Load Balancing for Future Internet: An Approach Based on Game Theory

Algorithm 1

Input:

Users’ generating rate: 𝐺¹,𝐺²,𝐺³,…,𝐺^𝑝;

Processors’ processing rate: 𝑃¹₁⋯𝑃^𝑛₁𝑃⋮⋱⋮_1𝑚⋯𝑃^𝑛_𝑚;

The number of users, load managers, processors for each load manager: 𝑘, 𝑛, 𝑚;

Transforming time: 𝑡_𝑖𝑗

Fault tolerant: 𝜀

Output:

 Fraction of job assignment for each user: 𝑔¹₁⋯𝑔^𝑛₁𝑔⋮⋱⋮_1𝑘⋯𝑔^𝑛_𝑘

While (1) do

𝜎^𝑗_𝑖←𝜎^𝑗_𝑖−∑^𝑝_{𝑞=1,𝑞!=𝑖}𝑔^𝑗_𝑞∗𝐺_𝑞

For 𝑖=1,2,3,…,𝑘

   𝑃←1;  𝛼←0;

While (1) do

   For 𝑗=1,2,3,…,𝑟 do   𝑆=∑^𝑟_𝑗=1𝜎^𝑗_𝑗−𝜎^𝑗_𝑖/(𝛼−𝑡_𝑖𝑗)𝐺_𝑖

   If 𝑠≤1𝜎^𝑝_𝑖𝑝←𝑝+1; Else  BREAK;

𝛼←(𝑠)²+𝑡_𝑖𝑗;

For 𝑗=1,2,3,…,𝑛

   if (𝑗<𝑃)   𝑔^𝑗_𝑖=𝜎^𝑗_𝑖−𝜎^𝑗_𝑖/(𝛼−𝑡_𝑖𝑗)𝐺_𝑖; else 𝑔^𝑗_𝑖←0;

     𝑇_𝑖←𝑇_𝑖+𝑔^𝑗_𝑖𝜎^𝑗_𝑖−𝑔^𝑗_𝑖𝐺_𝑖+𝑔^𝑗_𝑖𝑡_𝑖𝑗;

For 𝑖=1,2,3,…,𝑘 do

If 𝑇_𝑖−𝑇_𝑖^′>𝜀𝑇_𝑖^′←𝑇_𝑖;

    Else   BREAK;