Performance Analysis and Optimization of a $N$ -Class Bipolar Network

A wireless network with unsaturated traffic and N classes of users sharing a channel under random access is analyzed here. Necessary and sufficient conditions for the network stability are derived, along with simple closed formulas for the stationary packet transmission success probabilities and mean packet delays for all classes under stability conditions. We also show, through simple and elegant expressions, that the channel sharing mechanism in the investigated scenario can be seen as a process of partitioning a well-defined quantity into portions, each portion assigned to each user class, the size of which determined by system parameters and performance metrics of that user class. Using the derived expressions, optimization problems are then formulated and solved to minimize the mean packet delay and to maximize the channel throughput per unit of area. These results indicate that the proposed analysis is capable of assessing the trade-off involved in radio-resource management when different classes of users are considered.