## A New Approach for Asynchronous Distributed Rate Control of Elastic Sessions in Integrated Packet Networks (0)

Venue: | IEEE/ACM Trans. Networking |

Citations: | 5 - 0 self |

### BibTeX

@ARTICLE{Abraham_anew,

author = {Santosh P. Abraham and Anurag Kumar},

title = {A New Approach for Asynchronous Distributed Rate Control of Elastic Sessions in Integrated Packet Networks},

journal = {IEEE/ACM Trans. Networking},

year = {},

volume = {9},

pages = {15--30}

}

### OpenURL

### Abstract

We develop a new class of asynchronous distributed algorithms for the explicit rate control of elastic sessions in an integrated packet network. Sessions can request for minimum guaranteed rate allocations (e.g., MCRs in the ATM context), and, under this constraint, we seek to allocate the max-min fair rates to the sessions. We capture the integrated network context by permitting the link bandwidths available to elastic sessions to be stochastically time varying. The available capacity of each link is viewed as some statistic of this stochastic process (e.g., a fraction of the mean, or a large deviations Equivalent Service Capacity (ESC)). For fixed available capacity at each link, we show that the vector of max-min fair rates can be computed from the root of a certain vector equation. A distributed asynchronous stochastic approximation technique is then used to develop a provably convergent distributed algorithm for obtaining the root of the equation, even when the link flows and the ...

### Citations

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Citation Context ...., USA; e-mail spabraham@lucent.com tic process, the motivation being that higher priority stream traffic takes away a random amount of the bandwidth. The conventional notion of max-min fairness (see =-=[6]-=-) does not consider the case where some sessions may demand a minimum throughput. In [14] the authors define fair allocation over a constraint set as the lexicographically maximum vector in this set. ... |

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Citation Context ...er sessions it is sharing the link with. The former is inefficient, and the latter is impractical. Further, the source computationsj + ff j j changes the way ER is used in ABR source behaviour. Kelly =-=[19]-=- formulates the bandwidth sharing objective as the vector of rates that maximises the total user utility. The utility that a rate provides to a user is modelled as a strictly concave, increasing, and ... |

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Citation Context ...m x l B 2 k Fig. 5. A virtual buffer is associated with the best-effort output queue whose ESC has to be estimated. The available service applied to the virtual buffer is scaled by m; see text. As in =-=[12]-=-, it can be shown that Assumption VI.1 holds if the process fD(t)g is a Markov modulated service rate process. An estimation procedure motivated by the above discussion would be as follows. We take re... |

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Citation Context ...mation procedure [8], hence reducing the problem to the synchronous case [3]. For the synchronous case the proof consists of two parts. As in the case of proofs of stochastic approximation algorithms =-=[24]-=-, it is first shown that the evolution of the sequence of vector link control parameters, j l (k); l 2 L, is asymptotically equivalent to the solution of the following ordinary differential equation. ... |

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Citation Context ...ote the stationary queue length. We now state the main theorem without proof; the reader is referred to [26] for the proof in the discrete case. For the continuous case a proof can be developed as in =-=[11]-=-. Theorem VI.1:s! \Gamma\Gamma \GammaD (`) ` () lim B!1 1 B ln(P (Q() ? B))s\Gamma` 2 * B ln p* * -q ln P(Q( ) > B) B l l * q slope = Fig. 3. Relation between P (Q() ? B) and the QoS requirement (B ; ... |

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Citation Context ...arly efforts to develop explicit rate MMF algorithms attempted basically to implement variations of the well known centralised algorithm (see [6]) in a distributed fashion; the algorithms reported in =-=[9]-=- and [18] are important examples of this approach. A combination of clever heuristics gave rise to the ERICA algorithm [17], which was adopted almost as a benchmark by the ATM forum, and has seen many... |

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Citation Context ...e queue such that the overflow probability for a given threshold is bounded above by a given value. Thus ESC is the dual of the effective bandwidth formulation for a source with stochastic rates (see =-=[26]-=-). A. Equivalent Service Capacity With reference to Figure 2, letsdenote the constant arrival rate, and let D(t 1 ; t 2 ) denote the potential number of services 3 3 The best-effort queue will typical... |

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Citation Context ... process fD(t)g is a Markov modulated service rate process. An estimation procedure motivated by the above discussion would be as follows. We take recourse to the virtual buffer technique proposed in =-=[10]-=-. Consider a best-effort output queue associated with a link at a node. A virtual buffer (simply a counter) is associated with this output queue; see Figure 5. The ESC estimate is updated periodically... |

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Citation Context ...as the lexicographically maximum vector in this set. This is a natural generalisation of the usual MMF concept, and we adopt it in this paper. This MMF notion has also been used in the ABR context in =-=[21]-=- and [16]. The formulation that leads to MMF rates assumes that the link capacities available to sessions are fixed numbers. We reconcile this with our model of stochastic available link capacities by... |

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Citation Context ...ty stream traffic takes away a random amount of the bandwidth. The conventional notion of max-min fairness (see [6]) does not consider the case where some sessions may demand a minimum throughput. In =-=[14]-=- the authors define fair allocation over a constraint set as the lexicographically maximum vector in this set. This is a natural generalisation of the usual MMF concept, and we adopt it in this paper.... |

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Citation Context ...(cf. Table I) that the stochastic approximation is reset to. Adaptive rate control is known to be problematic when there are sudden changes in available capacity, and the propagation delays are large =-=[22]-=-. Further investigations needs to be carried out to obtain a strategy for adapting the gain in WAN2 environments to prevent such large queue build up. 9. We have also observed that during periods when... |

31 | Asynchronous stochastic approximations
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Citation Context ... of C l ; l 2 L, can be obtained on-line. Hence to obtain a sequence of iterates that converge to the MMF rates, we take recourse to a distributed asynchronous stochastic approximation algorithm (see =-=[8]-=-). The structure of the stochastic approximation iteration ensures provable convergence in the presence of asynchrony and delays. The algorithm has a simple update step, requires no explicit informati... |

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Citation Context ...und trip times a low starting gain is used in the initial phase of a control cycle. Early work on MMF rate control in packet networks was done in the context of packet voice sessions; see [15], [14], =-=[25]-=-. The basic framework is the one described in [14]. The design of explicit rate control algorithms for elastic sessions, in the ATM/ABR service context, has received much attention in the literature i... |

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Citation Context ...ised algorithm (see [6]) in a distributed fashion; the algorithms reported in [9] and [18] are important examples of this approach. A combination of clever heuristics gave rise to the ERICA algorithm =-=[17]-=-, which was adopted almost as a benchmark by the ATM forum, and has seen many implementations. In our work, we have shown the MMF rate allocation problem as being equivalent to obtaining the root of a... |

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Citation Context ...rder to keep the value ofsk computed in a bounded set we truncatesk to lie in a set [; ]. Equation 4 is replaced bysk = "sk\Gamma1 +sk\Gamma1 P k\Gamma1 i=0s2 i (g k \Gamma 1) #s(5) As pointed ou=-=t in [23]-=-, the algorithm is of stochastic approximation type, as the value ofsk is computed by adding tosk\Gamma1 an error term scaled by a decreasing gainsk\Gamma1 =( P k\Gamma1 i=0s2 i ) that goes to zero as... |

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Citation Context ...xicographically maximum vector in this set. This is a natural generalisation of the usual MMF concept, and we adopt it in this paper. This MMF notion has also been used in the ABR context in [21] and =-=[16]-=-. The formulation that leads to MMF rates assumes that the link capacities available to sessions are fixed numbers. We reconcile this with our model of stochastic available link capacities by defining... |

6 |
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Citation Context ...orts to develop explicit rate MMF algorithms attempted basically to implement variations of the well known centralised algorithm (see [6]) in a distributed fashion; the algorithms reported in [9] and =-=[18]-=- are important examples of this approach. A combination of clever heuristics gave rise to the ERICA algorithm [17], which was adopted almost as a benchmark by the ATM forum, and has seen many implemen... |

4 |
and Anurag Kumar, "A Stochastic Approximation Approach for Max-Min Fair Adaptive Rate Control of ABR Sessions with MCRs
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Citation Context ... technical assumptions that the effects of asynchrony and delays are suppressed by the tapering gains of the stochastic approximation procedure [8], hence reducing the problem to the synchronous case =-=[3]-=-. For the synchronous case the proof consists of two parts. As in the case of proofs of stochastic approximation algorithms [24], it is first shown that the evolution of the sequence of vector link co... |

4 |
Asynchronous Distributed Rate Control Algorithms for Best-Effort Sessions in Integrated Services Networks with Minimum Rate Guarantees
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(Show Context)
Citation Context ...ne saturated link. Notice that the rate allocation of the sessions so obtained is such that every session has at least one bottleneck link and hence the allocation is MMF; the details are provided in =-=[5]-=-. The algorithm just outlined is a centralised MMF rate computing algorithm and parallels the one without minimum session rates given in [6]. C. Comparison of MMF with other Fairness Notions Other fai... |

3 |
and Anurag Kumar, "Max-Min Fair Rate Control of ABR Connections with Nonzero MCRs
- Abraham
(Show Context)
Citation Context ...just that the j values that the algorithm yields have to be used differently. III. MAX-MIN FAIR ALLOCATION AS THE SOLUTION OF A VECTOR EQUATION A centralised algorithm outlined above and discussed in =-=[2]-=- restates the problem of finding the max-min fair rate vector as one of obtaining the appropriate link control parameters (LCPs). We now show that a correct (not necessarily unique) vector of link con... |

3 |
A Simulation Study of an Adaptive Distributed Algorithm for Max-Min Fair Rate
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- 1998
(Show Context)
Citation Context ...n of the algorithm. At such epochs the gain of the algorithm is reset to the initial large value (i.e., a l (k) is increased). We have reported simulations without such resetting of gain in our paper =-=[4]-=-. Large queue length build-ups can be avoided in large round trip time (rtt) networks if the gains are increased anticipatively. During the connection setup phase, for a CBR/VBR session, a switch is a... |

2 |
Veciana et al
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Citation Context ...tor equation, and have then developed a provably convergent algorithm using the distributed stochastic approximation approach. Other control theoretic approaches include the work reported in [21] and =-=[27]-=-. The paper is organised as follows. In Section I-A we provide a summary of the basic network model, and the various model related notation that runs through the entire paper. In Section II we review ... |

1 |
Walrand and Cheng-Shang Chang "Effective Bandwidths for Multiclass Markov Fluids and Other ATM Sources
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Citation Context ...t each link. A Markov model has been chosen since it is easy to compute the exact ESC for such a model (this involves the computation of the dominant eigenvalue of a certain matrix; see, for example, =-=[20]-=-). We associate a two state (0; 1) Markov chain with each controlled link in the network (Links 1 to 4 in Figure 8). Time at the switches is (conceptually) slotted into intervals whose size is the cel... |