I want to be able to write a unit test, in a suite of performance tests that is distinct from the fast functional tests that simulates the issue and fails, correct the issue such that the test passes. For example when execution time constraint is 20 Milliseconds, the test must fail if it takes more than 20ms otherwise passes. And what if I want to put a memory consumption constraint and if consumption is more than constraint, test must fail. Is it possible that I can write a test with memory consumption constraint?
For the timing constraint you can use @org.junit.rules.Timeout (although it's probably not what the rule is meant for) or write your own variation thereof. For the memory constraint you can write a org.junit.rules.TestRule that compares memory usage before and after the test. Two ways to measure memory usage are the java.lang.Runtime class and JMX.
As performance depends on many factors (load of the CI server, how much code has been jitted, etc.), it remains to be seen if the results will be conclusive/stable enough. It may be a good idea to run the tests many times and compare averages.