Efficient Two-Dimensional Packing Algorithms for Mobile WiMAX

We present the result of research, developed within Nokia Siemens Networks, to solve the downlink sub-frame allocation problem in Mobile WiMAX (IEEE 802.16) technology in its full complexity, while simultaneously fulfilling real-life constraints on processing power and delay. We describe the IEEE 802.16 standard, and introduce two system models. A theoretical analysis of the two-dimensional packing problems originated by such models shows that they are both NP-hard in the strong sense. From a practical point of view, the processing budget for scheduling in the base station was estimated to be 1 ms on a state-of-the-art PC. Thus, we introduce two highly efficient heuristics that were developed to handle the system practically. A thorough computational analysis of their optimization characteristics and a system-level evaluation in realistic scenarios proved that the algorithms offer significant capacity gain in Mobile WiMAX systems that translate to increased operator revenues. <i>This paper was accepted by Dimitris Bertsimas, optimization.</i>