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## Application of Network Calculus to General Topologies Using Turn-Prohibition (2002)

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Venue: | IEEE/ACM Transactions on Networking |

Citations: | 37 - 3 self |

### Citations

10623 | Introduction to Algorithms.
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Citation Context ... the last link of the path are the same, for instance, Note that the literature in graph theory typically defines a cycle as a path such that the first node and the last node in the path are the same =-=[9]-=-. We will refer to this latter definition as a cycle of nodes. Breaking all cycles of nodes is too strong a requirement for network calculus. For instance, referring to Fig. 1, the path (4, 1, 2, 4, 1... |

2215 | On the self-similar nature of Ethernet traffic (extended version).
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Citation Context ...s, termed stochastically bounded burstiness (SBB) calculus [24], [26] was developed in order to capture the multiple time scale and self-similar behavior of the traffic, as observed over the Internet =-=[17]-=-, [20], [27]. The SBB calculus provides general stochastic bounds at each node of a network. A central problem shared by all network calculi is of determining the conditions under which a network is s... |

2210 | Data Networks,
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- 1987
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Citation Context ... can be transmitted without saturating the network. Notice that flows that do not traverse the bottleneck link could in fact be transmitted at a higher rate. We may then resort to a max-min criterion =-=[2]-=-, or any other similar criteria, to determine the appropriate transmission rate for each flow. In such a case, our definition of throughput corresponds to the minimum possible rate allocated to any fl... |

2012 | A generalized processor sharing approach to flow control in integrated services networks: The multiplenode case.
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Citation Context ...ounds on various performance measures, such as delay and queue length, at each element of the network. A well-known network calculus is the calculus, first introduced in [10] and further developed in =-=[19]-=-, which provides deterministic bounds on delay and buffering requirements in a communication network. This model is useful for applications requiring deterministic QoS guarantees [22]. The network cal... |

1777 | Wide Area Traffic: the failure of Poisson modeling.
- Paxson, Floyd
- 1995
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Citation Context ...med stochastically bounded burstiness (SBB) calculus [24], [26] was developed in order to capture the multiple time scale and self-similar behavior of the traffic, as observed over the Internet [17], =-=[20]-=-, [27]. The SBB calculus provides general stochastic bounds at each node of a network. A central problem shared by all network calculi is of determining the conditions under which a network is stable,... |

667 | A calculus for network delay, Part I; network elements in isolation,” - Cruz - 1991 |

410 |
Network Calculus: A theory of deterministic queues for the Internet. Number 2050 in LNCS.
- Boudec, Thiran
- 2002
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Citation Context ...ks, network calculus, network stability, quality of service. I. INTRODUCTION NETWORK calculus is a general paradigm for the provi-sion of quality of service (QoS) in communication networks [6], [10], =-=[18]-=-. The main principle of network calculus is to show that if all the input flows to a network satisfy a certain set of constraints, then so do all the flows within the network. The formulation of the c... |

366 | A Calculus for Network Delay, Part II: Network Analysis. - Cruz - 1991 |

362 | The Turn Model for Adaptive Routing,"
- Glass, Ni
- 1994
(Show Context)
Citation Context .... 11, NO. 3, JUNE 2003 Instead, we propose to resort to a more sophisticated approach based on the prohibition of turns. Here, a turn is defined as a specific pair of input–output links around a node =-=[12]-=-. The main claim is that in order to break all the cycles in a network, it is sufficient to prohibit a set of turns instead of a set of links, as is the case with spanning trees (a turn around some no... |

295 | Performance Guarantees in Communication Networks. - Chang - 2000 |

231 | Stability, queue length and delay of deterministic and stochastic queueing networks,”
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Citation Context ... the Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ 07102 USA (e-mail: zakr@adm.njit.edu). Publisher Item Identifier 10.1109/TNET.2003.813040. (MER) =-=[5]-=- and exponentially bounded burstiness (EBB) [28] network calculi provide exponential bounds on various metrics of interest. More recently, a network calculus, termed stochastically bounded burstiness ... |

150 | Performance and stability of communication networks via robust exponential bounds.
- Yaron, Sidi
- 1993
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Citation Context ...neering, New Jersey Institute of Technology, Newark, NJ 07102 USA (e-mail: zakr@adm.njit.edu). Publisher Item Identifier 10.1109/TNET.2003.813040. (MER) [5] and exponentially bounded burstiness (EBB) =-=[28]-=- network calculi provide exponential bounds on various metrics of interest. More recently, a network calculus, termed stochastically bounded burstiness (SBB) calculus [24], [26] was developed in order... |

127 | Admission control for Statistical QoS: Theory and Practice”, In
- Knightly, &Shroff
- 1999
(Show Context)
Citation Context ...ng requirements in a communication network. This model is useful for applications requiring deterministic QoS guarantees [22]. The network calculus framework applies also to statistical services [4], =-=[15]-=-. In particular, the minimum envelop rate Manuscript received January 22, 2002; revised July 22, 2002; approved by IEEE/ACM TRANSACTIONS ON NETWORKING Editor N. Shroff. The work of the first author wa... |

118 |
An Architecture for Differentiated Services. Internet Engineering Task Force,
- Blake, Black, et al.
- 1998
(Show Context)
Citation Context ...alculus to feedforward routing networks may not represent a significant limitation, rendering this framework particularly appealing for implementation in practical QoS architectures, such as DiffServ =-=[3]-=-, [7]. We conclude this paper by noting that the TP-algorithm represents a universal method for breaking cycles, and, as such, can potentially improve the performance of many other networking applicat... |

77 | Statistical Service Assurances for Traffic Scheduling Algorithms.
- Boorstyn, Burchard, et al.
- 2000
(Show Context)
Citation Context ...ffering requirements in a communication network. This model is useful for applications requiring deterministic QoS guarantees [22]. The network calculus framework applies also to statistical services =-=[4]-=-, [15]. In particular, the minimum envelop rate Manuscript received January 22, 2002; revised July 22, 2002; approved by IEEE/ACM TRANSACTIONS ON NETWORKING Editor N. Shroff. The work of the first aut... |

76 | Stochastically bounded burstiness for communication networks.
- Starobinski, Sidi
- 2000
(Show Context)
Citation Context ...unded burstiness (EBB) [28] network calculi provide exponential bounds on various metrics of interest. More recently, a network calculus, termed stochastically bounded burstiness (SBB) calculus [24], =-=[26]-=- was developed in order to capture the multiple time scale and self-similar behavior of the traffic, as observed over the Internet [17], [20], [27]. The SBB calculus provides general stochastic bounds... |

67 |
Boudec. Delay bounds in a network with aggregate scheduling
- Charny, Le
- 2000
(Show Context)
Citation Context ...n networks of first-in-first-out (FIFO) queues with sessions may be unstable [1]. It is worth noting that an upper bound on the delay in arbitrary nonfeedforward networks has recently been derived in =-=[7]-=-. Unfortunately, this bound is useful only for very small link utilization. Specifically, the maximum achievable link utilization is inversely proportional to the maximum route length of any flow in t... |

49 |
Specification of Guaranteed Quality of Service. Internet draft-ietf-intserv-guaranteed-svc06.txt, work in progress
- Shenker, Partridge, et al.
- 1996
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Citation Context ...her developed in [19], which provides deterministic bounds on delay and buffering requirements in a communication network. This model is useful for applications requiring deterministic QoS guarantees =-=[22]-=-. The network calculus framework applies also to statistical services [4], [15]. In particular, the minimum envelop rate Manuscript received January 22, 2002; revised July 22, 2002; approved by IEEE/A... |

33 | An architecture for differentiated services. IETF RFC-2475. - Blake, Black, et al. - 1998 |

30 |
Instability of FIFO in session-oriented networks
- Andrews
- 1996
(Show Context)
Citation Context ...networks, it is no longer sufficient. A number of examples given in [16] illustrate this fact. Recent results show that even networks of first-in-first-out (FIFO) queues with sessions may be unstable =-=[1]-=-. It is worth noting that an upper bound on the delay in arbitrary nonfeedforward networks has recently been derived in [7]. Unfortunately, this bound is useful only for very small link utilization. S... |

22 | Modeling and Analysis of Power-Tail Distributions via Classical Teletrac Methods - Starobinski, Sidi - 2000 |

14 |
A calculus for network delay—Part I: Network elements in isolation
- Cruz
- 1991
(Show Context)
Citation Context ...networks, network calculus, network stability, quality of service. I. INTRODUCTION NETWORK calculus is a general paradigm for the provi-sion of quality of service (QoS) in communication networks [6], =-=[10]-=-, [18]. The main principle of network calculus is to show that if all the input flows to a network satisfy a certain set of constraints, then so do all the flows within the network. The formulation of... |

10 | Prevention of deadlocks and livelocks in lossless backpressured packet networks.
- Karol, Golestani, et al.
- 2003
(Show Context)
Citation Context ...orking applications. In particular, it has the potential of significantly improving the performance of LANs, such as Gigabit Ethernet, where packet-forwarding loops and deadlocks need to be prevented =-=[14]-=-, [25]. These networks currently implement the simple spanning-tree algorithm [21]. It can also be useful for preventing the appearance of deadlocks in wormhole routing networks, such as networks of w... |

9 |
A new method for deadlock elimination in computer networks with irregular topologies
- Zakrevski, Jaiswal, et al.
(Show Context)
Citation Context ...e networks currently implement the simple spanning-tree algorithm [21]. It can also be useful for preventing the appearance of deadlocks in wormhole routing networks, such as networks of workstations =-=[30]-=-, [31]. These examples illustrate the general problematic nature of cycles in networks and the promise of turn-prohibition to provide a unifying solution methodology. APPENDIX A Theorem 7: For any net... |

8 |
Interconnections Second Edition
- Perlman
- 2000
(Show Context)
Citation Context ...ork topology, unlike the spanning tree and up/down spanning tree algorithms. Nevertheless, the TP-algorithm can still be implemented in a decentralized fashion as a link-state algorithm, such as OSPF =-=[21]-=-. 4) Routing: A set of prohibited turns constructed by the TP-algorithm does not completely specify the routing strategy since several valid routes may exist between any source/destination pair (the c... |

7 | A tutorial on some new methods for performance evaluation of queueing networks
- Kumar
- 1995
(Show Context)
Citation Context ...icated, with only a few notable exceptions (e.g., [19]). While the throughput condition remains necessary for the stability of such networks, it is no longer sufficient. A number of examples given in =-=[16]-=- illustrate this fact. Recent results show that even networks of first-in-first-out (FIFO) queues with sessions may be unstable [1]. It is worth noting that an upper bound on the delay in arbitrary no... |

6 |
calculus for network delay—Part II: Network analysis
- “A
- 1991
(Show Context)
Citation Context ...all network calculi is of determining the conditions under which a network is stable, meaning that the queue length at each element of the network is bounded according to some appropriate metric [5], =-=[11]-=-. It turns out that network stability is easy to establish only for feedforward routing networks, i.e., networks where routes do not create cycles of interdependent packet flows. Such networks are sta... |

5 | Specification of Guaranteed Quality of Service,” IETF Request for Comments: 2212 - Shenker, Partridge, et al. - 1997 |

5 | Quality of Service in High Speed Networks with Multiple Time-Scale Traffic
- Starobinski
- 1999
(Show Context)
Citation Context ...lly bounded burstiness (EBB) [28] network calculi provide exponential bounds on various metrics of interest. More recently, a network calculus, termed stochastically bounded burstiness (SBB) calculus =-=[24]-=-, [26] was developed in order to capture the multiple time scale and self-similar behavior of the traffic, as observed over the Internet [17], [20], [27]. The SBB calculus provides general stochastic ... |

5 |
Traffic characteristics of the T1
- Claffy, Polyzos, et al.
- 1993
(Show Context)
Citation Context ... node of minimal degree, the generalized algorithm will select a node with minimum weight (excluding the special node, if there is such one). For instance, in Fig. 10 (inspired by the NSFNET topology =-=[8]-=-), node NE with weight is first selected. Next, node CO with weight is selected (recall that the links incident to node NE have been deleted in the previous step). The procedure continues until all th... |

5 |
Turn prohibition based routing in irregular computer networks
- Zakrevski, Mustafa, et al.
- 1999
(Show Context)
Citation Context ...orks currently implement the simple spanning-tree algorithm [21]. It can also be useful for preventing the appearance of deadlocks in wormhole routing networks, such as networks of workstations [30], =-=[31]-=-. These examples illustrate the general problematic nature of cycles in networks and the promise of turn-prohibition to provide a unifying solution methodology. APPENDIX A Theorem 7: For any network, ... |

3 |
et al., Autonet: a high-speed, self-configuring local area network using point-to-point links
- Shoreder
- 1991
(Show Context)
Citation Context ...is not the first algorithm based on the concept of turn-prohibition. In particular, the up/down routing scheme, developed in the context of a local area network called Autonet, uses a similar concept =-=[23]-=-. However, this scheme does not systematically attempt at minimizing the amount of prohibited turns in the network and its performance is much less predictable. In particular, we show in the sequel th... |

3 |
Fault-tolerant wormhole message routing in computer/communication networks
- Zakrevski
- 2001
(Show Context)
Citation Context ...f this link, as long as packets arrive from a predetermined set of input links. In this paper, we introduce a novel algorithm using this approach, called the turn-prohibition algorithm (TP-algorithm) =-=[29]-=-. This algorithm ensures that all the cycles in a network are broken, while maintaining global connectivity. Moreover, for any network topology, it never prohibits more than 1/3 of the total number of... |

2 |
Turn prohibition–based packet forwarding in gigabit ethernets, in: Gigabit Networking Workshop
- Starobinski, Karpovsky
- 2001
(Show Context)
Citation Context ... applications. In particular, it has the potential of significantly improving the performance of LANs, such as Gigabit Ethernet, where packet-forwarding loops and deadlocks need to be prevented [14], =-=[25]-=-. These networks currently implement the simple spanning-tree algorithm [21]. It can also be useful for preventing the appearance of deadlocks in wormhole routing networks, such as networks of worksta... |

2 |
Unicast wormhole message routing in irregular computer networks
- Jaiswal, Mustafa, et al.
(Show Context)
Citation Context ...ny source and destination, while forwarding packets only over permitted turns. It turns out that the traditional Bellman–Ford routing algorithm can easily be generalized in order to perform this task =-=[13]-=-, [29]. The only difference with respect to the original Bellman–Ford algorithm is that updates are now forwarded only over permitted turns. The memory required by this algorithm is on the order of , ... |

1 | Instability of FIFO - Andrews - 2000 |

1 | Unicast Wormhole Message Routing - Jaiswal, Mustafa, et al. |

1 | Prevention of Deadlocks and Livelocks - Karol, Golestani, et al. |

1 | Fault-Tolerant Wormhole Message Routing - Zakrevski - 2001 |

1 | Turn Prohibition Based Routing - Zakrevski, Mustafa, et al. |