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Smart metering, which reports the power activities to the control center, is a key task in smart grid and faces the challenges of realtime requirement and the large population of users. In this paper, the power consumptions of houses and offices are measured using a power clamp. It is found that the power consumption stays almost constant for most of the time, thus justifying the strategy of transmitting only when the power consumption is significantly changed. By using Kolmogorov- Smirnov test, it is also demonstrated that the arrival of changes of the power consumption satisfies Poisson distribution with proper time intervals. For such a random arrival of events, both the multiple access schemes using dedicated channels like TDMA and OFDMA and using contentions like Aloha and CSMA are considered and compared. Numerical simulations are carried out for evaluating the performance, measured by the delay and packet loss rate, using the measurement data and simple communication models. The results show that the contention based multiple access outperforms the dedicated channels, given the configuration of the simulation.