This page gives a brief summary of the research projects I have done while at UCSC.
We find that multiple scheduling slots does not have a significant affect on the number of concurrent conversations. Multiple slots may have beneficial effects on the mean waiting time of the transmit queue when packets are short. One of our Markov models has a good approximation of simulation for short packet lengths.
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It would be a simple modification to the class to generate all permutations. From the list of combinations, one could find all arrangements. For my purposes, it was sufficient to assume "identical" children, thus the multinomial was sufficient.
You can try out permtest on the web!
This problem is useful in multicast tree analysis. If there is some event that occurs at leaf nodes, such as successfully decoding a C(n,k) FEC code, then this class allows us to enumerate the state space.
Let N be the number of child nodes (adjacent descendents) of a node, say ni. Call the child nodes ck, k=1...N. Let V be the number of successful events under ni. Under ck, let M be the total number of leaf nodes, which is where these events occur (this assumes a tree of fixed degree sequence per level).
Then, this object class allows us to generate all the possible state spaces immediately descendant to ni where 0...V events happen under each child of ni, but no child receives more than M events, since there are only M leaf nodes under each child ck.
Marc Mosko
http://www.cse.ucsc.edu/~mmosko
mmosko@cse.ucsc.edu