By Zoran Constantinescu
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The x-axis in all three ﬁgures is a conﬁguration state for the QoS attributes considered. e. 5 are considered. e. C1 to C5) the weights are having values with an increasing mean from C1 to C5 and also an increasing standard deviation to represent variant weight vector settings. Note that upon moving from C1 to C5 the success rate tends to decrease which is normal as the more the mean of the weight vector increases the more the scheduling process relay on QoS other than the time and cost. This consequently minimizes the set of resource candidates for each task and causes less success rate.
The problem is assigning m resources to n tasks with k QoS parameters. There are three matrices, one is Tn*k matrix given by (5) for task requirements, another is Wn*k matrix given by (6) for weight of requirements, and the other is Rk*m matrix given by (7) for resource capabilities. These matrices are shown in below. ⎡ q1task1 ⎢ ⎢q task2 =⎢ 1 ⎢ ⎢q taskn ⎣ 1 Tn * k Wn * k ⎡ w1task1 ⎢ ⎢ wtask2 =⎢ 1 ⎢ ⎢ wtaskn ⎣ 1 Rk * m We define WdTn*k matrix as below. ⎡q1res1 ⎢ ⎢q res1 =⎢ 2 ⎢ ⎢q res1 ⎣ k q2task1 q2task2 q 2taskn w2task1 w2task2 w2taskn q1res2 q2res2 q kres2 q ktask1 ⎤ ⎥ 2 ⎥ q task k ⎥ ⎥ n ⎥ q task k ⎦ wktask1 ⎤ ⎥ wktask2 ⎥ ⎥ ⎥ taskn ⎥ wk ⎦ q1resm ⎤ ⎥ q2resm ⎥ ⎥ ⎥ q kresm ⎥⎦ (5) (6) (7) 36 Advances in Grid Computing WdTn * k ⎡ w1task1 ⎢ q1task1 ⎢ ⎢ wtask2 ⎢ 1 q1task2 =⎢ ⎢ ⎢ ⎢ wtaskn ⎢ 1 q1taskn ⎢⎣ w2task1 w2task2 w2taskn 1 wtask k q 2task1 2 wtask k q 2task2 n wtask k q 2taskn ⎤ ⎥ q ktask1 ⎥ ⎥ task2 ⎥ qk ⎥ ⎥ ⎥ ⎥ ⎥ q ktaskn ⎦⎥ (8) So, equation (4) is based on multiplying WdTn*k matrix to Rk*m matrix and the result is Vn*m matrix given by (9) and (10).
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Advances in Grid Computing by Zoran Constantinescu