Nonlinearly Perturbed Birth-Death-Type Semi-Markov Processes

2017 ◽  
pp. 81-106
Author(s):  
Dmitrii Silvestrov ◽  
Sergei Silvestrov
Keyword(s):  
Markov Processes ◽  
Semi Markov Processes ◽  
Birth Death

Filtering of Markov renewal queues, III: semi-Markov processes embedded in feedback queues

1984 ◽  
Vol 16 (2) ◽  
pp. 422-436 ◽  
Author(s):  
Jeffrey J. Hunter
Keyword(s):  
Markov Processes ◽  
Queue Length ◽  
Markov Renewal Process ◽  
Bernoulli Feedback ◽  
State Dependent ◽  
Special Cases ◽  
Transition Points ◽  
Semi Markov Processes ◽  
Feedback Queues ◽  
Birth Death

In Part I (Hunter) a study of feedback queueing models was initiated. For such models the queue-length process embedded at all transition points was formulated as a Markov renewal process (MRP). This led to the observation that the queue-length processes embedded at any of the ‘arrival', ‘departure', ‘feedback', ‘input', ‘output' or ‘external' transition epochs are also MRP. Part I concentrated on the properties of the embedded discrete-time Markov chains. In this part we examine the semi-Markov processes associated with each of these embedded MRP and derive expressions for the stationary distributions associated with their irreducible subspaces. The special cases of birth-death queues with instantaneous state-dependent feedback, M/M/1/N and M/M/1 queues with instantaneous Bernoulli feedback are considered in detail. The results obtained complement those derived in Part II (Hunter) for birth-death queues without feedback.

Filtering of Markov renewal queues, III: semi-Markov processes embedded in feedback queues

1984 ◽  
Vol 16 (02) ◽  
pp. 422-436 ◽  
Author(s):  
Jeffrey J. Hunter
Keyword(s):  
Markov Processes ◽  
Queue Length ◽  
Markov Renewal Process ◽  
Bernoulli Feedback ◽  
State Dependent ◽  
Special Cases ◽  
Transition Points ◽  
Semi Markov Processes ◽  
Feedback Queues ◽  
Birth Death

In Part I (Hunter) a study of feedback queueing models was initiated. For such models the queue-length process embedded at all transition points was formulated as a Markov renewal process (MRP). This led to the observation that the queue-length processes embedded at any of the ‘arrival', ‘departure', ‘feedback', ‘input', ‘output' or ‘external' transition epochs are also MRP. Part I concentrated on the properties of the embedded discrete-time Markov chains. In this part we examine the semi-Markov processes associated with each of these embedded MRP and derive expressions for the stationary distributions associated with their irreducible subspaces. The special cases of birth-death queues with instantaneous state-dependent feedback, M/M/1/N and M/M/1 queues with instantaneous Bernoulli feedback are considered in detail. The results obtained complement those derived in Part II (Hunter) for birth-death queues without feedback.

scholarly journals Quantum Semi-Markov Processes

2008 ◽  
Vol 101 (14) ◽  
Author(s):  
Heinz-Peter Breuer ◽  
Bassano Vacchini
Keyword(s):  
Markov Processes ◽  
Semi Markov Processes

scholarly journals A continuous-time semi-markov bayesian belief network model for availability measure estimation of fault tolerant systems

2008 ◽  
Vol 28 (2) ◽  
pp. 355-375 ◽  
Author(s):  
Márcio das Chagas Moura ◽  
Enrique López Droguett
Keyword(s):  
Hybrid Model ◽  
Markov Processes ◽  
Continuous Time ◽  
Fault Tolerant ◽  
Numerical Procedure ◽  
Bayesian Belief Networks ◽  
Operational Conditions ◽  
Fault Tolerant Systems ◽  
Semi Markov Processes ◽  
Availability Measure

In this work it is proposed a model for the assessment of availability measure of fault tolerant systems based on the integration of continuous time semi-Markov processes and Bayesian belief networks. This integration results in a hybrid stochastic model that is able to represent the dynamic characteristics of a system as well as to deal with cause-effect relationships among external factors such as environmental and operational conditions. The hybrid model also allows for uncertainty propagation on the system availability. It is also proposed a numerical procedure for the solution of the state probability equations of semi-Markov processes described in terms of transition rates. The numerical procedure is based on the application of Laplace transforms that are inverted by the Gauss quadrature method known as Gauss Legendre. The hybrid model and numerical procedure are illustrated by means of an example of application in the context of fault tolerant systems.

Cumulative constrained sojourn times in semi-Markov processes with an application to pensionable service

1978 ◽  
Vol 15 (3) ◽  
pp. 531-542 ◽  
Author(s):  
Izzet Sahin
Keyword(s):  
Markov Processes ◽  
Sojourn Time ◽  
Working Life ◽  
Partial Coverage ◽  
Sojourn Times ◽  
Semi Markov Processes

This paper is concerned with the characterization of the cumulative pensionable service over an individual's working life that is made up of random lengths of service in different employments in a given industry, under partial coverage, transferability, and a uniform vesting rule. This characterization uses some results that are developed in the paper involving a functional and cumulative constrained sojourn times (constrained in the sense that if a sojourn time is less than a given constant it is not counted) in semi-Markov processes.

Nonlinearly Perturbed Semi-Markov Processes

2017 ◽  
Author(s):  
Dmitrii Silvestrov ◽  
Sergei Silvestrov
Keyword(s):  
Markov Processes ◽  
Semi Markov Processes
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