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JVM and hardware interactions profiling

Hi.
I searched for a while and stumbled about the lack of specific instrument. There're many good, even free profilers for Java, which allow to see how much time the code parts took overall, but nothing for the next tasks.
Given.
A Java multithreading program, doing some calculations through the misc.unsafe, using a simple fork-join pool, ThreadPoolExecutor, running on one Oracle JVM and Intel Xeon based server-class node. Looks like nothing hard, hot-spots are obvious. I need to figure out is any optimizations possible, which are promising and their potential assessment.
Needed.
For this, among the other information, I need a decent information about what exactly happens inside the hardware. For the research start, I want at least the cache misses and memory boundary overhead, byte-code or hardware instructions' overall timings. This would be very useful for avoiding "box ticking" approach. For clarification what exactly I need, I put here a similar instrument's wiki link which I used for a C or Fortran legacy code https://en.wikipedia.org/wiki/VTune (especially look briefly at the "Hardware event sampling" paragraph) and it fulfilled all my purposes.
Thanks in advance.

A concrete Example of the effect of the JIT in java

So I am aware the java has just in time compilation (the JIT), which gives it an advantage over statically compiled languages like C++. Are there any examples illustrating the java JIT? Possible examples could be outperforming C or C++ code for a given algorithm? Or showing an algorithm's iterations getting faster with time (I am unsure if that would be an instance of the JIT). Or just any example which can show some sort of measurement of the existence of the JIT doing this? I ask this question because I have only ever read about the JIT and wish to prove it's existence as opposed to just believing in it like some sort of religious God.
Remark - If this question is too opinionated please comment and let me know why. I am just curious about the JIT and after using java for a few years still to this day am unaware of how I benefit from it, and if it lives up to the hype of outperforming its statically compiled counterparts.
Additional Information - I have read about when it does it, and am not looking for more information I will just need to believe is true, I want to see something which shows me doing what it is suppose to do.
EDIT - Good that I have allot of responses, what has been said is that comparing speed alone JIT optimised vs. C++ is not a good approach, and that a pure java comparison would be the least horrible. What about an example showing this with java:
So a JIT and Non-JIT optimised program doing the same are executed. At the start the JIT has not kicked in, and the program begins getting quicker whilst the static always has the same performance. Then the conditions change at 5.5 seconds or so and the application is being used slightly differently. The JIT has the ability to adapt to these changes again, firstly the time spikes and then it begins optimising again and can even reach a better optima becaue the application is being used slightly different.
Would this be an acceptable example to show a JIT? (I will endevour to achieve this and review everyones links and videos).

I do not think you can convincingly prove that java using JIT is faster than C/C++ statically compiled code.
You could find some code in java that beat its c/c++ implementation. For that you need to search for keywords like (benchmark,Java,JIT,C,C++ )
I have purposely not mentioned any code or links for the above because of my point below.
Most of the times people show java code beating statically compiled c/c++ in following ways
Find part where java is fast compared to c/c++(memory allocation)and write only code to highlight it.
Find weak points of c/C++ code and try to write java code that beat the c/c++ code in achieving the result.
Run code in environment where you have advantage like having fast hardware and good amount of memory .
My point being you are trying to find exception where java is faster that C/C++ and then generalizing it to the whole language. You could easily find more more examples of c/c++ beating java code just by using pointer in many algorithm.
Such code benchmark testing is of no value in real life application development.
Summarizing ( in real life application development )
Java was slow compared to c/c++ when it first came out. But in the past decade improvements made in JVM coupled with JIT,Hotspot etc have made java as good as C/C++. Java is not slow nowadays. But I would not call it fast over c/c++. Any difference in real life application development in negligible because of language improvement as well as better hardware.
You cannot generalize that java is faster than c/c++ by beating it one time in a particular environment with a particular algorithm or code.
You might find some interesting info in the following links
https://softwareengineering.stackexchange.com/questions/110634/why-would-it-ever-be-possible-for-java-to-be-faster-than-c
Is Java really slow?
Since question has been edited to now try and find the performance improvement of using JIT , I am editing my answer to add a few more points.
My understanding of JIT is that it improves the code that is most executed , to a version that can be run really fast by compiler. Most of the examples of JIT optimisation techniques I have come across shows actions which could also be done by the programmer but then would affect the readability of the program or may not confirm to the framework or coding styles the programmer is/has to use.
So what I am trying to say here is if you write a program that can be improved by JIT it will do so and you will see an increase in performace. But if you are someone who understand JVM and write java code that is already optimized then JIT may not give you much benefit.
So in effect if you see a performace improvement when running a program using JIT that improvement is not guaranteed for all java programs. It depends on the program.
These links below show some JIT improvements using code examples.
http://www.infoq.com/articles/Java-Application-Hostile-to-JIT-Compilation
https://plumbr.eu/blog/java/do-you-get-just-in-time-compilation
Anyway if we need to to differentiate the performance while using JIT, we would run a java program with JIT enabled and run the same program again with JIT disabled.
This link http://www.javacodegeeks.com/2013/07/java-just-in-time-compilation-more-than-just-a-buzzword.html has a case study on this topic and recommends the following
Assessing the JIT benefits for your application
In order to understand the impact of not using JIT for your Java application, I recommend that you preform the following experiment:
Generate load to your application with JIT enabled and capture some baseline data such as CPU %, response time, # requests etc
Disable JIT
Redo the same testing and compare the results.
This link http://people.cse.iitd.ac.in/~sbansal/csl862-virt/readings/CompileJava97.pdf does benchmark JIT and shows speed improvements over basic JVM interpretations.
To understand what JIT does to your code , you could use the tool JITwatch.
https://github.com/AdoptOpenJDK/jitwatch
The links below explain its utility.
http://www.oracle.com/technetwork/articles/java/architect-evans-pt1-2266278.html
http://zeroturnaround.com/rebellabs/why-it-rocks-to-finally-understand-java-jit-with-jitwatch/

First, you want to watch this video. It gives you tools to see the JIT in action.
Where I believe your questions is misled is that you are asking for an example of tailored code where you could potentially measure faster performance in some JVM-based language X vs some non JVM-based language Y (where, for instance, X is Java and Y is C).
This is not the way to think about the JIT. Unless you actually write a compiler for the JVM language by yourself, or have to debug some serious performance issue, and only after you have considered refactoring your code and seen it fail then you can delve that deep into details.
But otherwise, the principle is simple: the JIT is your friend and it does things right; all you have to do is write code which just works; if there are ways that the JIT can make it faster at runtime, it will most certainly do so.

There are countless examples on Stack Overflow of questions like "why is my code running faster all of a sudden?" - usually when people try to benchmark their code. The answer is, invariably, because the JIT was able to make optimizations mid-benchmark.
See: How do I write a correct micro-benchmark in Java?, What is going on in this java benchmark?, and Java benchmarking - why is the second loop faster? for some examples.
I have only ever read about the JIT and wish to prove it's existence as opposed to just believing in it like some sort of religious God.
This is an unnecessary line of thinking; there's a lot going on between your keyboard and your monitor that you've never noticed or don't understand. The JIT is documented behavior of the JVM, that's all you need to know. It's fine if you don't understand it and want to learn more, but it's not some mythical, ethereal construct.

JIT Just in Time compilation is a sort of pre compilation that is done prior of execution of byte code. From ORacle site:
"In theory, the JIT comes into use whenever a Java method is called,
and it compiles the bytecode of that method into native machine code,
thereby compiling it “just in time” to execute"
The most reliable effect of JIT is visible comparing java itself with and without jit.
JIT (Just In Time compilation) was introduced in java 1.2 so the best is to execute the same code with java 1.1 and java 1.2 and check the performances.
Prior to java 1.2 java was considered a very slow language and only after the introduction of JIT it has been extensively used in any field.
Instead is difficult to compare C++ or C and java. Potentially C++ is faster then java, because also with JIT java is an interpreted language. JIT compilation helps because the code that is executed more often is interpred only one time instead of each time it is executed.
Differences between java and C++ can involve how libraries are designed, presence or absence of certain primitive types, how code is compiled, level of optimizations, in case of java how gc is configured and so on.
Note that there can be differences also between java and java also with same jdk and same jvm depending on compilation parameters and execution parameters.
It is not possible to say that Java is faster than C or viceversa, too many parameters are involved in this kind of comparison. Sometime C++ is faster, sometime java is the best.
Here is a reference from Oracle on JIT compilation: http://docs.oracle.com/cd/E13150_01/jrockit_jvm/jrockit/geninfo/diagnos/underst_jit.html

Hotspot JIT optimizations

In a lecture about JIT in Hotspot I want to give as many examples as possible of the specific optimizations that JIT performs.
I know just about "method inlining", but there should be much more. Give a vote for every example.

Well, you should scan Brian Goetz's articles for examples.
In brief, HotSpot can and will:
Inline methods
Join adjacent synchronized blocks on the same object
Eliminate locks if monitor is not reachable from other threads
Eliminate dead code (hence most of micro-benchmarks are senseless)
Drop memory write for non-volatile variables
Replace interface calls with direct method calls for methods only implemented once
et cetera

There is a great presentation on the optimizations used by modern JVMs on the Jikes RVM site:
ACACES’06 - Dynamic Compilation and Adaptive Optimization in Virtual Machines
It discusses architecture, tradeoffs, measurements and techniques. And names at least 20 things JVMs do to optimize the machine code.

I think the interesting stuff are those things that a conventional compiler can't do contrary to the JIT. Inlining methods, eliminating dead code, CSE, live analysis, etc. are all done by your average c++ compiler as well, nothing "special" here
But optimizing something based on optimistic assumptions and then deoptimizing later if they turn out to be wrong? (assuming a specific type, removing branches that will fail later anyhow if not done,..) Removing virtual calls if we can guarantee that there exists only one class at the moment (again something that only reliably works with deoptimization)? Adaptive optimization is I think the one thing that really distinguishes the JIT from your run of the mill c++ compiler.
Maybe also mention the runtime profiling done by the JIT to analyse which optimizations it should apply (not that unique anymore with all the profile-guided optimizations though).

There's an old but likely still valid overview in this article.
The highlights seem to be performing classical optimizations based on available runtime profiling information:
JITting "hot spots" into native code
Adaptive inlining – inlining the most commonly called implementations for a given method dispatch to avoid a huge code size
And some minor ones like generational GC which makes allocating short lived objects cheaper, and various other smaller optimizations, plus whatever else was added since that article was published.
There's also a more detailed official whitepaper, and a fairly nitty-gritty HotSpot Internals wiki page that lists how to write fast Java code that should let you extrapolate what use cases were optimized.

Jumps to equivalent native machine code instead of JVM interpretation of the op-codes. The lack of a need to simulate a machine (the JVM) in machine code for a heavily used part of a Java application (which is the equivalent of an extension of the JVM) provides a good speed increase.
Of course, that's most of what HotSpot is.

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First of all I should mention that I'm aware of the fact that performance optimizations can be very project specific. I'm mostly not facing these special issues right now. I'm facing a bunch of performance issues with the JVM itself.
I wonder now:
which code-optimization make sense
from a compiler perspective: for
example to support the garbage
collector I declared variables as
final - very much following PMD's
suggestions here from Eclipse.
what best practices there are for: vmargs,
heap and other stuff passed to the
JVM for initialization. How do I get
the right values here? Is there any
formula or is it try and error?
Java automates a lot, does many optimization on byte-code level and stuff. However I think most of that must be planed by a developer in order to work.
So how do you speed up your programs in Java? :)

Which code-optimization make sense from a compiler perspective: for example to support the garbage collector I declared variables as final - very much following PMD's suggestions here from Eclipse.
Assuming you are talking about potential micro-optimizations you can make to your code, the answer is pretty much none. The best way to increase your application performance is to run a profiler to figure out where the performance bottlenecks are, then figure out if there is anything you can do to speed them up.
All of the classic tricks like declaring classes, variables and methods final, reorganizing loops, changing primitive types are pretty much a waste of effort in most cases. The JIT compiler can typically do a much better job than you can. For example, recent JIT compilers will analyse all loaded classes to figure out which method calls are not subject to overloading, without you declaring the classes or methods as final. It will then use a quicker call sequence, or even inline the method body.
Indeed, the Sun experts say that some programmer attempts at optimization fail because they actually make it harder for JIT compiler to apply the optimizations it knows about.
On the other hand, higher level algorithmic optimizations are definitely worthwhile ... provided that your profiler tells you that your application is spending a significant amount of time in that area of the code.
Using arrays instead of collections can be a worthwhile optimization in unusual cases, and in rare cases using object pools might be too. But these optimizations 1) will make your code more complicated and bug prone and 2) can slow your application down if used inappropriately. These kinds of optimizations should only be tried as a last resort. For example, if your profiling says that such and such a HashMap<Integer,Integer> is a CPU bottleneck or a memory hog, then it is a better idea to look for an existing specialized Map or Map-like library class than to try and implement the map yourself using arrays. In other words, optimize at the high level.
If you spend long enough or your application is small enough, careful micro-optimization will probably give you a faster application (on a given JVM version / hardware platform) than just relying on the JIT compiler. If you are implementing a smallish application to do large-scale number crunching in Java, the pay-off of micro-optimization may well be considerable. But this is clearly not a typical case! For typical Java applications, the effort is large enough and the performance difference is small enough that micro-optimization is not worthwhile.
(Incidentally, I don't see how declaring a variable can make any possible difference to GC performance. The GC has to trace a variable every time it is encountered whether or not it is final. Besides, it is an open secret that final variables can actually change under certain circumstances, so it would be unsafe for the GC to assume that they don't. Unsafe as in "creates a dangling pointer resulting in a JVM crash".)

I see this a lot. The sequence generally goes:
Thinking performance is about compiler optimizations, big-O, and so on.
Designing software using the recommended ideas, lots of classes, two-way linked lists, trees with pointers up, down, left, and right, hash sets, dictionaries, properties that invoke other properties, event handlers that invoke other event handlers, XML writing, parsing, zipping and unzipping, etc. etc.
Since all those data structures were like O(1) and the compiler's optimizing its guts out, the app should be "efficient", right? Well, then, what's that little voice telling one that the startup is slow, the shutdown is slow, the loading and unloading could be faster, and why is the UI so sluggish?
Hand it off to the "performance expert". With luck, that person finds out, all this stuff is done in the recommended way, but that's why it's cranking its heart out. It's doing all that stuff because it's the recommended way to do things, not because it's needed.
With luck, one has the chance to re-engineer some of that stuff, to make it simple, and gradually remove the "bottlenecks". I say, "with luck" because often it's just not possible, so development relies on the next generation of faster processors to take away the pain.
This happens in every language, but moreso in Java, C#, C++, where abstraction has been carried to extremes. So by all means, be aware of best practices, but also understand what simple software is. Typically it consists of saving those best practices for the circumstances that really need them.

which code-optimization make sense
from a compiler perspective?
All the ones that a compiler can't reason about, because a compiler is very dumb and Java doesn't have "design by contract" (which, hence, cannot help the dumb compiler reason about your code).
For example if you're crunching data and using use int[] or long[] arrays, you may know something about your data that is IMPOSSIBLE for the compiler to figure out and you may use low-level bit-packing/compacting to improve the locality of reference in that part of your code.
Been there, done that, saw gigantic speedup. So much for the "super smart compiler".
This is just one example. There are a huge number of cases like this.
Remember that a compiler is really stupid: it cannot know that if ( Math.abs(42) > 0 ) will always return true.
This should give some food for thoughts to people that think that those compilers are "smart" (things would be different here if Java had DbC, but it doesn't).
what best practices there are for:
vmargs, heap and other stuff passed to
the JVM for initialization. How do I
get the right values here? Is there
any formula or is it try and error?
The real answer is: there shouldn't be. Sadly the situation is so pathetic that such low-level hackery is needed, due to serious failure on Java's part. Oh, one more "tiny" detail: playing with VM fine-tuning only works for server-side app. It doesn't work for desktop apps.
Anyone who has worked on Java desktop applications installed on hundreds or thousands of machines, on various OSes knows all too well what the issue is: full GC pauses making your app look like it's broken. The Apple VM on OS X 10.4 comes to mind for it's particularly afwul, but ALL the JVMs are subject to that issue.
What is worse: it is impossible to "fine tune" the GC's parameters across different OSes / VMs / memory configuration when your application is going to be run on hundreds/thousands of different configuration.
Anyone disputing that: please tell me how you "fine tune" your app knowing that it is going to be run both on octo-cores Mac loaded with 20 GB of ram (I've got users with such setups) and old OS X 10.4 PowerBook that have 768 MB of ram. Please?
But it is not bad: you should not, in the first place, have to be concerned with super-low-level detail like GC "fine tuning". The very fact that this is hinted to is a testimony to one area where Java has a major issue.
Java fans will keep on saying "the GC is super fast, object creation is cheap" while this is blatantly wrong. There's a reason with Trove' TIntIntHashMap runs around circles an HashMap<Integer,Integer>.
There's also a reason why at every new JVM release you'll get countless release notes explaining why -XXGCHyperSteroidMultiTopNotch offers better performance than the last "big JVM param" that every cool Java programmer had to know: maybe the JVM wasn't that great at GC'ing after all.
So to answer your question: how do you speed up Java programs? Easy, do like what the Trove guys did: stop needlessly creating gigantic amount of objects and stop needlessly auto(un)boxing primitives because they will kill your app's perfs.
A TIntIntHashMap OWNS the default HashMap<Integer,Integer> for a reason: for the same reason my apps are now much faster than before.
I stopped believing in crap like "object creation costs nothing" and "the GC is super-optimized, don't worry about it".
I'm using Java to crunch data (I know, I'm a bit crazy) and the one thing that made my app faster was to stop believing all the propaganda surrounding the "cheap object creation" and "amazingly fast GC".
The truth is: INSTEAD OF TRYING TO FINE-TUNE YOUR GC SETTINGS, STOP CREATING THAT MUCH GARBAGE IN THE FIRST PLACE. This can be stated this way: if changing the GC settings radically changes the way your app run, it may be time to wonder if all the needless junk objects your creating are really needed.
Oh, you know what, I'm betting we'll see more and more release notes explaining why Java version x.y.z's GC is faster than version x.y.z-1's GC ;)

Generally there are two kinds of performance optimizations you need to do with Java:
Algorithmic optimization. Choose an algorithm which behaves like you need to. For instance, a simple algorithm may perform best for small datasets, but the overhead of preparing a smarter algorithm may first pay off for much larger datasets.
Bottleneck identification. Here you need to be familiar with a profiler that can tell you what the problem is (humans always guess wrong) - memory leak?, slow method? etc... A good one to start with is VisualVM which can attach to a running program, and is available in the latest Sun JDK. When you know the problem, you can fix it.

Todays JVM's are surprisingly robust when it comes to performance. Any microoptimizations you can apply will, in practically all cases, have only very minor impact on performance. This is easy to understand if you take a look on how typical language constructs (e.g. FOR vs WHILE) translate to bytecode - they are almost indistinguishable.
Making methods/variables final has absolutely no impact on performance on a decent JIT'd JVM. The JIT will keep track of which methods are really polymorphic and optimize away the dynamic dispatch where possible. Static methods can still be faster, since they don't have a this-reference = one less local variable (which at the same time, limits their application). Most efficient micro optimizations are not so much Java specific, for example code with lots of conditional statements can become very slow due to branch mispredictions by the processor. Sometimes conditionals can be replaced by other, sequential code flow constructs (often at the cost of readability), reducing the number of mispredicted branches (and this applies to all languages that somehow compile to native code).
Note that profilers tend to inflate the time spent in short, frequently called methods. This is due to the fact that profilers need to instrument the code to keep track of invocations - this can interfere with the JIT's ability to inline those methods (and the instrumentation overhead becomes significantly larger than the time spent actually executing the methods body). Manual inlining, while apparently very performance boosting under a profiler has in most cases no effect under "real world" conditions. Don't rely purely on the profilers results, verify that optimizations you make have real impact under real runtime conditions, too.
Notable performance boosts can only be expected from changes that reduce the amount of work done, more cache friendly data layout or superior algorytms. Java partially limits your possibilities for cache friendly data layouts, since you have no control where the parts (arrays/objects) that form your data structure will be located in memory in relation to each other. Still, there are plenty of opportunities where choosing the right data structure for the job can make a huge difference (e.g. ArrayList vs LinkedList).
There is little you can do to aid the garbage collector. However, a point worth noting is, while object allocation in Java is very very fast, there is still the cost of object initialization (which is mostly under your control). Poor performance of applications that creating lots of (short lived) objects is more likely to be attributed to poor cache utilization than to the garbage collectors work.
Different applications types require different optimization strategies - so before asking about specific optimizations, find out where your application really spends its time.

If you are experiencing performance issues with your application, you should seriously consider trying some profiling (eg: hprof) to see whether the problem is algorithmic in nature, and also checking the GC performance logging (eg: -verbose:gc) to see if you could benefit from tuning your JVM GC options.

It is worth noting that the compiler does next to no optimisations, and the JVM doesn't optimise at the byte code level either. Most of the optimisations are performed by the JIT in the JVM and it optmises how the code is converted to native machine code.
The best way to optimise your code is to use a profiler which measures how much time and resources your application is using when you give it a realistic data set. Without this information you are just guessing and you can change alot of code where it really, really doesn't matter and find you have added bugs in the process.
Many come to the conclusion that its never worth optmising you code, even counter productive as it can waste time and introduce bugs and I would say that is true for 95+% of your code. However, with aprofiler you can measure the critical pieces of code and optmise the <5% worth optimising and done carefully, you won't get too many issues from trying to optimise your code.

It's hard to answer this too thoroughly because you haven't even mentioned what sort of project you're talking about. Is it a desktop application? A server-side application?
Desktop applications favor application startup time, so the HotSpot client VM is a good start. Client applications don't necessarily need all of their heap space all the time, so a good balance between starting heap and max heap is useful. (Like, maybe -Xms128m -Xmx512m)
Server applications favor overall throughput, which is something the HotSpot server VM is tuned for. You should always allocate the min and max heap sizes the same on a server application. There is an added cost at the system level to it having to malloc() and free() during garbage collection. Use something like -Xms1024m -Xmx1024m.
There are several different garbage collectors also, which are tuned to different application types.
Take a read through the Java SE 6 Performance White Paper if you want more info on the garbage collector and other performance related items from Java 6.

Which programming language for compute-intensive trading portfolio simulation?

I am building a trading portfolio management system that is responsible for production, optimization, and simulation of non-high frequency trading portfolios (dealing with 1min or 3min bars of data, not tick data).
I plan on employing Amazon web services to take on the entire load of the application.
I have four choices that I am considering as language.
Java
C++
C#
Python
Here is the scope of the extremes of the project scope. This isn't how it will be, maybe ever, but it's within the scope of the requirements:
Weekly simulation of 10,000,000 trading systems.
(Each trading system is expected to have its own data mining methods, including feature selection algorithms which are extremely computationally-expensive. Imagine 500-5000 features using wrappers. These are not run often by any means, but it's still a consideration)
Real-time production of portfolio w/ 100,000 trading strategies
Taking in 1 min or 3 min data from every stock/futures market around the globe (approx 100,000)
Portfolio optimization of portfolios with up to 100,000 strategies. (rather intensive algorithm)
Speed is a concern, but I believe that Java can handle the load.
I just want to make sure that Java CAN handle the above requirements comfortably. I don't want to do the project in C++, but I will if it's required.
The reason C# is on there is because I thought it was a good alternative to Java, even though I don't like Windows at all and would prefer Java if all things are the same.
Python - I've read somethings on PyPy and pyscho that claim python can be optimized with JIT compiling to run at near C-like speeds... That's pretty much the only reason it is on this list, besides that fact that Python is a great language and would probably be the most enjoyable language to code in, which is not a factor at all for this project, but a perk.
To sum up:
real time production
weekly simulations of a large number of systems
weekly/monthly optimizations of portfolios
large numbers of connections to collect data from
There is no dealing with millisecond or even second based trades. The only consideration is if Java can possibly deal with this kind of load when spread out of a necessary amount of EC2 servers.
Thank you guys so much for your wisdom.

Pick the language you are most familiar with. If you know them all equally and speed is a real concern, pick C.

While I am a huge fan of Python and personaly I'm not a great lover of Java, in this case I have to concede that Java is the right way to go.
For many projects Python's performance just isn't a problem, but in your case even minor performance penalties will add up extremely quickly. I know this isn't a real-time simulation, but even for batch processing it's still a factor to take into consideration. If it turns out the load is too big for one virtual server, an implementation that's twice as fast will halve your virtual server costs.
For many projects I'd also argue that Python will allow you to develop a solution faster, but here I'm not sure that would be the case. Java has world-class development tools and top-drawer enterprise grade frameworks for parallell processing and cross-server deployment and while Python has solutions in this area, Java clearly has the edge. You also have architectural options with Java that Python can't match, such as Javaspaces.
I would argue that C and C++ impose too much of a development overhead for a project like this. They're viable inthat if you are very familiar with those languages I'm sure it would be doable, but other than the potential for higher performance, they have nothing else to bring to the table.
C# is just a rewrite of Java. That's not a bad thing if you're a Windows developer and if you prefer Windows I'd use C# rather than Java, but if you don't care about Windows there's no reason to care about C#.

I would pick Java for this task. In terms of RAM, the difference between Java and C++ is that in Java, each Object has an overhead of 8 Bytes (using the Sun 32-bit JVM or the Sun 64-bit JVM with compressed pointers). So if you have millions of objects flying around, this can make a difference. In terms of speed, Java and C++ are almost equal at that scale.
So the more important thing for me is the development time. If you make a mistake in C++, you get a segmentation fault (and sometimes you don't even get that), while in Java you get a nice Exception with a stack trace. I have always preferred this.
In C++ you can have collections of primitive types, which Java hasn't. You would have to use external libraries to get them.
If you have real-time requirements, the Java garbage collector may be a nuisance, since it takes some minutes to collect a 20 GB heap, even on machines with 24 cores. But if you don't create too many temporary objects during runtime, that should be fine, too. It's just that your program can make that garbage collection pause whenever you don't expect it.

Why only one language for your system? If I were you, I will build the entire system in Python, but C or C++ will be used for performance-critical components. In this way, you will have a very flexible and extendable system with fast-enough performance. You can find even tools to generate wrappers automatically (e.g. SWIG, Cython). Python and C/C++/Java/Fortran are not competing each other; they are complementing.

Write it in your preferred language. To me that sounds like python. When you start running the system you can profile it and see where the bottlenecks are. Once you do some basic optimisations if it's still not acceptable you can rewrite portions in C.
A consideration could be writing this in iron python to take advantage of the clr and dlr in .net. Then you can leverage .net 4 and parallel extensions. If anything will give you performance increases it'll be some flavour of threading which .net does extremely well.
Edit:
Just wanted to make this part clear. From the description, it sounds like parallel processing / multithreading is where the majority of the performance gains are going to come from.

It is useful to look at the inner loop of your numerical code. After all you will spend most of your CPU-time inside this loop.
If the inner loop is a matrix operation, then I suggest python and scipy, but of the inner loop if not a matrix operation, then I would worry about python being slow. (Or maybe I would wrap c++ in python using swig or boost::python)
The benefit of python is that it is easy to debug, and you save a lot of time by not having to compile all the time. This is especially useful for a project where you spend a lot of time programming deep internals.

I would go with pypy. If not, http://lolcode.com/.