Hybrid Wireless-Optical Broadband Access Network (WOBAN): Network Planning Using Lagrangean Relaxation

The concept of a hybrid wireless-optical broadband access network (WOBAN) is a very attractive one. This is because it may be costly in several situations to run fiber to every home (or equivalent end-user premises) from the telecom central office (CO); also, providing wireless access from the CO to every end user may not be possible because of limited spectrum. Thus, running fiber as far as possible from the CO toward the end user and then having wireless access technologies take over may be an excellent compromise. How far should fiber penetrate before wireless takes over is an interesting engineering design and optimization problem, which we address in this paper. We propose and investigate the characteristics of an analytical model for network planning, namely optimum placements of base stations (BSs) and optical network units (ONUs) in a WOBAN (called the primal model, or PM). We develop several constraints to be satisfied: BS and ONU installation constraints, user assignment constraints, channel assignment constraints, capacity constraints, and signal-quality and interference constraints. To solve this PM with reasonable accuracy, we use ldquoLagrangean relaxationrdquo to obtain the corresponding ldquoLagrangean dualrdquo model. We solve this dual problem to obtain a lower bound (LB) of the primal problem. We also develop an algorithm (called the primal algorithm) to solve the PM to obtain an upper bound (UB). Via simulation, we compare this PM to a placement heuristic (called the cellular heuristic) and verify that the placement problem is quite sensitive to a set of chosen metrics.