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Cellular networks are an attractive option for handling the growing number of sensing and monitoring devices due to their ubiquitous presence. While this growing popularity of cellular network based machine-to-machine (M2M) communications is opening new avenues for the mobile network operators, it is also bringing forth new system design challenges mainly because of the significant difference in the nature of M2M traffic and the current commercial traffic for which the cellular networks are designed and optimized. In this paper, we consider the M2M operational regime characterized by large number of small transactions and study the problem of power optimal uplink resource allocation both for Time Division Multiple Access (TDMA) and Frequency Division Multiple Access (FDMA). We derive tractable results for the maximum load a base station can handle and the optimal transmit power for both access strategies and show that FDMA supports an order of magnitude higher load than TDMA under the peak power constraint. We also show that the value of optimizing uplink resource allocation in the M2M parameter space of interest is typically insignificant and simpler access strategies, such as channel gain based allocation or even equal resource allocation, lead to near optimal performance. We also derive accurate closed form approximations for optimum power levels indicative of the actual performance in this regime.