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## Charging and rate control for elastic traffic (1997)

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Venue: | European Transactions on Telecommunications |

Citations: | 912 - 6 self |

### Citations

2194 | Data Networks
- Bertsekas, Gallager
- 1991
(Show Context)
Citation Context ...when the network is congested. In Section 3 we use a simple example to explore how various fairness criteria are associated with particular choices of utility function. We note that max--min fairness =-=[1]-=- emerges as a limiting special case, and describe a proportional fairness criterion associated with the logarithmic utility function. In the system decomposition of Section 2, price per unit flow is t... |

469 | Fundamental design issues for the future Internet
- Shenker
- 1995
(Show Context)
Citation Context ...is has utility U s (x s ) to the user. We assume that the utility U s (x s ) is an increasing, strictly concave and continuously differentiable function of x s over the range x ss0 (following Shenker =-=[12]-=-, we call traffic that leads to such a utility function elastic traffic). Assume further that utilities are additive, so that the aggregate utility of rates 2 x = (x s ; s 2 S) is P s2S U s (x s ). A ... |

320 | Pricing congestible network resources - MacKie-Mason, Varian - 1995 |

277 | Pricing the Internet
- MacKie-Mason, Varian
- 1995
(Show Context)
Citation Context ...oadband multiservice networks, described in [3] and [6]. A subsidiary aim is to investigate the relationship between various fairness criteria and `smart market' approaches to dynamic pricing [7],[9],=-=[10]-=-. The organization of the paper is as follows. Section 2 presents a system model of charging, routing and flow control, where the system comprises both users with utility functions and a network with ... |

152 |
Mathematical Programming – Theory and Algorithms
- Minoux
- 1986
(Show Context)
Citation Context ...ss = U 0 s (x s ) if x s ? 0sU 0 s (x s ) if x s = 0 (4)ss(r) = X j2rsj if y r ? 0 X j2rsj if y r = 0 (5)sj = 0 if z j ? 0s0 if z j = 0 (6) From the general theory of constrained convex optimization (=-=[8]-=-, chapter 5; [13], chapter 3) it follows that there exists a quadruple (; ; x; y) which satisfiessU 0 (x); Hy = x; \Gammas\Gamma U 0 (x) \Delta T x = 0 (7)s0; AxsC;sT (C \Gamma Ax) = 0 (8) T HsT A; ys... |

90 | A New Approach to Service Provisioning in ATM Networks
- Low, Varaiya
- 1993
(Show Context)
Citation Context ...s for broadband multiservice networks, described in [3] and [6]. A subsidiary aim is to investigate the relationship between various fairness criteria and `smart market' approaches to dynamic pricing =-=[7]-=-,[9],[10]. The organization of the paper is as follows. Section 2 presents a system model of charging, routing and flow control, where the system comprises both users with utility functions and a netw... |

60 | Charging and Accounting for Bursty Connections
- Kelly
- 1995
(Show Context)
Citation Context ...l designed to shed light on the issues of charging, rate control and routing. Its main purpose is to support ongoing work on charging schemes for broadband multiservice networks, described in [3] and =-=[6]-=-. A subsidiary aim is to investigate the relationship between various fairness criteria and `smart market' approaches to dynamic pricing [7],[9],[10]. The organization of the paper is as follows. Sect... |

36 |
Time scale analysis and scalability issues for explicit rate allocation in ATM networks
- Charny, Ramakrishnan, et al.
- 1996
(Show Context)
Citation Context ...of allocated rates are in equilibrium. We have not discussed convergence to equilibrium and an interesting and challenging question concerns whether rate control algorithms such as those described in =-=[2]-=-, [3], and [4] may be adapted to implement the proportional fairness criterion described in this paper. A further challenging question concerns how the choice of parameter m s might be implemented in ... |

35 | Integration of pricing and flow control for available bit rate services in atm networks
- Courcoubetis, Siris, et al.
- 1996
(Show Context)
Citation Context ...s a model designed to shed light on the issues of charging, rate control and routing. Its main purpose is to support ongoing work on charging schemes for broadband multiservice networks, described in =-=[3]-=- and [6]. A subsidiary aim is to investigate the relationship between various fairness criteria and `smart market' approaches to dynamic pricing [7],[9],[10]. The organization of the paper is as follo... |

35 | Distributed pricing for embedded ATM networks
- MURPHY, MURPHY, et al.
- 1994
(Show Context)
Citation Context ...r broadband multiservice networks, described in [3] and [6]. A subsidiary aim is to investigate the relationship between various fairness criteria and `smart market' approaches to dynamic pricing [7],=-=[9]-=-,[10]. The organization of the paper is as follows. Section 2 presents a system model of charging, routing and flow control, where the system comprises both users with utility functions and a network ... |

11 |
Rate control algorithms for the ATM ABR service
- Hernandez-Valencia, Benmohamed, et al.
- 1997
(Show Context)
Citation Context ...ates are in equilibrium. We have not discussed convergence to equilibrium and an interesting and challenging question concerns whether rate control algorithms such as those described in [2], [3], and =-=[4]-=- may be adapted to implement the proportional fairness criterion described in this paper. A further challenging question concerns how the choice of parameter m s might be implemented in an ATM network... |

2 |
Recommendation I371, Traffic control and congestion control in B–ISDN
- ITU
- 1995
(Show Context)
Citation Context ...d in this paper. A further challenging question concerns how the choice of parameter m s might be implemented in an ATM network. One possibility would be to use the Minimum Cell Rate of ATM standards =-=[5]-=- to buy a share of spare capacity, as well as to provide a lower bound on the rate. In [6] some of the consequential influences on user behaviour are discussed. 2 This deduction is incorrect: it may f... |

1 |
12 and rate control for elastic traffic Correction to published version Ramesh Johari and Frank Kelly University of Cambridge This document contains a revised Section 4 of
- Wiley
- 1971
(Show Context)
Citation Context ...) if x s ? 0sU 0 s (x s ) if x s = 0 (4)ss(r) = X j2rsj if y r ? 0 X j2rsj if y r = 0 (5)sj = 0 if z j ? 0s0 if z j = 0 (6) From the general theory of constrained convex optimization ([8], chapter 5; =-=[13]-=-, chapter 3) it follows that there exists a quadruple (; ; x; y) which satisfiessU 0 (x); Hy = x; \Gammas\Gamma U 0 (x) \Delta T x = 0 (7)s0; AxsC;sT (C \Gamma Ax) = 0 (8) T HsT A; ys0; ( T A \GammasT... |

1 |
Distributed pricing for embedded ATM networks. In The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks
- Murphy, Murphy, et al.
- 1994
(Show Context)
Citation Context ...r broadband multiservice networks, described in [3] and [6]. A subsidiary aim is to investigate the relationship between various fairness criteria and ‘smart market’ approaches to dynamic pricing [7],=-=[9]-=-,[10]. The organization of the paper is as follows. Section 2 presents a system model of charging, routing and flow control, where the system comprises both users with utility functions and a network ... |