Sequential rectangular packing problem in wireless telecommunications with fuzzy extensions

In this thesis, a rectangular packing problem in telecommunications context is considered. Namely, we introduce a resource allocation modeling framework for a sequential two-dimensional packing problem, which may have direct applications in wireless telecommunications area pertaining to the IEEE 802.16 standard. The time dimension implied by the sequential consideration of frames adds a third dimension to the packing problem to some extent. We extend the common features of the frame packing problem to include realistic and state-of-the-art features of the current wireless data transfer processes. Three novel and representative mathematical programming models are developed for the problem, which are intended for contribution both to academic literature and professional practice. The developed models aim optimal usage of the physical layer defined by the standard, which involves data packages sent from a base station to a fixed or mobile user station. The data transmitted for each user are modeled as rectangular blocks, dimensions of which correspond to time duration and frequencies used in data transfer. Placement of these rectangular blocks in a sequence of identical rectangle frames is optimized by the developed models, aiming to maximize profit, minimize waste or minimize the rectangle count. Quality of service constraints such as maximum delay in transfer and minimum data transmission rates restrict the placement of variable-sized rectangles. We present the framework for all models, which handle demand partitioning and rectangle packing simultaneously. The foundations for fuzzy measures and parametrization are also proposed in this thesis, in order to mimic more realistic evaluation of actual network resources for practical problems. Thorough extensive experimentation, the performance of the developed models in terms of both solution times and quality are investigated. We also discuss alternative approaches to improve solution performances for the new models.