Inequalities Between Arrival Averages and Time Averages in Stochastic Processes Arising from Queueing Theory

Article Abstract:

Queueing theory often includes a counting process that observes and interacts with another continuous time stochastic process. If the arrival process is Poisson, then the limiting stationary actual and virtual waiting time distributions are identical. The proportion of arrivals finding the process in some state is equal to the proportion of time spent under a lack of anticipation assumption. The related problem of when do the inequalities between these proportions exist is addressed.

Queuing theory, Poisson distribution, Scientific Research, Stochastic Model

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Valid Linear Inequalities for Fixed Charge Problems

Article Abstract:

Although branch-and-bound is the most widely used method for resolving integer and mixed-integer optimization problems, it is insufficient for solving a series of zero-one problems. The present paper addresses solving mixed zero-one problems in a way similar to Crowder's 1983 work with combinatorial problems investigating linear inequalities. Two classes of facet-defining linear equalities of the convex hull of X are desired. An example of a fixed arc network problem is presented.

Integer programming, Optimization, Methods, Branch and Bound

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Inequalities for NBUE and NWUE Life Distributions

Article Abstract:

Inequalities are useful in life testing and reliability modeling studies. Hazard rates and lower order moments can be studied with inequalities. Four new classes of failure distributions are introduced. They are based on the variance behavior. They help develop inequalities for New-Worse-Than-Used-in-Expectation (NWUE) and New-Better-Than-Used-in-Expectation (NBUE) distributions.

Reliability (Trustworthiness), Modeling, Data modeling software, Reliability, Markov Process, Failure Analysis

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