A wireless packet network is considered in which each user transmits a stream of packets to its destination. The transmit power of each user interferes with the transmission of all other users. A convex cost function of the completion times of the user packets are minimized by optimally allocating the users' transmission power subject to their respective power constraints. It is shown that, at all ranges of SINR, completion time minimization can be formulated as a convex optimization problem and hence can be efficiently solved. When channel knowledge is imperfect, robust power control is considered based on the channel fading distribution subject to outage probability constraints. The problem is shown to be convex when the fading distribution is log-concave in exponentiated channel power gains; e.g., when each user is under independent Rayleigh, Nakagami, or log-normal fading.
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