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3 results

Fair gambler’s ruin stochastically maximizes playing time
Part of
- Stochastic processes
Erol A. Peköz, Sheldon M. Ross
Journal:

Advances in Applied Probability / Volume 54 / Issue 2 / June 2022

Published online by Cambridge University Press:

10 March 2022, pp. 656-659

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June 2022
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For the gambler’s ruin problem with two players starting with the same amount of money, we show the playing time is stochastically maximized when the games are fair.

A Compound Poisson Approximation Inequality
Part of
Erol A. Peköz
Journal:

Journal of Applied Probability / Volume 43 / Issue 1 / March 2006

Published online by Cambridge University Press:

14 July 2016, pp. 282-288

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March 2006
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We give conditions under which the number of events which occur in a sequence of m-dependent events is stochastically smaller than a suitably defined compound Poisson random variable. The results are applied to counts of sequence pattern appearances and to system reliability. We also provide a numerical example.

The derivation of invariance relations in complex queueing systems with stationary inputs
Masakiyo Miyazawa
Journal:

Advances in Applied Probability / Volume 15 / Issue 4 / December 1983

Published online by Cambridge University Press:

01 July 2016, pp. 874-885

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December 1983
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We discuss a method of obtaining invariance relations in complex systems by using the theory of point processes. New formulae are given for obtaining them generally, and in particular in many-stage models such as tandem and network queues. The formulae are shown to be useful by applications to a many-server queue and a tandem queue. Stochastic inequalities in a tandem queue are also discussed using the invariance relations obtained.

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3 results

Fair gambler’s ruin stochastically maximizes playing time

A Compound Poisson Approximation Inequality

The derivation of invariance relations in complex queueing systems with stationary inputs