BIPS: transient probability study

1975 ◽  
Author(s):  
Keyword(s):  
Transient Probability

Analysis of transient behaviour of certain processes with return to a central state

1983 ◽  
Vol 20 (01) ◽  
pp. 61-70
Author(s):  
Peter G. Buckholtz ◽  
L. Lorne Campbell ◽  
Ross D. Milbourne ◽  
M. T. Wasan
Keyword(s):  
Probability Distribution ◽  
Diffusion Equation ◽  
Diffusion Approximation ◽  
Cash Management ◽  
Central State ◽  
Transient Behaviour ◽  
Management Problems ◽  
Transient Probability ◽  
Birth Death

In economics, cash management problems may be modelled by birth-death processes which reset to central states when a boundary is reached. The nature of the transient behaviour of the probability distribution of such processes symmetric about a central state is investigated. A diffusion approximation of such processes is given and the transient probability behaviour derived from the diffusion equation.

On the transient behavior of the repairman problem

1991 ◽  
Vol 23 (02) ◽  
pp. 327-354 ◽  
Author(s):  
Charles Knessl
Keyword(s):  
Finite Population ◽  
Transient Behavior ◽  
Boundary Layer Theory ◽  
Asymptotic Approximations ◽  
Perturbation Techniques ◽  
Ray Method ◽  
Repair Rate ◽  
Repairman Problem ◽  
Transient Probability

We consider the repairman problem which corresponds to the finite population M/M/1 queue. Asymptotic approximations for the transient probability distribution of the number of broken machines constructed when the number M of machines is large and the service (repair) rate is also large, specifically, O(M). The approximations are constructed by using singular perturbation techniques such as the ray method, boundary layer theory, and the method of matched asymptotic expansions. Extensive numerical comparisons show the quality of our approximations.

scholarly journals Exact overflow asymptotics for queues with many Gaussian inputs

2003 ◽  
Vol 40 (3) ◽  
pp. 704-720 ◽  
Author(s):  
Krzysztof Dębicki ◽  
Michel Mandjes
Keyword(s):  
Brownian Motion ◽  
Gaussian Processes ◽  
Continuous Time ◽  
Time Horizon ◽  
Exact Results ◽  
Service Capacity ◽  
Stationary Increments ◽  
Overflow Probability ◽  
Finite Time Horizon ◽  
Transient Probability

In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.

scholarly journals Transient Probability Functions: A Sample Path Approach

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Michael L. Green ◽  
Alan Krinik ◽  
Carrie Mortensen ◽  
Gerardo Rubino ◽  
Randall J. Swift
Keyword(s):  
Markov Processes ◽  
Solution Method ◽  
Sample Path ◽  
Dual Processes ◽  
New Approach ◽  
Probability Functions ◽  
Counting Approach ◽  
International Audience ◽  
Path Counting ◽  
Transient Probability

International audience A new approach is used to determine the transient probability functions of Markov processes. This new solution method is a sample path counting approach and uses dual processes and randomization. The approach is illustrated by determining transient probability functions for a three-state Markov process. This approach also provides a way to calculate transient probability functions for Markov processes which have specific sample path characteristics.

scholarly journals Exact overflow asymptotics for queues with many Gaussian inputs

2003 ◽  
Vol 40 (03) ◽  
pp. 704-720 ◽  
Author(s):  
Krzysztof Dębicki ◽  
Michel Mandjes
Keyword(s):  
Brownian Motion ◽  
Gaussian Processes ◽  
Continuous Time ◽  
Time Horizon ◽  
Exact Results ◽  
Service Capacity ◽  
Stationary Increments ◽  
Overflow Probability ◽  
Finite Time Horizon ◽  
Transient Probability

In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.

scholarly journals Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture

2019 ◽  
Vol 151 (17) ◽  
pp. 174108 ◽  
Author(s):  
Jeremy Copperman ◽  
David Aristoff ◽  
Dmitrii E. Makarov ◽  
Gideon Simpson ◽  
Daniel M. Zuckerman
Keyword(s):  
Steady State ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Transient Probability ◽  
Non Equilibrium

Analysis of transient behaviour of certain processes with return to a central state

1983 ◽  
Vol 20 (1) ◽  
pp. 61-70 ◽  
Author(s):  
Peter G. Buckholtz ◽  
L. Lorne Campbell ◽  
Ross D. Milbourne ◽  
M. T. Wasan
Keyword(s):  
Probability Distribution ◽  
Diffusion Equation ◽  
Diffusion Approximation ◽  
Cash Management ◽  
Central State ◽  
Transient Behaviour ◽  
Management Problems ◽  
Transient Probability ◽  
Birth Death

In economics, cash management problems may be modelled by birth-death processes which reset to central states when a boundary is reached. The nature of the transient behaviour of the probability distribution of such processes symmetric about a central state is investigated. A diffusion approximation of such processes is given and the transient probability behaviour derived from the diffusion equation.

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