Innovative Applications of O.R. A model for the capacitated, hop-constrained, per-packet wireless mesh network design problem Kevin P. Scheibe a, * , Cliff T. Ragsdale b a Department of Logistics, Operations, and Management Information Systems, Iowa State University, 2340 Gerdin Business Building, Ames, IA 50011, United States b Pamplin College of Business, Virginia Tech, Blacksburg, VA 24061, United States article info Article history: Received 19 February 2007 Accepted 14 July 2008 Available online 29 July 2008 Keywords: Network planning Broadband wireless mesh Hop-constrained Capacitated networks abstract Three critical factors in wireless mesh network design are the number of hops between supply and demand points, the bandwidth capacity of the transport media, and the technique used to route packets within the network. Most previous research on network design has focused on the issue of hop con- straints and/or bandwidth capacity in wired networks while assuming a per-flow routing scheme. How- ever, networks that employ per-packet routing schemes in wireless networks involve different design issues that are unique to this type of problem. We present a methodology for designing wireless mesh networks that consider bandwidth capacity, hop constraints, and profitability for networks employing a per-packet routing system. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction The popularity and rate of growth of the Internet over the last decade has been prodigious. What was once solely a medium for governmental and academic researchers to exchange ideas has now become an almost ubiquitous entity that enables many activities – from personal communications, to on-line shopping, to global information exchange. As more people, companies, and institutions do business on-line, the need for broadband (i.e., high speed, always ‘‘on”) telecommunications has become a necessity (TechNet 2002). Many wireless technologies have been developed to meet the demand for broadband access. Careful planning is required to de- sign and implement wireless broadband networks that are techni- cally and economically viable. Factors that must be considered for wireless networks include quality of service (QoS) requirements, service demands of broadband customers, line-of-sight (LOS) restrictions, and the type of routing scheme that will be employed within the network. Much prior research in network planning has focused on the problem of backbone network design. This work differs by addressing the last mile problem (i.e., designing wireless sub-net- works that attach to the backbone) using wireless mesh networks where capacity restrictions and the routing scheme used within the sub-network are critical considerations (Acampora, 2002; Fisher, 2004; Scheibe et al., 2006). We propose a methodology for optimizing the design of broadband, wireless mesh networks employing per-packet routing that simultaneously considers topology, capacity, quality of service, and cost. This problem ini- tially came to our attention during a discussion with a wireless Internet service provider (WISP). The WISP described challenges they faced providing mesh service to customers. The model pro- posed in this research reflects the method of service the WISP was attempting to provide, that is, a per-packet mesh network that supplied a guaranteed level of bandwidth, quality of service (hops), and survivability to customers. We begin with a review of background material on network de- sign problems, wireless communications and mesh networks. Next, we describe our proposed solution methodology along with the computational results of 2430 wireless mesh network solu- tions to demonstrate our model’s robustness. Finally, the paper concludes with a summary of contributions and suggestions for fu- ture work in this area. 2. Background 2.1. Wireless communications Wireless networks are rapidly growing in popularity as a means of bringing broadband communications to end-users. This connec- tion to end-users is called the ‘‘last mile” of the network – the con- nection from the backbone, often located at the telephone company’s central office, to the small business or home. This last mile connection does not exist for many people and is very expen- sive to implement – both in the US and Europe (Acampora, 2002; Cybersavvy UK, 2000; Fibercore, 2003; Wieland, 2002). Many types 0377-2217/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2008.07.020 * Corresponding author. Tel.: +1 515 294 0545; fax: +1 530 323 8323. E-mail addresses: kscheibe@iastate.edu (K.P. Scheibe), crags@vt.edu (C.T. Ragsdale). European Journal of Operational Research 197 (2009) 773–784 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor