Stochastic Monotonicity and Queueing Applications of Birth-Death Processes (eBook, PDF)
Erik Van Doorn
eBook, PDF

Stochastic Monotonicity and Queueing Applications of Birth-Death Processes (eBook, PDF)

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A stochastic process {X(t): 0 S t < =} with discrete state space S c ~ is said to be stochastically increasing (decreasing) on an interval T if the probabilities Pr{X(t) > i}, i E S, are increasing (decreasing) with t on T. Stochastic monotonicity is a basic structural property for process behaviour. It gives rise to meaningful bounds for various quantities such as the moments of the process, and provides the mathematical groundwork for approximation algorithms. Obviously, stochastic monotonicity becomes a more tractable subject for analysis if the processes under consideration are such that s...

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