How much power is needed for a billion-thread high-throughput server?

With the advent of Internet services, big data and cloud computing, high-throughput computing has generated much research interest, especially on high-throughput cloud servers. However, three basic questions are still not satisfactorily answered: (1) What are the basic metrics (what throughput and high-throughput of what)? (2) What are the main factors most beneficial to increasing throughput? (3) Are there any fundamental constraints and how high can the throughput go? This article addresses these issues by utilizing the fifty-year progress in Little's law, to reveal three fundamental relations among the seven basic quantities of throughput (lambda), number of active threads (L), waiting time (W), system power (P), thread energy (E), Watts per thread omega, threads per Joule theta. In addition to Little's law L = lambda W, we obtain P = lambda E and lambda = L omega I, under reasonable assumptions. These equations help give a first order estimation of performance and power consumption targets for billion-thread cloud servers.