Mann-Whitney-U test vs. Wilcoxon signed-rank for testing simulation results I am testing two multiprocessor scheduling algorithms, on the same task sets (same workload), using a simulator. I am comparing the response-time of task execution (end_time - start_time), to see which of the two algorithms performed better (produces lower response-times). Assume 30 unique tasks for the experiment. I have 2 sets of results (30 samples each), each representing the response-time of the 2 algorithms.
Visually I can see that Alg.A is better than Alg.B. I am unsure which test to run, to check if the improvement is indeed statistically significant, or by chance.
From a statistical viewpoint - its the same population (30 individuals), independent treatments, un-paired data, and both distributions non-normal, continuous values. Also the two distributions may/may-not be the same. Also, I do not think this can be considered as repeated measures, as its 2 treatments on the same population, being induced in an independent-way. But they are not also different groups - i.e. same initial population.
From what little I know about non-parametric statistics, I am not sure, if I should use Mann-Whitney-U test OR Wilcoxon signed-rank test. Or something else completely ?
Many thanks
EDIT
This is the experiment methodology:
1) Create a workload : $W_i = \{\tau_0, \tau_1..\tau_n\}$. Here, $W_i$ is a set of tasks ($\tau_i$) with properties (priority, computation cost etc.). We measure each task's response time $R(\tau_i) = time_{end} - time_{release}$ after execution (units: seconds). All tasks are release at same time. Different scheduling algorithms will produce different $R(\tau_i)$ due to the order of execution of tasks (e.g. if $\tau_2$ is executed first and $\tau_1$ is executed second, then $tau_1$ has a longer $R(\tau_1)$
2) We want to see the performance of two scheduling algorithms : algA and algB.
3) We schedule and execute $W_i$ using algA : this gives us a $R(\tau_i)$ distribution, lets call it $dist_A[R(\tau_i)]$
4) We schedule and execute $W_i$ using algB : this gives us a $R(\tau_i)$ distribution, lets call it $dist_B[R(\tau_i)]$
5) We draw box-plots for both $dist_A[R(\tau_i)]$ and $dist_B[R(\tau_i)]$. We can see $dist_A[R(\tau_i)]$ has a lower mean/median and slightly lower IQR. Hence, we deduce algA is better than algB (to reduce task response times)
6) Now we want to find if this improvement of algA over algB is 'statistically significant'
 A: The signed ranks test is for paired data.
You stated that your data are not paired.
That would seem to suggest the signed ranks test is not suitable.
Your criterion of "lower response times" isn't especially clear; what aspects of a distribution are we comparing exactly? 
If you're happy with the comparison made by the Wilcoxon-Mann-Whitney test then that would be suitable (which for a one sided alternative could be stated as something like $P(X<Y)>\frac12$ or equivalently as the median of cross-population pairwise differences$X_i-Y_j$ being negative), but since you consider the possibility that the distributional forms might differ, you could easily conclude that $P(X<Y)>\frac12$ but it could also be true at the same time that $E(X)>E(Y)$ ... so you need to be sure you're measuring what you want.
On the other hand, since with times you probably would be interested in measuring ratios -- percentage speed up might be relevant for example, you may be better off working with log times (or possibly even speeds - i.e. inverse-times).
[On the other hand it's not clear to me that a significance test is necessarily the best tool here -- it would seem more sensible to describe the distributions of times or differences of times (or perhaps, as I suggested, ratios of times or differences of log-times) with enough simulations to give CIs that either clearly exclude no difference or are so narrow you don't care what the true difference might be. But the first thing is to clearly identify what you really want to measure]
