Chapter 8: A Markov Chain Model for Capacity Events
M. Corless, C. King, Robert Noel Shorten, Fabian R. Wirth · Society for Industrial and Applied Mathematics eBooks · 2016
So far in the book, we have focused on the impact of capacity events from the viewpoint of an individual agent. We have explored two situations in this direction: the IID AIMD model and the state-dependent AIMD model. While both of these models are relevant in practice, they do not capture all important situations. We can imagine a situation where, due to communication constraints, there is a maximum number of agents that can be notified of a capacity event. For example, such a situation may arise in the context of intelligent transportation applications and the charging of electric vehicles. Here, due to the large number of vehicles, it may not be feasible to communicate capacity events to all agents, and a subset would have to be chosen for notification at each event. If the subset is chosen according to some random process that depends on the choice of subset at the prior capacity event, then the probability of the AIMD matrix A(k) would depend on the matrix A(k — 1). A second type of example may occur when agents have the option to select new growth rates each time they are notified of a capacity event.