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On a non-Markovian queueing problem under a control operating policy and start-up times

Arun Borthakur, Ruby Gohain (1982)

Aplikace matematiky

A non-Markovian queueing system with Poisson input is studied under a modified operating rule called “control operating policy” in which the server begins “start-up” only when the queue length reaches a fixed number n ( ≥ 1 ) . By using the supplementary variable technique, the distribution of the queue length (excluding those being served) in the form of a generating function is obtained. As a special case, a Markovian queueing system with exponential start-up is discussed in detail to analyse the economic...

On approximation in multistage stochastic programs: Markov dependence

Vlasta Kaňková, Martin Šmíd (2004)

Kybernetika

A general multistage stochastic programming problem can be introduced as a finite system of parametric (one-stage) optimization problems with an inner type of dependence. Evidently, this type of the problems is rather complicated and, consequently, it can be mostly solved only approximately. The aim of the paper is to suggest some approximation solution schemes. To this end a restriction to the Markov type of dependence is supposed.

On certain Markov processes attached to exponential functionals of Brownian motion: application to Asian options.

Catherine Donati-Martin, Raouf Ghomrasni, Marc Yor (2001)

Revista Matemática Iberoamericana

We obtain a closed formula for the Laplace transform of the first moment of certain exponential functionals of Brownian motion with drift, which gives the price of Asian options. The proof relies on an identity in law between the average on [0,t] of a geometric Brownian motion and the value at time t of a Markov process, for which we can compute explicitly the resolvent.

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