## Application of Network Calculus to Guaranteed Service Networks (1998)

Citations: | 37 - 6 self |

### BibTeX

@MISC{Boudec98applicationof,

author = {Jean-Yves Le Boudec},

title = {Application of Network Calculus to Guaranteed Service Networks},

year = {1998}

}

### OpenURL

### Abstract

We use recent network calculus results to study some properties of lossless multiplexing as it may be used in guaranteed service networks. We call network calculus a set of results that apply min-plus algebra to packet networks. We provide a simple proof that shaping a traffic stream to conform to a burstiness constraint preserves the original constraints satisfied by the traffic stream We show how all rate-based packet schedulers can be modeled with a simple rate latency service curve. Then we define a general form of deterministic effective bandwidth and equivalent capacity. We find that call acceptance regions based on deterministic criteria (loss or delay) are convex, in contrast to statistical cases where it is the complement of the region which is convex. We thus find that, in general, the limit of the call acceptance region based on statistical multiplexing when the loss probability target tends to 0 may be strictly larger than the call acceptance region based on lossless mult...

### Citations

3268 | Variational analysis
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Citation Context ...llustrated in Figure 6. Computation of the Optimum Since the cost function is linear, its minimum is attained on the border of R, and it can be only on a point of the border @R 2 of R 2 or at point A =-=[29]-=-. It is straightforward to see that in all cases, the cost at A is superior than or equal to the costs at Q and R, thus the cost is minimum for a point on @R 2 which lies between Q and R. Thus, the op... |

1673 | A generalized processor sharing approach to flow control in integrated services networks ⎯ the single node case
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Citation Context ...s that can be used for computing tight bounds on delays, backlogs and arrival envelopes in a lossless setting applicable to packet networks. Fundamental work has been pioneered by Parekh and Gallager =-=[1, 2]-=- and Cruz [3, 4, 5], where general bounds based on the concepts of arrival and service curves are derived. Other fundamental work for specific or general scheduling policies is described in [6, 7]. Re... |

563 | VirtualClock: A New Traffic Control Algorithm for Packet Switching Network
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Citation Context ...d D are computed during reservation setup, with a protocol such as the Resource Reservation Protocol (RSVP) [21]. A number of scheduling policies have been proposed in the literature (see for example =-=[1, 7, 22, 23, 13]-=-). Consider the general form of scheduling proposed in [13] under the name of Guaranteed Rate (GR) scheduling. It is shown in [13] that Guaranteed Rate scheduling includes as particular cases: virtual... |

557 |
A calculus for network delay, part I: Network elements in isolation
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- 1991
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Citation Context ...ed for computing tight bounds on delays, backlogs and arrival envelopes in a lossless setting applicable to packet networks. Fundamental work has been pioneered by Parekh and Gallager [1, 2] and Cruz =-=[3, 4, 5]-=-, where general bounds based on the concepts of arrival and service curves are derived. Other fundamental work for specific or general scheduling policies is described in [6, 7]. Recently, this work h... |

509 | Service disciplines for guaranteed performance service in packetswitching networks
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- 1995
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Citation Context ...curve" condition in [13] to ff(t \Gamma s) + l, where l is the maximum packet length. There are known forms of scheduling that do not belong to the GR type. One such form is the delay based sched=-=uler [25]-=-. As mentioned in Section II, a delay based scheduler offers a service curve of ffi T for some T , which is thus a particular case of a rate latency service curve. There are however other forms of sch... |

407 | Resource reservation protocol (RSVP) – version 1 functional specification
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Citation Context ...depends on the rate R according to T = C R +D for some constants C and D. The values of C and D are computed during reservation setup, with a protocol such as the Resource Reservation Protocol (RSVP) =-=[21]-=-. A number of scheduling policies have been proposed in the literature (see for example [1, 7, 22, 23, 13]). Consider the general form of scheduling proposed in [13] under the name of Guaranteed Rate ... |

300 |
A calculus for network delay, part II: Network analysis
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- 1991
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Citation Context ...ed for computing tight bounds on delays, backlogs and arrival envelopes in a lossless setting applicable to packet networks. Fundamental work has been pioneered by Parekh and Gallager [1, 2] and Cruz =-=[3, 4, 5]-=-, where general bounds based on the concepts of arrival and service curves are derived. Other fundamental work for specific or general scheduling policies is described in [6, 7]. Recently, this work h... |

249 | Synchronization and linearity: An Algebra for Discrete Event Systems - Baccelli, Cohen, et al. - 1992 |

210 | Quality of service guarantees in virtual circuit switched networks
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Citation Context ...ed for computing tight bounds on delays, backlogs and arrival envelopes in a lossless setting applicable to packet networks. Fundamental work has been pioneered by Parekh and Gallager [1, 2] and Cruz =-=[3, 4, 5]-=-, where general bounds based on the concepts of arrival and service curves are derived. Other fundamental work for specific or general scheduling policies is described in [6, 7]. Recently, this work h... |

195 | Specification of guaranteed quality of service
- Shenker, Partridge, et al.
- 1997
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Citation Context ...plied to derive general concepts for packet networks with guaranteed service. Firstly, in Section IV we show how rate based schedulers can be modeled simply in a way that fits with the IETF framework =-=[12, 7, 13]-=-. Secondly, in Section V, we introduce the general concept of deterministic effective bandwidth, which was introduced in a narrower context in [14, pages 270--273]. We give a simple, general definitio... |

182 | E ective bandwidths at multi-class queues
- Kelly
- 1991
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Citation Context ...convex. This is in contrast to call acceptance regions based on statistical multiplexing with large deviation asymp2 totics, in which case it is the complement in the positive orthant which is convex =-=[15]-=-. This also shows that, in general, the limit of the call acceptance region based on statistical multiplexing when the loss probability target tends to 0 may be strictly larger than the call acceptanc... |

143 |
On computing per-session performance bounds in high-speed multi-hop computer networks
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- 1992
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Citation Context ...ger [1, 2] and Cruz [3, 4, 5], where general bounds based on the concepts of arrival and service curves are derived. Other fundamental work for specific or general scheduling policies is described in =-=[6, 7]-=-. Recently, this work has been extended and simplified independently and simultaneously under equivalent forms by Sariowan [8] who gives a formal and general treatment of the concepts of arrival and s... |

132 | High-Performance Communication Networks
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- 1996
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Citation Context ...or a given ff and a given constraint on delay or buffer capacity. This problem has been studied in [14, pages 270--273], in the specific case of a flow constrained by one leaky bucket. The authors in =-=[14]-=- find that, if we impose a fixed delay constraint D to the flow, then the condition on C is that CsCD , where CD depends on the leaky bucket parameters and the delay constraint. CD is called the (dete... |

110 | Determining End-to-End Delay Bounds in Heterogeneous Networks
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- 1995
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Citation Context ...plied to derive general concepts for packet networks with guaranteed service. Firstly, in Section IV we show how rate based schedulers can be modeled simply in a way that fits with the IETF framework =-=[12, 7, 13]-=-. Secondly, in Section V, we introduce the general concept of deterministic effective bandwidth, which was introduced in a narrower context in [14, pages 270--273]. We give a simple, general definitio... |

69 | Scheduling for quality of service guarantees via service curves
- Cruz, Sariowan, et al.
- 1995
(Show Context)
Citation Context ...ample, the VBR trunk discussed in Section VI does not fit in that framework. A more general discussion of this point leads to the concept of service curve scheduling, which is defined and analyzed in =-=[26, 8]-=-. The restriction by IETF to rate latency curves is thus at the cost of loosing some flexibility. In practice, we use network calculus to compute bounds on delay variation and backlogs. Constant propa... |

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- 1998
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Citation Context ...networks with guaranteed service. In Section II we recall the main network calculus results we need in this paper. In Section III we give results on shapers. These results were found independently in =-=[10, 11]-=-. We also provide a simple proof that shaping a traffic stream to conform with a burstiness constraint preserves the original constraints satisfied by the traffic stream The Internet Engineering Task ... |

61 | Source time scale and optimal buffer/bandwidth tradeoff for regulated traffic in an ATM node
- LoPresti, Zhang, et al.
- 1997
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Citation Context ...ex sets is convex. Of course we have A ae C ffl for all ffl and thus A ae C. Ideally, we would like to have equality, but this may in general not be possible because A is usually strictly convex (see =-=[27]-=- for an example in the case of a call acceptance criterion based on a buffer requirement only). Thus, the limit of acceptance regions based on statistical multiplexing, as the loss probability tends t... |

50 |
Efficient Support of Delay and Rate Guarantees in an Internet
- Georgiadis, Guerin, et al.
- 1996
(Show Context)
Citation Context ...ger [1, 2] and Cruz [3, 4, 5], where general bounds based on the concepts of arrival and service curves are derived. Other fundamental work for specific or general scheduling policies is described in =-=[6, 7]-=-. Recently, this work has been extended and simplified independently and simultaneously under equivalent forms by Sariowan [8] who gives a formal and general treatment of the concepts of arrival and s... |

38 | Performance bounds for guaranteed and adaptive services,” presented at
- Agrawal, Rajan
- 1996
(Show Context)
Citation Context ...urve of fi 1\Omega fi 2 to the flow. In the next section we give a second family of results which we will need in this paper. III Shapers Most results on shapers were also discovered independently in =-=[8, 10, 11]-=-. A shaper, with shaping curve oe, is a bit processing device that forces its output to have oe as arrival curve, by delaying bits in a buffer whenever sending a bit would violate the constraint for t... |

23 |
A Service Curve Approach to Performance Guarantees in Integrated Service Networks
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- 1996
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Citation Context ...ental work for specific or general scheduling policies is described in [6, 7]. Recently, this work has been extended and simplified independently and simultaneously under equivalent forms by Sariowan =-=[8]-=- who gives a formal and general treatment of the concepts of arrival and service curves, two fundamental network calculus tools. The mathematics involved in network calculus uses min-plus algebra, as ... |

22 | Service guarantees for window flow control
- Cruz, Okino
- 1996
(Show Context)
Citation Context ...t algorithm for computing the optimal VBR trunk characteristics. II Background: Network Calculus In this section we recall a few definitions and results, which we collectively call "network calcu=-=lus" [18, 8, 11, 10, 19]. We consi-=-der wide-sense increasing functions of time, with non-negative, possibly infinite values (we say that function fl() is wide sense increasing , also called "non-decreasing", when fl(s)sfl(t) ... |

19 | generalized processor sharing approach to flow control-The multiple node case - “A - 1994 |

17 | calculus for network delay, part ii: Network analysis - “A - 1991 |

16 |
Bandwidth Management and Congestion Control Framework of the Broadband Network Architecture
- Gun, Guerin
- 1993
(Show Context)
Citation Context ...lity target tends to 0 may be strictly larger than the call acceptance region based on lossless multiplexing. We also define similarly the deterministic equivalent capacity, by analogy to the work in =-=[16]-=-. Thirdly, in Section VI (and this was our initial motivation), we consider a connection admission control (CAC) method, for the case where connections are admitted onto an Asynchronous Transfer Mode ... |

16 | Bandwidth scheduling for wide area ATM networks using virtual nishing times
- Hung, Kesidis
- 1996
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Citation Context ...duling includes as particular cases: virtual clock scheduling [23], packet by packet generalized processor sharing [1] and selfclocked fair queuing [22]. Essentially identical results can be found in =-=[24] using the-=- concept of "minimum bandwidth property". Following [13], we say that a scheduling policy is of the guaranteed rate type, with rate R and delay v for a given flow if it guarantees that packe... |

12 |
A Self-Clocked Fair Queuing Scheme for High Speed Applications
- Golestani
- 1994
(Show Context)
Citation Context ...d D are computed during reservation setup, with a protocol such as the Resource Reservation Protocol (RSVP) [21]. A number of scheduling policies have been proposed in the literature (see for example =-=[1, 7, 22, 23, 13]-=-). Consider the general form of scheduling proposed in [13] under the name of Guaranteed Rate (GR) scheduling. It is shown in [13] that Guaranteed Rate scheduling includes as particular cases: virtual... |

11 | A CAC algorithm for VBR Connections over a VBR Trunk - Boudec, Ziedins - 1997 |

7 | A Note on Time and Space Methods in Network calculus - Boudec, Thiran - 1998 |

6 | Boudec, \Network Calculus Made Easy - Le - 1996 |

5 | VBR over VBR: the homogeneous, loss-free case
- Giordano, Boudec, et al.
- 1997
(Show Context)
Citation Context ...ial motivation), we consider a connection admission control (CAC) method, for the case where connections are admitted onto an Asynchronous Transfer Mode (ATM) variable bit rate (VBR) trunk, or tunnel =-=[17]-=-. In such a case, the CAC method can be split into two subproblems: (1) predict the traffic for the next prediction period, and (2) given a predicted traffic, find the optimal VBR trunk parameters tha... |

2 |
Boudec Jean-Yves. Network calculus made easy
- Le
- 1996
(Show Context)
Citation Context ...t algorithm for computing the optimal VBR trunk characteristics. II Background: Network Calculus In this section we recall a few definitions and results, which we collectively call "network calcu=-=lus" [18, 8, 11, 10, 19]. We consi-=-der wide-sense increasing functions of time, with non-negative, possibly infinite values (we say that function fl() is wide sense increasing , also called "non-decreasing", when fl(s)sfl(t) ... |

2 |
Boudec J.-Y and Ziedins A. A CAC algorithm for VBR connections over a VBR trunk
- Le
- 1997
(Show Context)
Citation Context ... rather than constant bit rate trunks is advantageous in particular for trunks carrying medium amounts of traffic, that are thus best able to benefit from statistical multiplexing in a larger network =-=[28]-=-. More specifically, in this paper, we focus on one issue, namely, given a predicted traffic, find the optimal VBR trunk parameters that can carry the traffic. The same problem arises in prerecorded v... |

1 |
Boudec Jean-Yves and Thiran Patrick. A note on time and space methods in network calculus
- Le
- 1997
(Show Context)
Citation Context ...max-plus or min-plus algebra [9]. The theorem follows directly from Equation (5). An alternative proof is given in [19], which applies only to the discrete time case and is based on what is called in =-=[20]-=- the time method. A corollary follows. Consider a case where where re-shapers are introduced along a path. The shapers act as additional buffers, that could increase the end-to-end delay. However, we ... |

1 | Specification of guaranteed quality of service,” Aug - Shenker, Partridge, et al. - 1996 |