The Fluid Limit Approximation

The dynamic resource allocation problem arises in a variety of applications. The generic resource allocation setting involves a number of locations containing resources. The dynamic aspect of the problem is the arrivals of consumers, each of which requires a certain amount of service from the resources, and the control variable of the problem is the \allocation policy", which speciies at which location each consumer is to be served. Oftentimes in applications, locations contain nitely many resources, hence the main objective of the allocation policy is to guarantee low blocking probability. On the other hand, in some applications such as spread spectrum mobile radio networks, there are no sharp capacity constraints, and the goal becomes to dynamicallybalance the load. In either case, one wants the allocation policy to have low complexity, require little information about the system state, and be robust to changes in the traac parameters. An instance of resource allocation arises in the wireless network pictured in Figure 1.1. The network consists of a number of base stations and users. The users require communication channels that are available at the base stations, whereas each station may serve the users within its geographical range. The resource allocation problem in this setting concerns the question of station selection. Load balancing is a possible guiding principle for resource allocation, whereby the load is allocated across locations as evenly as possible. It is well known that load balancing can be an eeective allocation strategy, when the cost is convex (or the reward concave) as a function of the allocated loads. For example, x 2 +y 2 +z 2 U(1) U(2) U(3) V(1) V(2) Fig. 1.1. A typical wireless network with overlapping neighborhoods.