Coarse-Grain QoS-Aware Dynamic Instance Provisioning for Interactive Workload in the Cloud

Table 5

Revisions for Algorithms 1 and 2 with function approximations.

Revisions for Algorithm 1

Revisions for Algorithm 2

(i) In line 5, there is no need to test each instance provisioning policy in [MIN_NUM, MAX_NUM]. Instead, we can use either approach listed as follows.; (1) Define a positive integer variable stepsize which is; greater than 1, and increase 𝑘 by stepsize rather than 1.; (2) Pick a small set of 𝑘 randomly from [MIN_NUM, MAX_NUM].; (ii) Compute 𝑎𝑖 and 𝑏𝑖 using (13) and (15) after line 19.; (iii) The output of the algorithm is func_app[𝑁].

(i) The input of the algorithm is func_app[𝑁].; (ii) The exhausted search approach (lines 2–7) is replaced by the inverse functions of (8) and (9) as follows.; (1) For linear approximation case,; 𝐾𝑖=𝑥−func_app[𝑖]⋅afunc_app[𝑖]⋅b.; (2) For nonlinear approximation case,; 𝐾𝑖=^func_app[𝑖]⋅𝑏𝑥func_app[𝑖]⋅𝑎,; where [𝑥] is the smallest integer no less than 𝑥.