## Analysis Of A Fluid Approximation To Flow Control Dynamics (1992)

Venue: | In Proc. IEEE INFOCOM '92 |

Citations: | 27 - 6 self |

### BibTeX

@INPROCEEDINGS{Bolot92analysisof,

author = {Jean-chrysostome Bolot and A. Udaya Shankar},

title = {Analysis Of A Fluid Approximation To Flow Control Dynamics},

booktitle = {In Proc. IEEE INFOCOM '92},

year = {1992},

pages = {2398--2407}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider a flow control mechanism that dynamically regulates the rate of data flow into a network based on feedback information about the network state. Such mechanisms have been introduced recently in a variety of networks including the Internet, and have been advocated for future high-speed networks. We first model the flow control mechanism by a discrete-space stochastic process and define appropriate performance measures for transient and steady-state regimes. However, the model does not appear to be analytically tractable and we study it through simulation. We then simplify it to a continuous-space deterministic (or fluid) model for which we can easily derive closed-form solutions. We find the analytical results for the fluid model to agree well with the simulation results obtained using the discrete-space model. Both models explicitly consider delay of the feedback information, thus making them relevant for high-speed networks. 1 Introduction In a computer network, packets g...

### Citations

2339 | Congestion Avoidance and Control
- Jacobson
- 1988
(Show Context)
Citation Context ...se their sources do not maintain constant data rates. Recently, flow control mechanisms have been proposed where the source rate is dynamically regulated based on feedback from the intermediate nodes =-=[9, 15, 37, 18, 25, 31, 13, 38, 19]-=-. These mechanisms attempt to adapt the source rate to the bottleneck rate in minimum time and with minimum packet delay or loss. A variety of feedback schemes are possible. In the binary feedback sch... |

1117 | Analysis and simulation of a fair queueing algorithm
- Demers, Keshav, et al.
- 1989
(Show Context)
Citation Context ...sit. state approach technique [34]. Finally, it should be pointed out that due to the lack of analytical results, a number of flow control mechanisms have been evaluated with discreteevent simulation =-=[28, 39, 11]-=- or experimental approaches [15, 22, 32]. Summary of the rest of the paper In this paper, we consider a rate-based flow control mechanism with feedback similar to that of the binary feedback scheme. I... |

388 | A Control-Theoretic Approach to Flow Control
- Keshav
- 1991
(Show Context)
Citation Context ...se their sources do not maintain constant data rates. Recently, flow control mechanisms have been proposed where the source rate is dynamically regulated based on feedback from the intermediate nodes =-=[9, 15, 37, 18, 25, 31, 13, 38, 19]-=-. These mechanisms attempt to adapt the source rate to the bottleneck rate in minimum time and with minimum packet delay or loss. A variety of feedback schemes are possible. In the binary feedback sch... |

317 | A binary feedback scheme for congestion avoidance in computer networks
- Ramakrishnan, Jain
- 1990
(Show Context)
Citation Context ... adapt the source rate to the bottleneck rate in minimum time and with minimum packet delay or loss. A variety of feedback schemes are possible. In the binary feedback scheme, which is used in DECNET =-=[28]-=- and is being advocated for ISO TP4 [23] and high-speed networks [38], each data packet received by the destination has a bit indicating whether or not the packet encountered an intermediate node with... |

285 |
closed, and mixed networks of queues with different classes of customers
- Chandy, Muntz, et al.
- 1985
(Show Context)
Citation Context ...t the steady-state behavior of queueing systems, when the service and job arrival rates are stationary (i.e., have distributions that do not change with time) and certain product-form conditions hold =-=[1, 20]-=-. These results have been used extensively to study fixed-window flow control mechanisms in loss-less networks [30, 33]. However, to model flow control mechanisms that dynamically regulate the source ... |

202 | Improving round-trip time estimates in reliable transport protocols - Karn, Partridge - 1987 |

124 |
A new architecture for packet switched network protocols
- Zhang
- 1989
(Show Context)
Citation Context ...e in a wide-area network. Keshav [19] describes a scheme in which the source adjusts its rate to keep the bottleneck queue size around some fixed value. Other rate-based schemes have been proposed in =-=[8, 39, 10, 18, 31, 37, 13, 38]-=-. However, most protocols currently in operation [33, 28, 15] use a window-based scheme, rather than the rate-based scheme. Here, a limit referred to as the window size is placed on the number of pack... |

114 | NETBLT: A High Throughput Transport Protocol
- Clark, Lambert, et al.
- 1987
(Show Context)
Citation Context ...se their sources do not maintain constant data rates. Recently, flow control mechanisms have been proposed where the source rate is dynamically regulated based on feedback from the intermediate nodes =-=[9, 15, 37, 18, 25, 31, 13, 38, 19]-=-. These mechanisms attempt to adapt the source rate to the bottleneck rate in minimum time and with minimum packet delay or loss. A variety of feedback schemes are possible. In the binary feedback sch... |

112 |
Queueing Systems, Volume 2: Computer Applications
- Kleinrock
- 1976
(Show Context)
Citation Context ...t the steady-state behavior of queueing systems, when the service and job arrival rates are stationary (i.e., have distributions that do not change with time) and certain product-form conditions hold =-=[1, 20]-=-. These results have been used extensively to study fixed-window flow control mechanisms in loss-less networks [30, 33]. However, to model flow control mechanisms that dynamically regulate the source ... |

110 |
Flow control: A Comparative survey
- Gerla, Kleinrock
- 1980
(Show Context)
Citation Context ...rt different sourcedestination pairs; their hardware may differ; etc. If the network is in steady-state, the ideal flow control policy is to limit the source rate to the bottleneck rates= min i ( i ) =-=[12]-=-, or equivalently the interpacket gap to 1=; a higher rate would result in packet delay or loss, and a lower rate in underutilization. In reality, however, the bottleneck rate changes with time becaus... |

86 |
VMTP: A transport protocol for the next generation of communications systems
- CHERITON
- 1987
(Show Context)
Citation Context ... source rate based on the feedback information. In rate-based mechanisms, the source rate is regulated by adjusting interpacket gaps. Examples are found in the transport protocols NETBLT [9] and VMTP =-=[7]-=-, although it is not clear in these protocols exactly how interpacket gaps are adjusted or what the feedback would be in a wide-area network. Keshav [19] describes a scheme in which the source adjusts... |

83 | REAL: a Network Simulator
- Keshav
- 1988
(Show Context)
Citation Context ...re n is the lowest index greater than k such that g n ? 1=). 2.1 Simulations We now present simulations of the above queueing system. They were obtained using a modified version of the REAL simulator =-=[17]-=-. In all cases, we assume that the data packet sizes fS i g are independent and identically distributed with a uniform distribution over an interval [s min : : : s max ]. We characterize the distribut... |

64 |
Discrete flow networks: Bottleneck analysis and fluid approximation
- Chen, Mandelbaum
- 1991
(Show Context)
Citation Context ...d the performance of a single connection with rate-based flow control. Fluid approximations have been found convenient for studying the timedependent behavior of networks with more general topologies =-=[6]-=-. We are extending our model to consider multiple connections sharing one or more bottleneck nodes. Preliminary results indicate that the source sending rates and the bottleneck queue sizes follow a r... |

59 |
Applications of Queueing Theory
- NEWELL
- 1971
(Show Context)
Citation Context ...mation, where the basic idea is to replace discrete-space stochastic processes by corresponding continuous-space deterministic processes, which are related by means of ordinary differential equations =-=[27, 20, 5]-=-. An extension of this is the diffusion approximation [20, 26]. Another technique is the 1 Otherwise a packet can be retransmitted while its previous copy is still in transit. state approach technique... |

50 |
Random drop congestion control
- Mankin
- 1990
(Show Context)
Citation Context ...lly, it should be pointed out that due to the lack of analytical results, a number of flow control mechanisms have been evaluated with discreteevent simulation [28, 39, 11] or experimental approaches =-=[15, 22, 32]-=-. Summary of the rest of the paper In this paper, we consider a rate-based flow control mechanism with feedback similar to that of the binary feedback scheme. In Section 2, we present a queueing model... |

46 |
Dynamic adaptive windows for high speed data networks: theory and simulations
- Mitra, Seery
- 1990
(Show Context)
Citation Context |

45 |
Dynamical behavior of rate-based flow control mechanism
- Bolot, Shankar
- 1990
(Show Context)
Citation Context ...lytical results for the fluid model with the simulation results obtained using the discrete-space model, and find them to correspond closely. A preliminary version of the fluid model was presented in =-=[2]-=-. Section 4 concludes the paper. 2 A Discrete-space Stochastic Model In this section, we present a discrete-space stochastic model of a connection with rate-based flow control. Each data packet sent b... |

39 |
A queueing network analysis of computer communication networks with window flow control
- REISER
- 1979
(Show Context)
Citation Context ...tributions that do not change with time) and certain product-form conditions hold [1, 20]. These results have been used extensively to study fixed-window flow control mechanisms in loss-less networks =-=[30, 33]-=-. However, to model flow control mechanisms that dynamically regulate the source rate based on feedback information, we need queueing models where the service times and job arrivals are time-varying a... |

37 |
Numerical methods for modeling computer networks under nonstationary conditions
- Tipper, Sundarehasan
- 1990
(Show Context)
Citation Context ... An extension of this is the diffusion approximation [20, 26]. Another technique is the 1 Otherwise a packet can be retransmitted while its previous copy is still in transit. state approach technique =-=[34]-=-. Finally, it should be pointed out that due to the lack of analytical results, a number of flow control mechanisms have been evaluated with discreteevent simulation [28, 39, 11] or experimental appro... |

32 | Some Diffusion Approximations with State-Space Collapse - Reiman - 1983 |

20 |
Statistical Analysis of Simulation Output Data
- Law
- 1983
(Show Context)
Citation Context ...is method, the duration of the transient regime in a series of values fX(t i ): is1g is equal to the smallest t j such that X(t j ) is neither the maximum nor the minimum of the series fX(t i ): isjg =-=[21]-=- D F = D R = 20 ms. Throughout the rest of the paper, we let D = D F + D R . The values of D F and D R are different for the ordinary and the high-speed networks. This is because D F , for example, in... |

13 |
Design and analysis of a flow control algorithm for a network of rate allocating servers
- Keshav, Agrawala
- 1991
(Show Context)
Citation Context |

11 |
Congestion control by adaptive admission
- Haas, Winters
- 1991
(Show Context)
Citation Context |

11 |
Fairness and congestion control on a large ATM data network with dynamically adjustable windows
- Hahne, Kalmanek, et al.
- 1991
(Show Context)
Citation Context ...rce decreases the window size by a multiplicative factor if the feedback congestion bit is set to 1; otherwise, it increases the window size linearly. Other window-based schemes have been proposed in =-=[25, 14]-=-. The window size is intended to be a bound on the number of data and acknowledgement packets of this connection in transit in the network. Note that because packets can be lost, a good roundtrip time... |

10 |
Time-dependent analysis of queueing systems
- Tripathi, Duda
- 1986
(Show Context)
Citation Context ... job arrivals are time-varying and state-dependent. Unfortunately, the analysis of such systems is extremely difficult and it has received limited attention. Only a few special cases have been solved =-=[35]-=-. More complex systems are often analyzed by numerically solving the ChapmanKolmogorov equations describing the system state [36, 3], but this rapidly becomes unmanageable for realistic models. These ... |

8 |
Sojourn times in cyclic queues– the influence of the slowest server,” in Computer Pe~fi)rmunce curd Re/iubility
- Boxma
- 1988
(Show Context)
Citation Context ...ode by a queue of service ratesbits/s. Let Q(t) denote the queue size at time t. We do not explicitly model the non bottleneck nodes. It has been shown that this does not introduce significant errors =-=[29, 4]-=-. We use a constant delay D F to represent the queueing and propagation delays from the source to the bottleneck, and another constant delay D R to represent the queueing and propagation delays from t... |

8 | Strikwerda, "Analysis of dynamic congestion control protocols: A Fokker-Plank approach - Mukherjee, C - 1991 |

8 | Congestion control in BBN packet switched networks
- Robinson, Friedman, et al.
- 1990
(Show Context)
Citation Context |

8 |
A dynamic rate control mechanism for integrated networks
- Yin, Hluchyi
(Show Context)
Citation Context |

7 |
A rate-based congestion avoidance and control scheme for packet switched networks
- Comer, Yavatkar
- 1990
(Show Context)
Citation Context ... sending a packet and receiving its acknowledgement and uses them to maintain a running roundtrip time estimate [15]. Other schemes rely on feedback information that includes average link utilization =-=[10, 31]-=-, interarrival times between successive acknowledgement packets [18], etc. There is also a variety of ways to regulate the source rate based on the feedback information. In rate-based mechanisms, the ... |

7 |
A TCP instrumentation and its use in evaluating roundtrip-time estimators
- Sanghi, Subramaniam, et al.
- 1990
(Show Context)
Citation Context ...cause packets can be lost, a good roundtrip time estimate is an essential part of window-based schemes. 1 Obtaining a good roundtrip time estimate in a network when losses are frequent is not trivial =-=[16, 15, 32]-=-, and maybe as difficult as the original flow control problem. Performance evaluation of flow control schemes We are interested in evaluating the performance of dynamic flow control mechanisms. Perfor... |

7 |
Access control in metropolitan area networks
- WONG, SCHWARTZ
- 1990
(Show Context)
Citation Context |

6 |
Performance analysis of transport protocols over congestive channels
- Bolot, Shankar, et al.
- 1990
(Show Context)
Citation Context ... received limited attention. Only a few special cases have been solved [35]. More complex systems are often analyzed by numerically solving the ChapmanKolmogorov equations describing the system state =-=[36, 3]-=-, but this rapidly becomes unmanageable for realistic models. These difficulties led to the development of approximate techniques. One such technique is the fluid approximation, where the basic idea i... |

5 |
Control Mechanisms for High-Speed Networks
- Cidon, Gopal
- 1990
(Show Context)
Citation Context ...e in a wide-area network. Keshav [19] describes a scheme in which the source adjusts its rate to keep the bottleneck queue size around some fixed value. Other rate-based schemes have been proposed in =-=[8, 39, 10, 18, 31, 37, 13, 38]-=-. However, most protocols currently in operation [33, 28, 15] use a window-based scheme, rather than the rate-based scheme. Here, a limit referred to as the window size is placed on the number of pack... |

5 |
Transient analysis of Markovian queueing systems and its application to congestioncontrol modeling
- AS
- 1986
(Show Context)
Citation Context ... received limited attention. Only a few special cases have been solved [35]. More complex systems are often analyzed by numerically solving the ChapmanKolmogorov equations describing the system state =-=[36, 3]-=-, but this rapidly becomes unmanageable for realistic models. These difficulties led to the development of approximate techniques. One such technique is the fluid approximation, where the basic idea i... |

3 |
Performance analysis of the SNA virtual route pacing control
- Schwartz
- 1982
(Show Context)
Citation Context ...usts its rate to keep the bottleneck queue size around some fixed value. Other rate-based schemes have been proposed in [8, 39, 10, 18, 31, 37, 13, 38]. However, most protocols currently in operation =-=[33, 28, 15]-=- use a window-based scheme, rather than the rate-based scheme. Here, a limit referred to as the window size is placed on the number of packets that can be outstanding at the source, but no constraint ... |

2 |
Zarki, "Routing and Flow Control in High Speed Networks
- Maxemchuk, El
- 1990
(Show Context)
Citation Context ... c increases, whereas Q and X appear to be independent of c. We note that the larger bandwidth-delay product of the high-speed network requires larger buffers at the bottleneck to avoid packet losses =-=[24]-=-. Fixed length packets In this subsection, we consider the case where c = 0, i.e., all data packets have a fixed size of 8000 bits. We examine the variations of the performance measures versussfi and ... |

1 |
A unified model for flow control in packet switched networks
- Browning
- 1988
(Show Context)
Citation Context ...mation, where the basic idea is to replace discrete-space stochastic processes by corresponding continuous-space deterministic processes, which are related by means of ordinary differential equations =-=[27, 20, 5]-=-. An extension of this is the diffusion approximation [20, 26]. Another technique is the 1 Otherwise a packet can be retransmitted while its previous copy is still in transit. state approach technique... |

1 |
et al., "Evaluation of Internet Performance
- Mankin
- 1990
(Show Context)
Citation Context ... rate in minimum time and with minimum packet delay or loss. A variety of feedback schemes are possible. In the binary feedback scheme, which is used in DECNET [28] and is being advocated for ISO TP4 =-=[23]-=- and high-speed networks [38], each data packet received by the destination has a bit indicating whether or not the packet encountered an intermediate node with average queue size greater than 1; this... |