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84
How to Model an Internetwork
 In Proceedings of IEEE INFOCOM
, 1996
"... Graphs are commonly used to model the structure of internetworks, for the study of problems ranging from routing to resource reservation. A variety of graph models are found in the literature, including regular topologies such as rings or stars, "wellknown" topologies such as the original ARPAnet, ..."
Abstract

Cited by 676 (8 self)
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Graphs are commonly used to model the structure of internetworks, for the study of problems ranging from routing to resource reservation. A variety of graph models are found in the literature, including regular topologies such as rings or stars, "wellknown" topologies such as the original ARPAnet, and randomly generated topologies. Less common is any discussion of how closely these models correlate with real network topologies. We consider the problem of efficiently generating graph models that accurately reflect the topological properties of real internetworks. We compare properties of graphs generated using various methods with those of real internets. We also propose efficient methods for generating topologies with particular properties, including a TransitStub model that correlates well with Internet structure. Improved models for internetwork structure have the potential to impact the significance of simulation studies of internetworking solutions, providing basis for the validi...
An Architecture for WideArea Multicast Routing
"... Existing multicast routing mechanisms were intended for use within regions where a group is widely represented or bandwidth is universally plentiful. When group members, and senders to those group members, are distributed sparsely across a wide area, these schemes are not efficient; data packets or ..."
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Cited by 484 (21 self)
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Existing multicast routing mechanisms were intended for use within regions where a group is widely represented or bandwidth is universally plentiful. When group members, and senders to those group members, are distributed sparsely across a wide area, these schemes are not efficient; data packets or membership report information are occasionally sent over many links that do not lead to receivers or senders, respectively. Wehave developed a multicast routing architecture that efficiently establishes distribution trees across wide area internets, where many groups will be sparsely represented. Efficiency is measured in terms of the state, control message processing, and data packet processing, required across the entire network in order to deliver data packets to the members of the group. Our Protocol Independent Multicast (PIM) architecture: (a) maintains the traditional IP multicast service model of receiverinitiated membership; (b) can be configured to adapt to different multicast group and network characteristics; (c) is not dependent on a specific unicast routing protocol; and (d) uses softstate mechanisms to adapt to underlying network conditions and group dynamics. The robustness, flexibility, and scaling properties of this architecture make it well suited to large heterogeneous internetworks.
A quantitative comparison of graphbased models for internet topology
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1997
"... Graphs are commonly used to model the topological structure of internetworks, to study problems ranging from routing to resource reservation. A variety of graphs are found in the literature, including fixed topologies such as rings or stars, "wellknown" topologies such as the ARPAnet, and randomly ..."
Abstract

Cited by 223 (3 self)
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Graphs are commonly used to model the topological structure of internetworks, to study problems ranging from routing to resource reservation. A variety of graphs are found in the literature, including fixed topologies such as rings or stars, "wellknown" topologies such as the ARPAnet, and randomly generated topologies. While many researchers rely upon graphs for analytic and simulation studies, there has been little analysis of the implications of using a particular model, or how the graph generation method may a ect the results of such studies. Further, the selection of one generation method over another is often arbitrary, since the differences and similarities between methods are not well understood. This paper considers the problem of generating and selecting graph models that reflect the properties of real internetworks. We review generation methods in common use, and also propose several new methods. We consider a set of metrics that characterize the graphs produced by a method, and we quantify similarities and differences amongst several generation methods with respect to these metrics. We also consider the effect of the graph model in the context of a speciffic problem, namely multicast routing.
The Tradeoffs of Multicast Trees and Algorithms
, 1994
"... Multicast trees can be shared across sources (shared trees) or may be sourcespecific (shortest path trees). Inspired by recent interests in using shared trees for interdomain multicasting, we investigate the tradeoffs among shared tree types and source specific shortest path trees, by comparing pe ..."
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Cited by 122 (6 self)
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Multicast trees can be shared across sources (shared trees) or may be sourcespecific (shortest path trees). Inspired by recent interests in using shared trees for interdomain multicasting, we investigate the tradeoffs among shared tree types and source specific shortest path trees, by comparing performance over both individual multicast group and the whole network. The performance is evaluated in terms of path length, link cost, and traffic concentration. We present simulation results over a real network as well as random networks under different circumstances. One practically significant conclusion is that member or sendercentered trees have good delay and cost properties on average, but they exhibit heavier traffic concentration which makes them inappropriate as the universal form of trees for all types of applications. Keywords: Multicast, Routing, Scalability, Center Placement Strategy 1 Introduction Multimedia communication is often multipoint and has contributed to the dem...
Evaluation of multicast routing algorithms for realtime communication on highspeed networks
 IEEE Journal on Selected Areas in Communications
, 1997
"... Multicast (MC) routing algorithms capable of satisfying the quality of service (QoS) requirements of realtime applications will be essential for future highspeed networks. We compare the performance of all of the important MC routing algorithms when applied to networks with asymmetric link loads. ..."
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Cited by 78 (4 self)
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Multicast (MC) routing algorithms capable of satisfying the quality of service (QoS) requirements of realtime applications will be essential for future highspeed networks. We compare the performance of all of the important MC routing algorithms when applied to networks with asymmetric link loads. Each algorithm is judged based on the quality of the MC trees it generates and its efficiency in managing the network resources. Simulation results over random networks show that unconstrained algorithms are not capable of fulfilling the QoS requirements of realtime applications in widearea networks. Simulations also reveal that one of the unconstrained algorithms, reverse path multicasting (RPM), is quite inefficient when applied to asymmetric networks. We study how combining routing with resource reservation and admission control improves RPM’s efficiency in managing the network resources. The performance of one semiconstrained heuristic, MSC, three constrained Steiner tree (CST) heuristics, KPP, CAO, and BSMA, and one constrained shortest path tree (CSPT) heuristic, CDKS are also studied. Simulations show that the semiconstrained and constrained heuristics are capable of successfully constructing MC trees which satisfy the QoS requirements of realtime traffic. However, the cost performance of the heuristics varies. BSMA’s MC trees are lower in cost than all other constrained heuristics. Finally, we compare the execution times of all algorithms, unconstrained, semiconstrained, and constrained.
The design and evaluation of routing algorithms for realtime channels
, 1994
"... The Tenet Scheme specifies a realtime communication service that guarantees performance through network connections with reserved resources, admission control, and rate control. Within this framework, we develop and evaluate algorithms that find routes for these multicast connections. The main goal ..."
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Cited by 77 (0 self)
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The Tenet Scheme specifies a realtime communication service that guarantees performance through network connections with reserved resources, admission control, and rate control. Within this framework, we develop and evaluate algorithms that find routes for these multicast connections. The main goals are to maximize the probability of successful establishment of the routed connection, to maximize the useful utilization of the network, and to be timely. The primary problem to be solved is finding a minimum cost tree where each source to destination path is constrained by a delay bound. This problem is NPcomplete, so heuristics based mainly on minimum incremental cost are developed. Algorithms we develop use those heuristics to calculate minimum cost paths that are then merged into a tree. We evaluate our design decisions through simulation, measuring success through the number of successfully established connections. These experiments demonstrate that our evaluation methodology is a useful tool The growing speed of widearea networks has spawned much interest in new kinds of communicationbased applications, which require more predictable performance from the network. The Tenet
Pricing Multicast Communication: A CostBased Approach
 Telecommunication Systems
, 2001
"... Multicast and unicast traffic share and compete for network resources. A costbased approach to multicast pricing, based on accurate characterization of multicast scalability, will facilitate the efficient and equitable resource allocation between traffic types. Through the quantification of link us ..."
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Cited by 72 (0 self)
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Multicast and unicast traffic share and compete for network resources. A costbased approach to multicast pricing, based on accurate characterization of multicast scalability, will facilitate the efficient and equitable resource allocation between traffic types. Through the quantification of link usage, this paper establishes a multicast scaling relationship: the cost of a multicast distribution tree varies at the 0.8 power of the multicast group size. This result is validated with both real and generated networks, and is robust across topological styles and network sizes. Since multicast cost can be accurately predicted given the membership size, there is strong motivation to price multicast according to membership size. Furthermore, a price ceiling should be set to account for the effect of tree saturation. This tariff structure is superior to either a purely membershipbased or a flatrate pricing scheme, since it reflects the actual tree cost at all group membership levels. Keywords: multicast pricing, multicast scaling 1.
QoSMIC: Quality of Service sensitive Multicast Internet protoCol
, 1998
"... In this paper, we present, QoSMIC, a multicast protocol for the Internet that supports QoSsensitive routing, and minimizes the importance of a priori configuration decisions (such ascore selection). The protocol is resourceefficient, robust, exible, and scalable. In addition, our protocol is prova ..."
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Cited by 65 (3 self)
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In this paper, we present, QoSMIC, a multicast protocol for the Internet that supports QoSsensitive routing, and minimizes the importance of a priori configuration decisions (such ascore selection). The protocol is resourceefficient, robust, exible, and scalable. In addition, our protocol is provably loopfree. Our protocol starts with a resourcessaving tree (Shared Tree) and individual receivers switch to a QoScompetitive tree (SourceBased Tree) when necessary. In both trees, the new destination is able to choose the most promising among several paths. An innovation is that we use dynamic routing information without relying on a link state exchange protocol to provide it. Our protocol limits the effect of preconfiguration decisions drastically, by separating the management from the data transfer functions; administrative routers are not necessarily part of the tree. This separation increases the robustness, and flexibility of the protocol. Furthermore, QoSMIC is able to adapt dynamically to the conditions of the network. The QoSMIC protocol introduces several new ideas that make it more exible than other protocols proposed to date. In fact, many of the other protocols, (such asYAM, PIMSM, BGMP, CBT) can be seen as special cases of QoSMIC. This paper presents the motivation behind, and the design of QoSMIC, and provides both analytical and experimental results to support our claims.
CostDistance: Two Metric Network Design
 In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science
, 2000
"... Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the numbe ..."
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Cited by 61 (7 self)
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Abstract We present the CostDistance problem: finding a Steiner tree which optimizes the sum of edge costs along one metric and the sum of sourcesink distances along an unrelated second metric. We give the first known O(log k) randomized approximation scheme for CostDistance, where k is the number of sources. We reduce many common network design problems to CostDistance, obtaining (in some cases) the first known logarithmic approximation for them. These problems include singlesink buyatbulk with variable pipe types between different sets of nodes, facility location with buyatbulk type costs on edges, and maybecast with combind cost and distance metrics. Our algorithm is also the algorithm of choice for several previous network design problems, due to its ease of implementation and fast running time. 1 Introduction Consider designing a network from the ground up. We are given a set of customers, and need to place various servers and network links in order to cheaply provide sufficient service. If we only need to place the servers, this becomes the facility location problem and constantapproximations are known. If a single server handles all customers, and we impose the additional constraint that the set of available network link types is the same for every pair of nodes (subject to constant scaling factors on cost) then this is the single sink buyatbulk problem. We give the first known approximation for the general version of this problem with both servers and network links. We reduce the network design problem to an elegant theoretical framework: the CostDistance problem. We are given a graph with a single distinguished sink node (server). Every edge in this graph can be measured along two metrics; the first will be called cost and the second will be length. Note that the two metrics are entirely independent, and that there may be any number of parallel edges in the graph. We are given a set of sources (customers). Our objective is to construct a Steiner tree connecting the sources to the sink while minimizing the combined sum of the cost of the edges in the tree and sum over sources of the weighted length from source to sink.
ARIES: A Rearrangeable Inexpensive Edgebased Online Steiner Algorithm
 IEEE Journal of Selected Areas in Communications
, 1995
"... In this paper, we propose and evaluate ARIES, a heuristic for updating multicast trees dynamically in large pointtopoint networks. The algorithm is based on monitoring the accumulated damage to the multicast tree within local regions of the tree as nodes are added and deleted, and triggering a rea ..."
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Cited by 53 (1 self)
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In this paper, we propose and evaluate ARIES, a heuristic for updating multicast trees dynamically in large pointtopoint networks. The algorithm is based on monitoring the accumulated damage to the multicast tree within local regions of the tree as nodes are added and deleted, and triggering a rearrangement when the number of changes within a connected subtree crosses a set threshold. We derive an analytical upperbound on the competitiveness of the algorithm. We also present simulation results to compare the averagecase performance of the algorithm with two other known algorithms for the dynamic multicast problem, GREEDY and EBA (EdgeBounded Algorithm). Our results show that ARIES provides the best balance among competitiveness, computational effort, and changes in the multicast tree after each update. Keywords: multicast algorithms, online Steiner problem, rearrangeable multicast algorithms. 1 Introduction Many future applications of computer networks such as distance educati...