Web server performance model (continued)

Revenue server earns from serving request i to completion under a service policy p is defined as

g_{i_p}(t_{i_p}) = e ^{-c(t_{i_p} - x_i)}
where x_i is the arrival time of request i, c is the revenue decay rate, and t_{i_p} is the departure time of job i under policy p
Potential revenue for request i under policy p at time t: g_{i_p}(t), x_i < t < t_{i_p}
E[Z₁] = expected length of one busy/idle cycle; N = number served in a busy cycle
By the Renewal Reward Theorem, the average reward earned by the server per unit time under a policy p is

V_p(Ø) = E[sum of all individual revenues of all jobs in a busy cycle]/E[Z₁]
The optimal service policy maximizes revenue per unit time: V = max_p V_p(Ø)