User Allocation in Multi-System, Multi-Service Scenarios: Upper and Lower Performance Bound of Polynomial Time Assignment Algorithms

In this paper we cover the problem of how users of different service classes should be assigned to a set of radio access technologies (RAT). All RAT have overlapping coverage and the aim is to maximize a weighted sum of assignable users. Under the constraint that users cannot be split between multiple air-interfaces the problem is identified as NP-complete. In the first part of the paper we derive upper and lower bounds of polynomial assignment algorithms. Using Lagrangian theory and continuous relaxation we show for polynomial assignments that in scenarios with M air-interfaces there are at most M users less assigned than in the optimum solution. In the second part we present an algorithm and compare its performance to standard load-balancing strategies.