Memory management common patterns

I am writing a memory allocator and I want to test it against patterns (of calls on malloc and free) that are most common in programs. Have common patterns in memory management ever be identified? If so, is there any good book or internet source on this? I am both interested in single-thread programs' patterns as well as for multi-threaded ones. Additional: I am currently thinking that some typical mathematically models could describe such patterns. A sin/cos function could describe a Producer(malloc)/Consumer(free) algorithm where the producer must finish to produce all its product before these can be sold by the consumer. The fibonacci sequence could describe a program where the number of malloc(ed) regions grows naturally (for example on modelling some real-world problems). If you have any other ideas, that would be a lot appreciated. But again, it would be preferable to have a book/paper/PhD thesis on it.