Resource Allocation with Population Dynamics

There are resource-allocation problems encountered in almost every aspect of human lives: from utilities such as power systems and water systems, to transportation, and office space allocation. Many analyses of resource-allocation problems employ simplistic models of the population which ignore much of the complexity of human behaviour. Notice, for example, that the demand for a resource is often non-stationary, as exemplified by the work-day morning rush hour in transportation and the existence of predictable peaks in the demand in many other domains. Notice, further, that humans may have access to only very limited amount of information, but may still consider multiple criteria, and that their appreciation of the criteria may vary over time. As an example of a particular resource-allocation problem, we introduce a model of behaviour and the related demand process, which captures both the multi-criteria aspects of the decision making and non-stationarity of the demand process. Still, we show that the distribution of agents across resources converges in distribution, for suitable means of information provision and under certain assumptions. As our running example, we consider the problems faced by transportation authorities in charge of a road network composed of a number of road segments. For each road segment, the travel time is, in principle, a time series with a data point per a vehicle passing across the road segment.