A two-phase greedy algorithm to locate and allocate hubs for fixed-wireless broadband access
Introduction
In the broadband-access business, fixed-wireless technology is gaining popularity as a fast, cost-effective alternative to other telecommunication technologies. Worldwide service revenues for fixed-wireless access are expected to exceed $41 billion in 5 years, according to the ARC Group (www.arcgroup.com; see the report titled “Broadband access: opportunities in fixed-wireless”). Faced with the challenge of designing and expanding wireless networks to balance coverage, capacity, time to market, and cost, both practitioners and researchers have extensively studied problems in deploying telecommunication networks.
This paper focuses on a last-mile, fixed-wireless network-planning problem with a two-phase planning horizon. At the beginning of each phase, the main decision is to determine the number, type, and location of hubs (aggregation nodes) to be installed. There are multiple hub types, differing in cost and capacity. An installation budget is specified for each phase. In the second phase, some of the hubs installed in the first phase may be moved at a fraction of the cost of installing new hubs. It may be desirable to move hubs when the geographical distribution of demand changes over time, when move costs are low, and when the second-phase budget is limited. We formulate the problem as a stochastic program with recourse actions contingent on realized demand: after each phase of hub-installation or move decisions are made, demand for the wireless service materializes at the different buildings. The available hubs are then used to capture as much demand as possible, subject to technological constraints. Demand is uncertain and it also changes over time; this is modeled using multiple scenarios and time periods. The objective is to maximize the expected total demand covered over the planning horizon.
We present a new network-planning model and an effective greedy solution heuristic, which we implement efficiently. We evaluate the quality of the heuristic by comparing its coverage with the optimal (for small problems) or with an upper bound obtained by solving a linear-programming relaxation. We also explore the robustness of heuristic solutions to problem parameters like density of buildings (urban vs. rural) and budget levels.
After the review of literature in Section 2, we develop the model in Section 3 and the greedy algorithm in Section 4. We present computational results and parameter analysis in Section 5 and we identify areas for future research in Section 6.
Section snippets
Literature review
Our problem is one of facility location [10], [12], [15] and is most closely related to the maximum-covering-location problem (MCLP). Unlike the traditional MCLP, which is deterministic and has binary (yes/no) coverage, we model a two-phase, budgeted, capacitated location problem under uncertain demand that may be partially covered.
The capacitated MCLP has been studied in [8], [14]. Stochastic versions of the MCLP have been mainly uncapacitated [16]; Daskin [9] and Batta et al. [4] studied a
Model
The problem is formulated as a two-stage stochastic program with stage-one hub-installation decisions made at the beginning of each phase and subsequent stage-two hub-to-demand allocation decisions made after customer demand materializes. The objective is to maximize the total expected demand covered by the hubs installed on, or moved to, buildings over the two phases. In addition to technological constraints, the model includes hub-capacity constraints and installation/move budget limitations.
The greedy algorithm
Because L1 is NP-hard, fast heuristics, such as greedy approaches, are commonly used to solve industrial-size (large-scale) instances approximately. We first introduce our greedy algorithm and then present some properties that help improve its solution time.
Let be the set of (location, hub-type) pairs corresponding to hubs available for use in phase k. We include multiple copies of (j,h) in when multiple hubs of type h are installed at j. For , let Fk be the total
Computational testing
We now discuss the heuristic's performance and present results from parameter analysis.
Data generation: We use two sets of test instances: small (with 10–20 buildings, typically solvable to optimality using CPLEX6.5 MILP) and large (with 200–400 buildings). Most of the data (demand, building locations, line-of-sight or not) are chosen to be consistent with the motivating industrial environment and with [5]. Accordingly, we set the number of hub types H to four, with increasing hub capacity/cost
Future research
Possible extensions of this paper include: (i) investigation of mathematical-programming-based heuristics for stochastic hub location, (ii) study of robust solutions for the multi-phase problem in which demand scenarios are updated at the end of each phase, (iii) linking the hub-location problem to other network-planning problems like hub configuration (engineering) and long-haul backbone network design and (iv) modeling multi-technology systems including both wireless hubs and a wire-line
Acknowledgements
We thank the area editor Dr. Martin Savelsbergh, two anonymous referees, and Dr. David Kelton and Dr. Sharon McFarland for their many comments that helped us to improve this paper. Ramesh Bollapragada would like to dedicate his contributions in loving memory to his mother, Mangatayaru Bollapragada, who was a great source of inspiration in his academic career.
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