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The performance improvement is observed to be negligible or very small for small loads; as the load size increases, the performance penalty paid by the algorithm in [9] becomes more significant. Example 1 Consider a cluster in which Cm = Cp = 1, and consider a job of size σ = 30 which arrives at timeinstant zero, and is assigned two processors P1 and P2 in this cluster, with ready-times r1 = 0 and r2 = 21 respectively. , at r2 ). First, we need to compute ξ(σ, 2) according to Equation 3 — the completion time of this job were to be scheduled optimally upon two homogeneous processors that are always available.

The value is computed by observing that allocating a fraction αi of the load requires this node to be receiving data for Cm αi σ time units and then executing this data for Cp αi σ time units. , at time-instant ∆); since Pi may only begin receiving data at time-instant si , we require that si +Cm αi σ +Cp αi σ = ∆ , from which we derive the value of αi given in line 5. Once Pi ’s share is computed, we can compute the time at which Pi+1 may begin execution. This is the later of its ready time and the time at which Pi has finished receiving data (and the head-node is thus able to commence datatransmission to Pi+1 ).

We determined the minimum number of processors as computed using both algorithms, under a variety of system and • The two graphs in the top row of Figure 2 evaluate the relative performance of the two algorithms as the communication cost parameter of the cluster – Cm – is increased, for clusters of 16 and 32 processors respectively. As can be seen, the performance improvement for our algorithm increases as Cm increases. • The two graphs in the bottom row of Figure 2 evaluate the relative performance of the two algorithms as the processing cost parameter of the cluster – Cp – is increased, for clusters of 16 and 32 processors respectively.

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