scholarly journals Reliability of a Clustered-Task Server under Modulated Correlation

2017 ◽  
Vol 6 (2) ◽  
pp. 93
Author(s):  
Rachel Lunde Traylor ◽  
Andrzej Korzeniowski
Keyword(s):  
Resource Allocation ◽  
Random Process ◽  
Explicit Form ◽  
Continuous Time ◽  
Traffic Management ◽  
Survival Function ◽  
Large Area ◽  
Task Selection ◽  
Reliability Models ◽  
Server Reliability

Server resource allocation and traffic management is a large area of research and business concern in order to ensure proper functionality and maintenance procedures. As a result, good server reliability models that can incorporate workload and traffic stress are necessary. This paper generalizes previous dynamic server reliability models for partitioned servers with clustered-task selection by relaxing the assumption that the correlation between channels in the server remain constant. We allow the correlation to vary deterministically with time, or as a function of a random process in discrete or continuous time. The explicit form of the survival function is derived in such cases. Numerical illustrations demonstrate the dangers of erroneously assuming independence among channels, which can lead to costly and unnecessary interventions in the system. In addition, we numerically explore the effects of a variable correlation on the survival function.

scholarly journals Period-Life of a Branching Process with Migration and Continuous Time

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 868
Author(s):  
Khrystyna Prysyazhnyk ◽  
Iryna Bazylevych ◽  
Ludmila Mitkova ◽  
Iryna Ivanochko
Keyword(s):  
Random Process ◽  
Generating Function ◽  
Continuous Time ◽  
Branching Process ◽  
Probability Generating Function ◽  
Time Interval ◽  
The Moment ◽  
First Time ◽  
Critical Branching Process ◽  
Number Of Particles

The homogeneous branching process with migration and continuous time is considered. We investigated the distribution of the period-life τ, i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time. The probability generating function of the random process, which describes the behavior of the process within the period-life, was obtained. The boundary theorem for the period-life of the subcritical or critical branching process with migration was found.

Sojourn times, exit times and jitter in multivariate Markov processes

1974 ◽  
Vol 6 (04) ◽  
pp. 747-756 ◽  
Author(s):  
J. Keilson
Keyword(s):  
Continuous Time ◽  
Exit Time ◽  
Survival Function ◽  
Transient Behavior ◽  
Reliability Theory ◽  
Exit Times ◽  
Sojourn Times ◽  
Ergodic Distribution ◽  
Stationary Markov Process ◽  
Good Set

To treat the transient behavior of a system modeled by a stationary Markov process in continuous time, the state space is partitioned into good and bad states. The distribution of sojourn times on the good set and that of exit times from this set have a simple renewal theoretic relationship. The latter permits useful bounds on the exit time survival function obtainable from the ergodic distribution of the process. Applications to reliability theory and communication nets are given.

ABR traffic management using minimal resource allocation (neural) networks

2002 ◽  
Vol 25 (1) ◽  
pp. 9-20 ◽  
Author(s):  
N. Hock Soon ◽  
N. Sundararajan ◽  
P. Saratchandran
Keyword(s):  
Neural Networks ◽  
Resource Allocation ◽  
Traffic Management ◽  
Minimal Resource

ENHANCING SAFETY IN SHIP'S CRITICAL SYSTEMS USING MARKOV MODELING

2009 ◽  
Vol 16 (01) ◽  
pp. 59-72
Author(s):  
EVANGELOS MENNIS ◽  
AGAPIOS PLATIS ◽  
NIKITAS NIKITAKOS ◽  
JEAN GUY FONTAINE
Keyword(s):  
Continuous Time ◽  
Markov Models ◽  
Markov Modeling ◽  
Critical Systems ◽  
System Failures ◽  
Reliability Models ◽  
Sea Pollution ◽  
System A ◽  
Bilge Water ◽  
Water Separator

The current study uses reliability models for the improvement of the operation of a ship's "bilge — water separator" system. A "bilge-water separator" is a mechanism which cleans and inspects the ship's bilge water before it is discharged into the sea. Homogeneous continuous time Markov models have been used to record and estimate possible hazards and system failures in two different operational scenarios. If the photocell unit of the system fails, the ship may cause severe sea pollution. This study attempts to estimate the probability of sea pollution based on empirical data. In addition, the results of the model are compared with those of a system in which a second metering unit is added in an effort to to find out if this alteration improves the systems' efficiency.

Sojourn times, exit times and jitter in multivariate Markov processes

1974 ◽  
Vol 6 (4) ◽  
pp. 747-756 ◽  
Author(s):  
J. Keilson
Keyword(s):  
Continuous Time ◽  
Exit Time ◽  
Survival Function ◽  
Transient Behavior ◽  
Reliability Theory ◽  
Exit Times ◽  
Sojourn Times ◽  
Ergodic Distribution ◽  
Stationary Markov Process ◽  
Good Set

To treat the transient behavior of a system modeled by a stationary Markov process in continuous time, the state space is partitioned into good and bad states. The distribution of sojourn times on the good set and that of exit times from this set have a simple renewal theoretic relationship. The latter permits useful bounds on the exit time survival function obtainable from the ergodic distribution of the process. Applications to reliability theory and communication nets are given.

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