Current demand response (DR) programs focus on industrial consumers as they can provide a large magnitude of demand modification. In order to extend DR programs to the residential sector, aggregating service demands from a large number of residential consumers is necessary in order to achieve a sensible benefit to the power network. In this paper, we propose a methodology for residential demand aggregation, based on a multi-class queueing system. Each class represents demand blocks of a specific power level, time duration, and a service delay requirement. We use this model to minimize the cost of the appliances’ aggregated power consumption under day-ahead pricing (DAP). Using realistic appliances’ data, we show that the proposed framework achieves a cost reduction that is close to the best achievable one.