The world has been on a fast track of industrial development thanks to human activities. On the back of the same coin is the fact that people are consuming more and more energy to support the fast-paced development. Studies have pointed out an increasing consumption on traditional, non-renewable energies such as coal and oil, while the application of renewable energies, such as wind power and solar power, are still quite far away from mass application because of various restrains. Therefore, it is essential to search for a better way for people to consume energy, especially electricity since it is a necessary every-day energy and it is overwhelmingly generated with non-renewable resources. Researches about smart grid have been quite fruitful with demand response being the most promising research area. A large number of previous studies have been done in the area of real-time pricing schemes and fairness in bill and cost for theses schemes, but real-time demand response using energy consumption scheduling algorithms did not attract much attention until recently because of the two-way communication capacity of smart grid and fair delay problem of the energy scheduling. Also, using optimal stopping rule to model these problems has yet to be studied. Solution to these problems will essentially make demand response program more flexible or even smart grid participation a more attractive choice to customers. This dissertation looks at three problems. The first problem is the cost minimization problem with real-time demand response using energy consumption scheduling modeling in a neighborhood area network. We simulate this problem with discrete event simulation with different sets of parameters, and provide the results analysis under several circumstances. The second problem explores the importance of fairness in terms of delay. A formal concept of delay is defined using the energy scheduling model, and then the problem is formed based on a cost minimization problem with a fairness boundary constraint. The proposed algorithm solves the cost minimization while bounding the delays of all customers. The simulation results show that the algorithm with fair delay has much better performance than the algorithm without fair delay in terms of fairness index metric. In the third problem, we adopt the optimal stopping rule method to model the energy consumption scheduling problem. Then a cost minimization problem with comfortable delay is presented, and an optimal stopping rule based energy consumption scheduling algorithm is proposed to solve this problem. The simulation results show that the optimal stopping rule algorithm has better performance in terms of total cost than a greedy algorithm while satisfying the comfortable level constraint.