Revenue Maximization in an Optical Router Node Using Multiple Wavelengths

In this paper, an optical router node with multiple wavelengths is considered. We introduce revenue for successful transmission and study the ensuing revenue maximization problem. We present an efficient and accurate heuristic procedure for solving the NP-hard revenue maximization problem and investigate the advantage offered by having multiple wavelengths

How to detect a counterfeit coin: Adaptive versus non-adaptive solutions

In an old weighing puzzle, there are n3 coins that are identical in appearance. All the coins except one have the same weight, and that counterfeit one is a little bit lighter or heavier than the others, though it is not known in which direction. What is the smallest number of weighings needed to identify the counterfeit coin and to determine its type, using balance scales without measuring weights? This question was fully answered in 1946 by Dyson [The Mathematical Gazette 30 (1946) 231–234]. For values of n that are divisible by three, Dyson's scheme is non-adaptive and hence its later weighings do not depend on the outcomes of its earlier weighings. For values of n that are not divisible by three, however, Dyson's scheme is adaptive. In this note, we show that for all values n3 there exists an optimal weighing scheme that is non-adaptive

Realizing small tournaments through few permutations

Every tournament on 7 vertices is the majority relation of a 3-permutation profile, and there exist tournaments on 8 vertices that do not have this property. Furthermore every tournament on 8 or 9 vertices is the majority relation of a 5-permutation profile

A REVERSIBLE ERLANG LOSS SYSTEM WITH MULTITYPE CUSTOMERS AND MULTITYPE SERVERS

We consider a memoryless Erlang loss system with servers S = {1, …, J}, and with customer types C = {1, …, I}. Servers are multitype, so that server j can serve a subset of customer types C(j). We show that the probabilities of assigning arriving customers to idle servers can be chosen in such a way that the Markov process describing the system is reversible, with a simple product form stationary distribution. Furthermore, the system is insensitive; these properties are preserved for general service time distributions