Profit Optimization in SLA-Aware Cloud Services with a Finite Capacity Queuing Model

Algorithm 1

OPC algorithm.

Input Data:

(1) Arrival rate 𝜆.

(2) Potential abandonment index and expected revenue [𝑑(𝑠, 𝑡),𝑁(𝑠, 𝑡)].

(3) Cost matrix [𝐶_𝐻, 𝐶_𝑊, 𝐶_𝑈, 𝐶_𝑅].

(4) A given execution rate 𝜇 and a baseline rate 𝜇_𝐵.

(5) Loss probability threshold T.

(6) The upper bound parameters (𝑢 and 𝑏) for server

   quantity and system capacity, respectively.

Output Data:

𝑅^∗ and 𝐾^∗ and 𝐹(𝑅^∗,𝐾^∗)

Step  1. For 𝑖=1; 𝑖 = 𝑢; 𝑖++

    Set 𝑅_𝑖← 𝑎 current server quantity;

Step  2. For 𝑗=0; 𝑗=𝑏; 𝑗++

    Set 𝐾_𝑗← 𝑎 current system capacity;

Step  3. Calculate 𝜌_𝑠, 𝑃_𝐾, 𝐿_𝑞, 𝜆_𝑑, 𝜆^∗ and loss probability using

   (5)–(14) and (15), respectively.

Step  4. If loss probability < 𝑇

     Then, record the current joint value of (𝑅_𝑖, 𝐾_𝑗) and

       identify it as an approved test

       parameter;

    Else

       Return to Step 1 and begin to test next

     index of parameters;

   End

Step  5. When all test parameters have been done,

   {𝑅_𝑖+𝑎,𝐾_𝑗+𝑎},…,{𝑅_𝑢,𝐾_𝑏}← current approved

    parameters;

    Bring all revenue and cost parameters into the

    developed profit function and test all current approved

    parameters

Step  6. If a joint value of (𝑅_𝑖+𝑎, 𝐾_𝑗+𝑎) obtains the maximum

    profit value in all tests,

    Then

       Output (𝑅_𝑖+𝑎, 𝐾_𝑗+𝑎) and F(𝑅_𝑖+𝑎, 𝐾_𝑗+𝑎);

    Else

        Return to Step 5 and begin to test next index

        of the approved parameters.

   End