A Game Theory Approach to Fair and Efficient Resource Allocation in Cloud Computing

Algorithm 1

The FUGA algorithm.

Input: 𝐶^⇀(𝑚), 𝑅

Output: A*

(1)  Initialization: combinLists, selectedServerList, 𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛𝑝+1

(2)   Step  1.: Pre-combination Phase

(3)  // Each physical server with idle resources is a game player

(4)   𝑃←1,…,𝑚,…,𝑝

(5)   for each physical server 𝑚  do

(6)      List any possible coordinate placement combinations of this server to be fulfilled by different

    types of VMs without exceeding the capacity in the 𝑐𝑜𝑚𝑏𝑖𝑛𝐿𝑖𝑠𝑡_𝑚

(7)      combinLists.add(𝑐𝑜𝑚𝑏𝑖𝑛𝐿𝑖𝑠𝑡_𝑚)

(8)   end for

(9)   Step  2.: Strategies Set for Each Player

(10)   for each physical server 𝑚  do

(11)  Pick up top 𝜂 of combinations 𝑂^(𝑚)={com₁,com₂,…,com_𝜂} and calculate min(𝑂^(𝑚))

(12)  // each 𝑐𝑜𝑚_𝑥(𝑚) can be represented as an allocation matrix 𝐴_𝑥^(𝑚)

(13)   end for

(14)   Step  3.: Generate the Extension-form Game Tree

(15)  The orginal array min𝑂⁽¹⁾,…,min𝑂^(𝑝) is rearranged in a non-decreasing order with

    indices 𝑖₁,…,𝑖_𝑝 such that min(𝑂^(𝑖1))≤⋯≤min(𝑂^(𝑖𝑝))

(16)  The game players take action as the order of 𝑖₁,…,𝑖_𝑝

(17)   Step  4.: Find the SPNE for a game G

(18)   for each strategy 𝐴^{(𝑖𝑝−1)}_𝑥,𝐴^(𝑖𝑝)_𝑦 of physical server 𝑖_𝑝−1, 𝑖_𝑝  do

(19)      Calculate the utility pair 𝑈^{(𝑖𝑝−1)}[𝑥]𝑦,𝑈^(𝑖𝑝)[𝑥]𝑦

(20)   end for

(21)   max[𝑥]←argmax_𝑦𝑈^(𝑖𝑝)[𝑥][𝑦]

(22)   𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛𝑖_𝑝−1←argMax_𝑥𝑈^{(𝑖𝑝−1)}[𝑥][max[𝑥]]

(23)   𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛𝑖_𝑝−1←argMax_𝑥(max[𝑥])

(24)     Add 𝑖_𝑝−1,𝑖_𝑝 to the selectedServerList

(25)   for each physical server m from 𝑖_𝑝−1 to 1 do

(26)      Add up the total amount of resources 𝜑 for physical servers in selectedServerList

(27)      for each strategy 𝐴_𝑥^(𝑚)of physical server m do

(28)        Calculate the ske(𝑚) if 𝐴_𝑥^(𝑚) is chosen

(29)        Add up the total allocated resource 𝜑=𝐴^𝑚+𝜑

(30)        Calculate the 𝑣(𝐴)

(31)        utilityCalculation(ske(𝑚),𝑣(𝐴))

(32)      end for

(33)      𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛[𝑚]←argMax_𝑥𝑈^(𝑚)[𝑥]

(34)      Add server m to selectedServerList

(35)   end for

(36)  The best strategy of each player m in 𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛[𝑚] can be represented as an allocation

    matrix 𝐴^(𝑚), and 𝐴^∗=𝐴⁽¹⁾,…,𝐴^(𝑚),…,𝐴^(𝑝)