Hub location in backbone/tributary network design: a review
Introduction
A communications network consists of a set of nodes that transmit messages or information, in the form of voice, data and/or video, over communication links (e.g., copper cables, fiber-optic cables, radio links, or satellite links). A communication network may serve areas as small as a single building, but can also serve large geographic areas, and even span the globe. The uses of such networks include simple telephone calls, video teleconferences, packet data transmission, and distributed computer processing, among others.
Designing an efficient yet cost-effective network is a difficult problem, especially in the case of large scale networks with many nodes that share traffic. A common architecture for such networks, which has proved robust in practice, involves the use of hub nodes that can act as switching points for the communications traffic. A number of “tributary” networks connect the various nodes to the hubs. A “backbone” network then interconnects the hubs. Typically, “backbone” links carry larger volumes of traffic than tributary links. Traffic originating at a particular location can pass through a tributary network to get to a hub node. After passing through the backbone network, the traffic again uses a tributary network to travel from a hub to its destination at another location.
Depending on the context or application, hub nodes are called by various names including “switches”, “gates”, “concentrators”, “control points” or “access points”. Likewise, tributary networks are also called “local” or “access” networks. Backbone networks may sometimes be referred to by other names as well, such as “hub-level networks”.
Often, because of the size of the problem or the nature of the application, the design of the backbone network and the tributary networks are considered independently. However, in many cases, it is desirable or necessary to treat backbone and tributary design as an integrated problem. A key decision in the integrated problem is choosing the locations of the hubs. In communications, success is dependent on the timeliness, reliability and cost of transmission, which depend, among other things, on the number, placement and capacity of the hubs. Therefore, such hub location problems are important in communications applications.
A unified treatment of approaches to the integrated design of backbone and tributary networks has not been available, partly because of the specialized nature of many of the applications, and partly because the relevant references are dispersed among the facility location, network design, telecommunications, computer systems and transportation literatures. However, surveys of hub location articles in the facility location literature were provided by Campbell (1994a) and O'Kelly and Miller (1994). Campbell (1994a) also discusses a number of hub location articles in the communications literature. Skorin-Kapov and Skorin-Kapov (1995) likewise provide an overview of some recent work in hub location. More general surveys or texts on facility location and network design include Brandeau and Chiu, 1989, Daskin, 1995, Domschke and Krispin, 1997, Fotheringham and O'Kelly, 1989, Francis and Mirchandani, 1990, Hakimi and Schmeichel, 1997, Jaillet and Song, 1996, Lo, 1988, Tansel et al. (1983), and Wong (1985).
We note that existing taxonomies for hub location problems, such as Campbell (1994a) and O'Kelly and Miller (1994) have been derived primarily from the perspective of the facility location literature. In this review, we seek to broaden the range of problems and papers considered and to provide a classification or taxonomy based on the backbone/tributary paradigm that typically is used in communications networks.
Because of the complexity of these problems, backbone design and tributary design are often considered separately. For example, Gavish, 1987, Balakrishnan et al., 1991 and Balakrishnan et al. (1995) consider algorithms for tributary network design. There is also a considerable body of literature that addresses backbone network design, given a predetermined set of backbone nodes; see for example, Agarwal (1989), Altinkemer and Yu (1992), Balakrishnan and Altinkemer, 1992, Baybars and Edahl, 1988, Baybars and Kortanek, 1984, Chang and Gavish, 1993, and Gavish and Altinkemer (1990). A complete discussion of the issues related to backbone design is beyond the scope of this review.
In this review, we focus on problems in which the tributary and backbone networks are designed together and in which a decision regarding hub, or backbone node, location is a key part of the problem. We also focus on problems in which the hub locations must be chosen from among a discrete set of choices. Related problems in which hub locations are chosen from among a continuous set of points in the plane are beyond the scope of this review. Examples include Aykin, 1988, Aykin, 1995a, Aykin and Brown, 1992, Campbell, 1990, Fisher and Hochbaum, 1980 and O'Kelly (1986a). There are also papers that consider backbone/tributary networks, but where the hub locations are predetermined. The network issues that are considered in such papers include, for example: choice of network links (such as Altinkemer, 1994 for ring networks, and Powell, 1986 for motor carrier networks), routing of traffic (such as Leung et al., 1990), choice of transportation modes (O'Kelly and Lao, 1991), analysis of delays at the hubs (Grove and O'Kelly, 1986), assignment of tributary nodes to hubs (Aykin, 1990), and analysis of direct shipment versus shipment via the hubs (Garfinkel et al., 1996).
Another related body of work concerns the issue of locating databases in computer communications networks. Each user communicates with a copy of the database, and the copies then communicate with each other for the purposes of updating, etc. While not a hub location problem in the sense considered in this review, there can be similar tradeoffs involved. A sampling of references includes: Filho and Galvao, 1996, Grove and O'Kelly, 1986, Gavish, 1982, Gavish and Altinkemer, 1990, and Pirkul (1986). Likewise, researchers have considered models in which tasks must be allocated to various processors in a network. See, for example, Ben Hadj-Alouane et al., 1996, Dutta et al., 1982 and Lo (1988).
Although our motivation is the design of communications networks, we also mention in this review some papers that address a backbone/tributary network, but that are motivated by other applications. Because of the similarity in network structure, the algorithmic techniques that are employed in these other applications can potentially be carried over to applications in communications. Because the relevant body of literature is so extensive, an exhaustive review would be virtually impossible to compile. We have attempted, as far as possible, however, to select papers that best represent work in the area.
Section snippets
Backbone/tributary networks
Fig. 1 can be used to illustrate a backbone/tributary network. In this figure, A, B, C and D represent hub nodes. The thick lines interconnecting these hub nodes represent the backbone network. In this example, the backbone network is a fully interconnected network (i.e., each hub node is linked to every other hub node). If one or more of those backbone links were not present, (say, the link between A and C were missing) it would represent a “mesh” network. In a mesh network, traffic between
Decomposition approaches
A particular application would have associated with it one or more allowable backbone structures (fully interconnected, mesh, star, ring, etc.), one or more allowable tributary structures (star, tree, ring, etc.), and particular costs, capacity constraints, reliability requirements and performance requirements. Depending on the particular combination of problem elements, the resulting network optimization problem could be quite difficult. For large networks, a common approach has been to
Special cases
The most general network design problems still require ad hoc methods built around decomposition. Fortunately, however, there are particular cases that have proved more tractable, and which have attracted attention in the literature. These particular cases assume specific structures for the backbone and tributary networks, respectively, and, generally deal with limited sets of costs and constraints. Although, in some cases, the heuristics for these special cases can be presented in a way that
Future directions
As can be seen from the breadth and variety of models considered in Section 4, the backbone/tributary paradigm provides a quite general framework for hub location models. Given this breadth and variety, research on hub location is likely to continue to be pursued in a number of directions. In this final section, some research topics in hub location are suggested that are likely to be of interest in the future, from both applied and theoretical points of view.
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Ring networks: Because of the
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