Elsevier

Computer Networks

Volume 53, Issue 7, 13 May 2009, Pages 913-925
Computer Networks

On graph-based characteristics of optimal overlay topologies

https://doi.org/10.1016/j.comnet.2008.11.018Get rights and content

Abstract

In this paper, we address the challenge of overlay topology design by considering which overlay topology best minimizes cost function, taking into account overlay link creation cost and routing cost. First, we formulate the problem as Integer Linear Programming (ILP) given a traffic matrix and assuming cooperative behavior of nodes. Then, we propose some heuristics to find near-optimal overlay topologies with a reduced complexity. The solutions to the ILP problem on real network topologies have been analyzed, showing that the traffic demands between the nodes affect the decision to create new overlay links. Next, the obtained optimal and near-optimal overlay topologies are thoroughly analyzed and the heuristics are compared through extensive numerical evaluations. Finally guidelines for the selection of the best heuristic as a function of the cost parameters are also provided.

Introduction

Peer-to-peer and many multimedia applications have recently grown, necessitating high Quality of Service (QoS) [1], [2], [3], [4], [5], [6]. Providing the required quality of service for these applications over a packet switching network has been a critical task for a long time. A recent approach to providing QoS without changing the network architecture is based on the overlay network, an application-layer logical network created on top of the physical network. It is formed by all, or a subset, of the underlying physical nodes. The connection between each pair of overlay nodes is provided by overlay links, which consist of paths composed of underlying physical links. Overlay networks can improve performance and provide quality of service on the IP network by routing data on the overlay links based on performance measurements. Among the most interesting open problems in overlay network design is topology creation such as node location and link setup.

In overlay topology, node behavior can be either selfish or cooperative. In the cooperative mode of operation, each node creates overlay links to send its traffic demands and to allow other nodes to route their traffic demands over them, while in the selfish mode of operation, nodes create overlay links in the network to maximize their own benefits. Consequently, the global overlay network obtained by selfish nodes can be different from the global overlay network that could be created if the nodes behaved in a cooperative way to maximize common benefits. This difference is often called the cost of Anarchy. Selfish and cooperative behaviors of the nodes in the networks have a great impact on the selection of the topology and its cost. In [7], nodes operate selfishly and create overlay links to minimize a cost function which is proportional to the number of created overlay links and the obtained reduction in the delay or the distance. However, the cost function used in [7] does not consider the demand volume between nodes as an important factor. Instead, we believe that when considering traffic demands, we can obtain topologies that have better characteristics with respect to some keys graph-theoretic metrics introduced in [8], such as node degree distributions, diameter, and clustering coefficient. In [9], the authors consider the static and the dynamic overlay topology design problems. The static overlay topology design is applied when there are no changes in the traffic requirements. In case the communication requirements change over time, the authors consider the dynamic overlay topology design based on two cost components: occupancy cost and reconfiguration cost. However, this approach is suited for service overlay networks, where an overlay service provider designs the overlay network. The authors in [10] address many topics concerning selfish routing in Internet-like environments. They use the fully connected overlay topology to limit the parameter space and to reduce the complexity of the problem. They study the performance of selfish overlay routing when all the network nodes are included in the overlay network. Notably, routing constraints are shown to have little effect on the network-wide cost when varying network load. In [11], the authors show the effect of traffic demands on the overlay topology given different demand scenarios. They consider a fully connected underlay topology over which the overlay topology was built. However, some of the obtained overlay topologies are not resilient to targeted node failures or attacks. Resilient Overlay Network (RON) [12] was proposed to increase the performance of the network in case of a link failure. RON routes packets based on minimizing routing cost function. Also, the construction of a resilient service overlay network (SON) under path failure in the physical network and under performance degradation has been studied in [13]. The authors concluded that the performance of overlay routing service depends heavily on the construction of overlay topologies. However, they did not mention the effect of the traffic demands on the performance of an overlay routing service. In our previous work [14], we studied the creation of optimal overlay topologies taking into account homogeneous and randomly uniform traffic demands in the network. Consequently, the resulting optimal overlay topologies are different from the regular topologies obtained when neglecting traffic demands among nodes.

In the literature, the creation of virtual networks has been proposed for various network technologies. For example, in optical networks, virtual links are created to enhance the utilization of the ample bandwidth. In [15], the authors addressed the limitation of the available throughput because of the low processing speed of electronic devices at the switching nodes in the network. Instead, they proposed the Lightnet, which is a virtual topology in the wavelength domain created on top of the optical network. Light-paths are used to create the virtual links in Lightnet. The authors found that a regular virtual topology established on irregular underlay networks, offers high performance.

In [16], the concept of the light-tree is introduced to decrease the hop distance by increasing the logical connectivity on the optical network. A light-tree is a point-to multipoint communication scheme and is a generalization for a light-path, which is an optical point-to-point communication. The problem of creating a light-tree is formulated as an optimization problem with the objective of minimizing the average number of packet hops in the network and the number of transceivers used in the WDM network.

Many heuristics and algorithms exist to solve the incapacitated network design problem or fixed charge network design problem in the operations research literature. For example, some papers and books, included in the literature but not limited to [17], [18], [19], [20], [21], presented heuristics to solve this problem. Some heuristics are based on generating valid inequalities for the problem to decrease the complexity, other heuristics generate generic lower and upper bounds, while other heuristics linearize nonlinear constraints that may exist in the problem. Those methods are generally based on centralized optimal design problem.

The goal of this paper is to study the problem of designing effective optimal overlay topology taking into account traffic demands and to analyze the characteristics of the obtained optimal and near-optimal overlay topologies to provide simple guidelines for overlay topology design.

In this paper, we consider the problem of finding the overlay topology that minimizes a cost function which is given by the weighted sum of the overlay link creation cost and the transport cost. The link creation cost is proportional to the number of hops composing the path between overlay neighbors in the underlay network, while the transport cost is proportional to the traffic demand. First, we formulate the problem as Integer Linear Programming (ILP) for a given traffic matrix in case of cooperative behavior of nodes. Each node creates overlay links to send its traffic demands and to allow other nodes to route their traffic demands over them. The assumption of selfish node behavior avoids transit traffic being routed on newly created overlay links. We have studied the selfish behavior of nodes in [14] while in this paper we concentrated on the cooperative behavior, which represents a more realistic scenario for many applications. Obviously, construction of overlay topologies when the nodes are cooperative is complex because each node should minimize not only its own cost but also the social cost of the network. Consequently, cooperative behavior implies the formulation of the global optimum while the selfish node implies the formulation of multiple optimization problems, one for each source node.

The solutions were analyzed for realistic network topologies, showing that the traffic demands between the nodes affects the decision to create new overlay links, and the resulting optimal topologies are different from the regular topologies obtained when neglecting traffic demands. Furthermore, two heuristics were proposed to find near-optimal overlay topologies with a reduced complexity. Each heuristic is based on the selection of the best destination toward which to build an overlay link. The first heuristic is based on the comparison between the overlay link creation cost and the transport cost. The second heuristic is based on the Dijkstra algorithm given for a full mesh overlay topology with weighted links. The link weight is a function of the traffic demand, overlay cost coefficient, and the shortest path on the overlay network.

Extensive testing and simulations were performed on the heuristics to compare the generated topologies with the optimal ones. Guidelines for the selection of the best heuristic among the set of the proposed ones, as a function of the cost weight, were then determined. In summary, our research contributions follow:

  • (i)

    Formulate the problem of establishing new overlay links in the network using ILP.

  • (ii)

    Propose two heuristics to generate near-optimal overlay topology.

  • (iii)

    Characterize the obtained optimal and near-optimal overlay topologies.

  • (iv)

    Investigate the effect of traffic demands on the creation of overlay topologies.

  • (v)

    Study the effect of the underlay topology on the overlay topologies.

In Section 2, we define the cost function and the ILP formulation of the optimal overlay network topology. In Section 3, we present the proposed heuristics. Section 4 thoroughly discusses the underlay networks’ characteristics, some topological characteristics, and the traffic demand model. In Section 5, we show and explain the results of both the ILP problem formulation and the proposed heuristics. Finally, we conclude and discuss some directions for future work in Section 6.

Section snippets

Problem formulation

Overlay networks are created at the application-layer, over a given physical network. Specifically, overlay network nodes select their neighbors and establish direct overlay links creating an overlay topology. Let Gu=(N,E) be the graph representing the underlay, or physical network and G=(N,L) be the graph representing the overlay network. We have assumed that the same set of nodes N are in both the overlay and physical networks, while the set of overlay links can be different from the set of

Proposed heuristics

In this section, we introduce two heuristics based on a greedy approach and the Dijkstra algorithm to generate near-optimal overlay topologies.

Underlay networks

The ILP formulations and the heuristics were applied to a 24-node network representing a US nation-wide IP backbone network topology [24], a 35-node, and a 112-node Rocketfuel network topology [25]. The characteristics of each underlay network are shown in Table 2.

Topology characteristics

Topology metrics are required to characterize any large topology in terms of connectivity, local and global robustness, and node reachability [26], [27], [28]. Accordingly, we selected the following subset of metrics to analyze the

Results and discussion

The ILP formulation, which provides optimal overlay topologies and the heuristics, were applied to the network topologies discussed in Section 4. Extensive testing and simulations were done on the heuristics to compare the generated topologies with the optimal ones. The generated topologies were thoroughly analyzed to understand the effect of the traffic demands, overlay cost coefficient and the underlay topology on the created overlay topology.

The main changed parameter in the analysis is the

Conclusion and future work

The objective of this paper was to find the optimal overlay network topology considering both the transport cost and the overlay link creation cost. We formulated the problem using the Integer Linear Programming for the cooperative behavior of nodes. In addition, we proposed two heuristics to generate near-optimal topologies when the problem size increases. The heuristics were based on the structure of the selected cost function. We considered bimodal traffic demands, which simulate a high

Acknowledgements

The authors would like to thank Prof. Jennifer Rexford and Mr. Benjamin McBride for the helpful comments and discussion.

Mina Youssef received the B.Sc. degree in Electrical and Electronics Engineering Department from Alexandria University, Egypt in May 2004 and the M.S. degree in electrical and computer engineering from Kansas State University in December 2007. Mina is currently a PhD student and a Research Assistant in Electrical and computer Engineering at Kansas State University. He is a member of the Sunflower Networking Group. His research interests are in the area of overlay networks, optical networks,

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    Mina Youssef received the B.Sc. degree in Electrical and Electronics Engineering Department from Alexandria University, Egypt in May 2004 and the M.S. degree in electrical and computer engineering from Kansas State University in December 2007. Mina is currently a PhD student and a Research Assistant in Electrical and computer Engineering at Kansas State University. He is a member of the Sunflower Networking Group. His research interests are in the area of overlay networks, optical networks, traffic matrix estimation and complex networks.

    Caterina Scoglio is currently an Associate Professor in the Department of Electrical and Computer Engineering at Kansas State University. She received the Dr. Eng. degree in Electronics Engineering from the University of Rome “La Sapienza” , Italy in 87. She had been with Fondazione Ugo Bordoni, Roma, where she was a research scientist at the TLC Network Department – Network Planning Group. She had been with the “Broadband and Wireless Networking Laboratory” of the Georgia Institute of Technology as a Research Engineer. She is co-director of the “Sunflower Networking Group” SNG at Kansas State University. Her research interests include Overlay and Virtual Networks, Future Internet Design and Management, Modeling and Control of Epidemics, Network Measurements.

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