutes a fair bandwidth allocation has been discussed in a number of recent papers =-=[20, 26, 24]-=-. A significant range of fairness notions can be expressed as the solution to the following optimization problem [26]: Maximize � B 1−α r wrxr , subject to constraints (11), 1 − α r (12) where α �= 1 ... |

270 | Bandwidth Sharing: Objectives and Algorithms
- Massoulie, Roberts
- 2000
(Show Context)
Citation Context ...of these flows. The Br must satisfy the capacity constraints: � xrBr ≤ Cl, for l ∈L. (11) r∋l The issue of what constitutes a fair bandwidth allocation has been discussed in a number of recent papers =-=[20, 26, 24]-=-. A significant range of fairness notions can be expressed as the solution to the following optimization problem [26]: Maximize � B 1−α r wrxr , subject to constraints (11), 1 − α r (12) where α �= 1 ... |

227 | Dynamics of IP traffic: A study of the role of variability and the impact of control
- Feldmann, Huang, et al.
- 1999
(Show Context)
Citation Context ...11 capacity. In the interests of simplicity, we ignore the impact of non-responsive flows and assume all traffic is elastic. Characteristics of IP traffic at packet level are notoriously complex (see =-=[17]-=-, for example). Arguably, however, these characteristics are less an exogenous expression of user demand than a result of the closed loop control implemented by TCP. A study of throughput performance ... |

166 | A Stochastic Model of TCP/IP with Stationary Random Losses
- Altman
- 2005
(Show Context)
Citation Context ...d by a permanent flow is given by the approximate relation: B(p) ≈ K rtt √ (4) p where K is a constant that depends on second-order statistics of the loss process (K = � 3/2 for periodic losses); see =-=[1]-=- and cited references. When several permanent TCP connections use the same bottleneck link, the effect of congestion avoidance is to share the link bandwidth between them. Assuming all flows experienc... |

163 | Bandwidth sharing and admission control for elastic traffic
- Roberts, Massoulié
- 1998
(Show Context)
Citation Context ...the means of the document size and thinktime and not on their precise distributions. Berger and Kogan [4] have further explored this model in an asymptotic heavy traffic regime. Massoulié and Roberts =-=[25]-=- propose a model similar to that of Heyman where however the flow arrival process is Poisson. They identify the underlying fluid flow model as an M/G/1 processor sharing queue. The Poisson arrival ass... |

156 | Impact of Fairness on Internet Performance
- Bonald, Massoulie
- 2001
(Show Context)
Citation Context ...link exceeds capacity. A recent study by Fayolle et al [13] illustrates the difficulty of evaluating statistical throughput performance on a path containing multiple bottlenecks. Bonald and Massoulié =-=[6]-=- have further explored statistical bandwidth sharing in a network, notably illustrating the impact on stability of certain service differentiation mechanisms. The main contribution of the present pape... |

87 | Stability and performance analysis of networks supporting elastic services
- Lee, Veciana, et al.
- 1999
(Show Context)
Citation Context ...rate estimates when connection arrivals are Poisson. Bu and Towsley [8] incorporate a discriminatory processor sharing model in their study of TCP performance with finite size flows. De Veciana et al =-=[11]-=- consider statistical bandwidth sharing in a network setting assuming Poisson flow arrivals. They notably highlight the potential for a form of congestion collapse when demand on any link exceeds capa... |

77 |
The multiple phase service network with generalized processor sharing
- Cohen
- 1979
(Show Context)
Citation Context ...llustrated in Figure 3. Assume all users have a common maximum rate limit r<C. This bandwidth sharing model can be recognized as a generalization of the processor sharing queue considered by Cohen in =-=[9]-=-. Corresponding results derived therein for π(n) andR(s) are as follows: π(n) =(1− ρ)f(ρ) × � m! ρC ( n! r )n−m , for n<m, ρ n−m , for n ≥ m, � � 1 f(ρ) C R(s) =s + (1 − ( − m)(1 − ρ)) (8) r C(1 − ρ) ... |

65 |
mixed networks of queues with different classes of customers
- Open
- 1975
(Show Context)
Citation Context ...k An essential characteristic of a customer in a stochastic network is its “class”. This is a versatile attribute which 3 Broadly equivalent results can be derived using the alternative formalisms of =-=[2]-=- or [9]. 117 allows us to distinguish different kinds of customer as well as the number of times the customer has previously visited the current station. In the present context we use the class to spe... |

53 |
Fixed Point Approximation for TCP behavior in an AQM Network
- Towsley
- 2001
(Show Context)
Citation Context ...ave studied the statistical bandwidth sharing performance realized by TCP and confirm that the processor sharing model provides accurate estimates when connection arrivals are Poisson. Bu and Towsley =-=[8]-=- incorporate a discriminatory processor sharing model in their study of TCP performance with finite size flows. De Veciana et al [11] consider statistical bandwidth sharing in a network setting assumi... |

40 |
Queueing Systems, Volumes I and 2
- Kleinrock
- 1975
(Show Context)
Citation Context ... flow of size s. Let ρ = λσ/C denote the link load and assume ρ<1. With Poisson flow arrivals, the number of flows in progress behaves like the number of customers in an M/G/1 processor sharing queue =-=[22]-=- and we have immediately the well known results: π(n) =ρ n (1 − ρ), (5) s R(s) = . (6) C(1 − ρ) Note that R(s)/s is the mean of the inverse of the throughput received by flows of size s. Thus γ(s) = s... |

39 | Global fairness of additive-increase and multiplicative-decrease with heterogeneous round-trip times
- Vojnovic, Boudec, et al.
- 2000
(Show Context)
Citation Context ...s � r∋l xrBr = Cl, itmay readily be verified by applying the Kuhn-Tucker theorem that the allocation satisfying (13) is the unique solution to optimization problem (12) with α =2andwr =1/rtt 2 r (see =-=[30]-=- for further discussion on the type of bandwidth sharing realized by TCP). 6.2 Statistical bandwidth sharing Assume now that flows on route r arrive at rate λr and have mean size σr. Letρl = � r∋l λrσ... |

38 | Dimensioning bandwidth for elastic traffic in high-speed data networks
- Berger, Kogan
(Show Context)
Citation Context ...ly predicts throughput performance. A notable result is that expected performance depends only on the means of the document size and thinktime and not on their precise distributions. Berger and Kogan =-=[4]-=- have further explored this model in an asymptotic heavy traffic regime. Massoulié and Roberts [25] propose a model similar to that of Heyman where however the flow arrival process is Poisson. They id... |

26 |
Data Networks as Cascades: Explaining the Multifractal
- Feldmann, Gilbert, et al.
(Show Context)
Citation Context ...f-similarity is the heavy-tailed nature of the size distribution of transferred documents while multifractal behavior appears to be a manifestation of the burstiness induced by TCP congestion control =-=[17, 16]-=-. The complexity of the packet arrival process is such that it proves very difficult to derive a packet level traffic characterization which is useful for performance modeling. We note further that mo... |

20 |
On the transient behavior of the processor sharing queue
- Jean-Marie, Robert
- 1994
(Show Context)
Citation Context ... Bandwidth sharing performance during transient overload It is interesting to note that the rate of increase in the number of flows actually depends significantly on the form of the size distribution =-=[18]-=-. The rate of increase is smaller as the proportion of mice is greater. The latter manage to complete although their throughput continues to decrese, while the response time of elephants tends rapidly... |

18 | Insensitivity results in statistical bandwidth sharing - Bonald, Proutière, et al. - 2001 |

18 | Best-effort networks: Modeling and performance analysis via large networks asymptotics
- Fayolle, la, et al.
- 2001
(Show Context)
Citation Context ...g in a network setting assuming Poisson flow arrivals. They notably highlight the potential for a form of congestion collapse when demand on any link exceeds capacity. A recent study by Fayolle et al =-=[13]-=- illustrates the difficulty of evaluating statistical throughput performance on a path containing multiple bottlenecks. Bonald and Massoulié [6] have further explored statistical bandwidth sharing in ... |

14 | Performance Analysis of TCP with Nonpersistent Sessions. Workshop on Modeling
- Kherani, Kumar
- 2000
(Show Context)
Citation Context ...d flow model as an M/G/1 processor sharing queue. The Poisson arrival assumption is more appropriate when the considered link receives traffic from a very large population of users. Kheranisand Kumar =-=[21]-=- have studied the statistical bandwidth sharing performance realized by TCP and confirm that the processor sharing model provides accurate estimates when connection arrivals are Poisson. Bu and Towsle... |

13 | Measurement-based admission control for elastic traffic
- Fredj, Oueslati-Boulahia, et al.
- 2001
(Show Context)
Citation Context ...s is not necessarily a disadvantage. Indeed, one advantage of admission control is that it can be applied selectively with different admission thresholds applying to different classes of traffic (see =-=[3]-=-). 121 8. CONCLUSIONS To evaluate the throughput performance of elastic transfers it is necessary to account for the dynamic nature of traffic. Traffic variations are most naturally modeled in terms o... |

12 |
Arguments in favor of admission control for TCP flows,” ITC 16, Edinbourg
- Massoulié, Roberts
- 1999
(Show Context)
Citation Context ...efficiency would gain from a more proactive reaction to congestion. 7.4 Admission control An alternative to allowing an overloaded link to stabilize through impatience is to perform admission control =-=[23]-=-. If flows arriving when the bandwidth they would achieve is less than an acceptable threshold were rejected immediately, there would be no cause for impatience. The advantage is that goodput is maint... |

11 |
Sharing a processor among many classes
- Fayolle, Mitrani, et al.
- 1980
(Show Context)
Citation Context ...tion (e.g., with HTTP 1.0). To fully explore the implications of unequal sharing is beyond present scope. We note simply that evaluations using simulation and a discriminatory processor sharing model =-=[14]-=- reveal the following (see [6, 29]): • discrimination in realized throughput is significant mainly at loads close to saturation; • size dependent throughput γ(s) is roughly the same for all s except f... |

11 | Quality of Service by Flow Aware Networking
- Roberts, Oueslati
- 2000
(Show Context)
Citation Context ...fully explore the implications of unequal sharing is beyond present scope. We note simply that evaluations using simulation and a discriminatory processor sharing model [14] reveal the following (see =-=[6, 29]-=-): • discrimination in realized throughput is significant mainly at loads close to saturation; • size dependent throughput γ(s) is roughly the same for all s except for the very largest documents whos... |

8 |
Dynamics of IP traffic: A study of the role of variability and the impact of control, in
- Feldman, Gilbert, et al.
- 1999
(Show Context)
Citation Context ...11 capacity. In the interests of simplicity, we ignore the impact of non-responsive flows and assume all traffic is elastic. Characteristics of IP traffic at packet level are notoriously complex (see =-=[17]-=-, for example). Arguably, however, these characteristics are less an exogenous expression of user demand than a result of the closed loop control implemented by TCP. A study of throughput performance ... |

3 |
Characteristics of TCP Connection Arrivals
- Feldman
(Show Context)
Citation Context ...nd to very long flows as “elephants”. In many cases flows are generated within sessions. The flow arrival process thus tends to be bursty and has indeed been shown to be self-similar in certain cases =-=[28, 15]-=-, a plausible explanation being that the number of flows per session has a heavy-tailed distribution. It may nevertheless be appropriate in certain circumstances to suppose flows arrive according to a... |

2 |
method for analyzing feedback protocols with applications to engineering web traffic over the Internet
- New
- 1997
(Show Context)
Citation Context ... performance-related network provisioning procedures. There is relatively little work in the literature on the evaluation of throughput performance under statistical traffic assumptions. Heyman et al =-=[12]-=- consider the performance of a bottleneck link shared by a fixed number of homogeneous sources alternately emitting documents and remaining inactive during a random think-time. Their results confirm t... |

1 |
A compound model of tcp arrivals
- Nuzman, Saniee, et al.
- 2000
(Show Context)
Citation Context .... Some authors have arbitrarily defined a session by partitioning a set of flows according to the inter-flow interval: a new session is assumed to start when this interval exceeds a certain threshold =-=[27]-=-. In all cases it is noted that session arrivals in any period where the traffic intensity is approximately constant are accurately modeled by a Poisson process. This observation is not surprising sin... |