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An important problem in maintenance planning is the repair versus replacement problem which consists of a sequence of decision points over time, whereby decisions are made to repair or replace a machine based on its condition. This problem can be further complicated by prevailing failure characteristics, and costs. The failure modes for many machines are such that failure emerges through a series...
The discrete-state continuous-time processes occurring in binding and release of analytes in affinity-based biosensors are formulated using stochastic differential equations (SDEs). The Fokker Planck (FP) equation is used to solve for the governing probability density function (pdf) of the number of captured analytes. A derivation method from the Markovian Master equation to the Fokker Planck equation...
We introduce Markov decision evolutionary games with N players, in which each individual in a large population interacts with other randomly selected players. The states and actions of each player in an interaction together determine the instantaneous payoff for all involved players. They also determine the transition probabilities to move to the next state. Each individual wishes to maximize the...
We analyze the average-case behaviour of the Next-Fit algorithm for bin-packing, and obtain closed-form expressions for distributions of interest. Our analysis is based on a novel technique of partitioning the interval (0, 1) suitably and then formulating the problem as a matrix-differential equation. We compare our analytic results with previously known simulation results and show that there is an...
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