This isn't going to have a definite answer mainly due to the way computers work, but I'll try to give some guidelines as to how to figure out what is the fastest.
I'll analyze your statements in order to tell you what you can and can not figure out.
From your first paragraphs you stated you loaded and read all data into and from memory. This is good for speed, as in terms of bandwidth, memory is second to none. If your program used a disk (regardless of it being a HDD, a SSD or a pen drive), it could be a possibility that could be a bottleneck in your program's running speed.
This is due to transfer speed. RAM has almost direct access to the processor. Disks have to pass through a connection with a bandwidth much lower than RAM, and in the case of HDD's, there is the time needed to fetch and store data in consideration.
The OS used does pack some influence on speed, but can be considered residual.
3. Processor Architecture (or Instruction Sets)
This is a relevant aspect. Although you stated the machines used amd64 processors, there might be some differences in the instruction sets being used.
Consider for instance the Opteron and the Sempron series of processors. A key difference in them is that the latter has SSE3 support.
SSE3 allows newer and more efficient ways to deal with data (specifically array operations), operations that in earlier instruction sets would be done using less efficient processes.
So, in this aspect, newer processors are faster by design, as they support more efficient instruction sets.
4. System load
This is the final nail in the coffin, as you might put. You can't calculate load in a computer in a linear way, unless you know how each program works. With this being said, you might have 10.000 processes running but with a residual load or with a single multi-threaded process wasting all processor time.
However... let's analyze this further. Adding processes implies adding some sort of data to the underlying system, in order for it to know the process exists and how much of the processor's time should be made ready for it. In this aspect, less processes are better for speed, as the kernel/processor can decide better how much time to made available.
Another thing to consider is the priority the kernel gives to the processes. The processes with biggest priority will occupy most of the processor's time.
You can ultimately conceive of a system that can give your process maximum priority, and leave all other processes waiting eternally until your process halts. In this, your process speed will be determined by the CPU.
Let's consider your points: cores and CPU clock speed.
It can be conceivable that the kernel can shift some processes to other cores. In a limit case, your process can have a full core designated to it. In this aspect, more cores can enable more processes to run simultaneously (and by consequence, faster).
I don't know much about multi-threading so I'll leave that for someone who knows.
Clock speed is not a clear indicator of processor efficiency. To ground this, I present you the "battle" between the use of Intel and PowerPC processor in Apple hardware. Apple argued that the main reason for preferring PowerPC processors to Intel despite increasing processor speeds in Intel processors was that PowerPC performed better, because they could handle more operations per second that it's rival. In the end, Apple opted for Intel due to power concerns and other economical factors.
FLOPS (for FLoating-point Operations Per Second) is a measure of computer performance, especially in fields of scientific calculations that make heavy use of floating-point calculations, similar to the older, simpler, instructions per second. This could be a better measure than clock speed, if your work relies heavily on these kinds of operations that, for you using Matlab, could be a possibility.
It isn't however a very divulged quantity (as it depends on what kind of operations are you executing). I found some benchmarks on Overclock.net. I point these two out:
- AMD Phenom Ix4 9850 @ 2.83GHz RAM 754MHz 5-5-5-15 GFLOPS:27.5
- AMD Phenom IIx2 555 @ 4.12GHz RAM 1000MHz 5-5-5-18 GFLOPS:26
As you can see, even processors with twice the speed can perform worse than processors with half the speed.
There isn't a clear formula you can use to estimate running time, due to the endless amount of factors involved in the processing of a program. There are some rules of thumb I sum up (I've tried to sort them by importance):
- It is faster to have all (or mostly-used) data on RAM. (data storage is the main bottleneck in any process).
- The less processes running in the same machine, the better.
- More cores are better.
- Newer processors are faster by design.
- CPU speed is a rough indicator of speed (as RAM latency and other factors intervene)
- You can ask the machine to give your process the highest priority. The machine will try to allocate more time to your process. (when I say will try, I mean that the machine has no obligation to give your process more time, it tries to balance everything out, which is why the 2nd item exists).
I'm still a little hesitant to give an all-out formula, but I believe I can give you a very, very approximate one, based on your comments' output. I can't speak about multi-threading so I will consider all cores to be independent. For this demonstration the following is assumed:
- All processes have the same load.
- Processes aren't waiting for input/output.
- Memory speed is assumed not to be a factor.
- All processes are single-threaded. They have the same priority.
With this, the bottleneck will be the CPU's capacity. So, for any CPU, the relative load for any process would be the following:
R = min(C / N ; 1)
With R being the relative load, C the number of cores in the CPU and N the number of active processes. This assumes however that the system can distribute evenly and perfectly all load throughout the cores, which it might not be always true.
With the relative load of the CPU, multiply it by the unit of measurement (UM) of your choice (e.g. GHz or GFLOPS) and then you get a measure of how "fast" the process might be.
Speed = R * UM
So, with this, your formula is correct. But please, pretty please note the amount of assumptions I had to make. This is far from a real case. This will not give you an exact quantity, but rather, an educated guess.
Your second point is the same as the first (in fact, you answer it on your question). In short, it is the machine's performance indicator (as
R = 1), so the question here is how to choose one. This is something you should analyze yourself: you can use GHz times number of cores, or GFLOPS or some combination of the two.
There are programs (that I should have remembered earlier when writing the first answer) that can do some benchmarks on CPU's and from those, you can get some values that might help your decision. I have SiSoftware Sandra (that has, on my rather old version, a Processor Arithmetic benchmark) but I suppose there are others.
In this case, multiplying 1) and 2) wouldn't give any difference, unless you used different measure units.