5.3 Experimental Evaluation
5.3.2 Performance evaluation using randomly generated PTGs
Experimental Setup: In this section, we have considered randomly generated PTGs in place of benchmark PTGs, to evaluate the performance of our proposed schemes. For this purpose, we have used the following parameters: (1) the number of tasks (n) in the PTG: varied from 25 to 100, (2) the total number of levels in the PTG (denoted by L): generated from a normal distribution having hµ, σi values equal to D√
n,√
n∗0.1E, (3) the number of nodes at any level in the PTG: generated from another normal distribution having hµ, σi values beingn/L,(n/L)∗0.1, (4) the number of processors (p): varied from 2 to 16, (5) heterogeneity (h): varied from 10 to 40. For a given value of h, the execution times of a task on different processors have been generated by selecting values from a uniform distribution [(30−h/2),(30 +h/2)]. It may be observed that heterogeneity in the execution times of a task on different processors monotonically increase withh. All result points on any given line in the plots in Figures 5.11a and 5.11b are generated by running a specific algorithm on the same task graph and the same value of deadline. To compute this deadline, the PEFT algorithm is used to schedule the task graph and obtain its makespan for the case when p = 2, h = 10, and n = 100. The deadline is then given by the minimum number D, which is a multiple of 100 and is greater than or equal to the obtained makespan. For example, let the average makespan produced by PEFT after 100 iterations to be 1556. So, the deadline D for this case becomes 1600.
Experiment-5: Varying the number of tasks and processors: In this exper- iment, we compare the performance of G-SAQA and T-SAQA by varying the number of task nodes in the PTG from 25 to 100 and number of processors from 2 to 16. Also, we set CCR to 1, the number of service-levels |SLi| to 5 for all tasks. Figure 5.11a depicts the results for this experiment. It may be observed that the obtained trends for randomly generated PTGs are very similar to those obtained for benchmark PTGs.
Even for this case,N Rimproves as #processors become higher because residual capacity increases. For example, when n = 100, the normalized reward obtained using T-SAQA for p= 4 andp= 8 are∼96% and∼100%, respectively. The N R values may be seen to
30 40 50 60 70 80 90 100
2 4 8 12 16
Normalized Reward (in %)
Number of Processors G-SAQA: n = 25
T-SAQA: n = 25 G-SAQA: n = 50 T-SAQA: n = 50 G-SAQA: n = 75 T-SAQA: n = 75 G-SAQA: n = 100 T-SAQA: n = 100
(a) Varyingnandp
20 30 40 50 60 70 80 90 100
2 4 8 12 16
Normalized Reward (in %)
Number of Processors G-SAQA: h = 10
T-SAQA: h = 10 G-SAQA: h = 20 T-SAQA: h = 20 G-SAQA: h = 30 T-SAQA: h = 30 G-SAQA: h = 40 T-SAQA: h = 40
(b) Varyinghandp
20 30 40 50 60 70 80 90 100
2 4 8 12 16
Normalized Reward (in %)
Number of Processors G-SAQA: h = 10
T-SAQA: h = 10 G-SAQA: h = 20 T-SAQA: h = 20 G-SAQA: h = 30 T-SAQA: h = 30 G-SAQA: h = 40 T-SAQA: h = 40
(c)Varying handpkeepingWsame
Figure 5.11: Effect of varying #tasks, #processors and heterogeneity
decrease with the increase in the number of tasks. As the number of tasks increase with the deadline remaining fixed, the total available slack decreases, which in turn leads to lower rewards. For example, at p= 4 the N R value obtained using G-SAQA forn = 25 and n = 100 are ∼100% and ∼59%, respectively. Similar to the previous experiments, T-SAQA returns higher or equal N R values than G-SAQA, for all cases.
Experiment-6: Varying heterogeneity: This experiment compares the perfor- mance of G-SAQA and T-SAQA by varying the heterogeneity (h) among processors from 10 to 40 and number of processors from 2 to 16. Also, we set n to 100, CCR to 1, number of service-levels |SLi| to 5. Figure 5.11b depicts the results for this exper-
iment. It can be observed that the normalized reward N R increases with increase in the heterogeneity among processors. With the increase in heterogeneity, difference in the execution times of a task on different processors, also increase. This shows that both G-SAQA and T-SAQA can effectively harness task-to-processor affinities resulting from the underlying system heterogeneity and conduct efficient resource allocation so that the overall aggregate reward is maximized. For example, theN R values obtained using T-SAQA for h= 10 andh= 40 are∼80% and∼96%, respectively, at p= 4. It can also be seen that in all cases, T-SAQA outperforms G-SAQA.
Experiment-7: Varying the number of processors while keeping normal- ized workload same: In this experiment, we have maintained thenormalized workload same instead ofabsolute workload. Here, we have definednormalized workload Wof the task nodes in a PTG as,
W=
Pn i=1
P|SLi| l=1
Pp r=1eilr
D×p2×Pni=1|SLi| (5.3)
where, D is the deadline, pis the number of processors, |SLi| is the number of service- levels of task Ti and eilr is the execution time of Ti at service-level slil on processor Pr.
The results of the experiment are reported in Figure 5.11c. It can be seen from the figure that the normalized rewards (N R) decrease with increase in the number of processors. This is because in order to maintain normalized workload at a particular value, the average execution time of each task must be increased p00/p0 times, when the number of processors is increased from p0 to p00 (say). When the execution time of a task is relatively higher, the difference in execution times of the task between consecutive service-levels will also be higher. On the other hand, although the total system capacity increases with the increase in the number of processors, the capacity of individual processors remain same. The non-preemptive task nodes which are now bigger in terms of their execution times must still be entirely executed within the capacity of a single processor. From these observations, it may be easily inferred that increase in the number of processors (with normalized workload remaining same) leads to the possibility of, (i) decrease in the number of tasks which may be feasibly accommodated within a
single processor (leading to decrease in resource utilization), (ii) reduction in the degree of service-level enhancement of tasks (leading to decrease in rewards). In addition, it may be observed that the structure of the PTG (number of task nodes and their inter dependencies) used as input to the experiment continues to remain same as the number of processors is increased. With the structure remaining same, the inherent available parallelism associated with the input PTG do not change when the available number of processors increase. Thus, when the total number of processors is sufficiently high, the total resource utilization will ultimately start to exhibit a decreasing trend.