  Motivated by demand-side management in smart grids, a decentralized
controlled Markov chain formulation is proposed to model a homogeneous
population of users with binary demands (i.e., off or on). The binary demands
often arise in scheduling applications such as plug-in hybrid vehicles.
Normally, an independent service operator (ISO) has a finite number of options
when it comes to providing the users with electricity. The options represent
various incentive means, generation resources, and price profiles. The
objective of the ISO is to find optimal options in order to keep the
distribution of demands close to a desired level (which varies with time, in
general) by imposing the minimum price on the users. A Bellman equation is
developed here to identify the globally team-optimal strategy. The proposed
strategy is fair for all users and also protects the privacy of users.
Moreover, its computational complexity increases linearly (rather than
exponentially) with the number of users. A numerical example with 100 users is
presented for peak-load management.
