An important open problem in wormhole routing has been to find a necessary and sufficient condition for deadlock-free adaptive routing. Recently, Duato has solved this problem for a restricted class of adaptive routing algorithms. In this paper, a necessary and sufficient condition is proposed that can be used for any adaptive or nonadaptive routing algorithm for wormhole routing, as long as on...

Abstract: A new method to solve a Lyapunov equation for a discrete delay system is proposed. Using this method, a Lyapunov equation can be solved from a simple linear equation and N -th power of a constant matrix, where N is the state delay. Combining a Lyapunov equation and frequency domain stability, a new stability condition is proposed for a discrete state delay system whose state delay is ...

We present a necessary and almost sufftcient condition for subgame perfect implementation of social choice correspondences. In societies with at least three individuals, any social choice correspondence which satisfies no veto power and our necessary Condition a is subgame perfect implementable. Thus Condition GL is analogous to monotonicity which, by Maskin’s celebrated characterization, is ne...

In this technical note, cluster consensus of discretetime linear multi-agent systems is investigated. A set of stochastic matrices P is said to be a cluster consensus set if the system achieves cluster consensus for any initial state and any sequence of matrices taken from P . By introducing a cluster ergodicity coefficient, we present an equivalence relation between a range of characterization...

we develop a two phase sampling procedure to determine the sample size necessary to estimatethe population mean of a normally distributed random variable and show that the resulting estimator has preassigned variance and is unbiased under a regular condition. we present a necessary and sufficient condition under which the final sample mean is an unbiased estimator for the population mean.