Optimum and equilibrium in assignment problems with congestion: mobile terminals association to base stations

​Alonso Silva, Hamidou Tembine, Eitan Altman, Merouane Debbah

optimal transport theory, static mean field game, optimal placement, cell formation

2013

​The classic optimal transportation problem consists in finding the most cost-effective way of moving masses from one
set of locations to another, minimizing its transportation cost. The formulation of this problem and its solution have been useful
to understand various mathematical, economical, and control theory phenomena, such as, e.g., Witsenhausen’s counterexample
in stochastic control theory, the principal-agent problem in microeconomic theory, location and planning problems, etc. In
this work, we incorporate the effect of network congestion to the optimal transportation problem and we are able to find
a closed form expression for its solution. As an application of our work, we focus on the mobile association problem in
cellular networks (the determination of the cells corresponding to each base station). In the continuum setting, this problem
corresponds to the determination of the locations at which mobile terminals prefer to connect (by also considering the congestion
they generate) to a given base station rather than to other base stations. Two types of problems have been addressed: a global
optimization problem for minimizing the total power needed by the mobile terminals over the whole network (global optimum),
and a user optimization problem, in which each mobile terminal chooses to which base station to connect in order to minimize
its own cost (user equilibrium). This work combines optimal transportation with strategic decision making to characterize
both solutions.