Asymptotic performance of a multistate coherent system

1988 ◽  
Vol 20 (1) ◽  
pp. 241-243 ◽  
Author(s):  
Srinivas Iyer
Keyword(s):  
Steady State ◽  
Markov Process ◽  
Coherent System ◽  
Renewal Processes ◽  
Asymptotic Performance ◽  
System Availability ◽  
Performance Function ◽  
Semi Markov Process ◽  
Mutually Independent ◽  
Steady State Performance

An expression for the asymptotic or steady-state performance function is derived for a multistate coherent system when each component changes states in time according to a semi-Markov process, the stochastic processes being mutually independent. This generalizes the expression for system availability of a binary coherent system when the components are governed by mutually independent alternating renewal processes.

scholarly journals Asymptotic performance of a multistate coherent system

1988 ◽  
Vol 20 (01) ◽  
pp. 241-243 ◽  
Author(s):  
Srinivas Iyer
Keyword(s):  
Steady State ◽  
Markov Process ◽  
Coherent System ◽  
Renewal Processes ◽  
Asymptotic Performance ◽  
System Availability ◽  
Performance Function ◽  
Semi Markov Process ◽  
Mutually Independent ◽  
Steady State Performance

An expression for the asymptotic or steady-state performance function is derived for a multistate coherent system when each component changes states in time according to a semi-Markov process, the stochastic processes being mutually independent. This generalizes the expression for system availability of a binary coherent system when the components are governed by mutually independent alternating renewal processes.

Loss tandem networks with blocking - a semi-Markov approach

2010 ◽  
Vol 58 (4) ◽  
pp. 673-681
Author(s):  
W. Oniszczuk
Keyword(s):  
Steady State ◽  
Markov Process ◽  
Markov Model ◽  
Markov Models ◽  
State Graph ◽  
State Equations ◽  
Semi Markov Process ◽  
Tandem Networks ◽  
Measures Of Effectiveness

Loss tandem networks with blocking - a semi-Markov approachBased on the semi-Markov process theory, this paper describes an analytical study of a loss multiple-server two-station network model with blocking. Tasks arrive to the tandem in a Poisson fashion at a rate λ, and the service times at the first and second stations are non-exponentially distributed with means sAand sB, respectively. Between these two stations there is a buffer with finite capacity. In this type of network, if the buffer is full, the accumulation of new tasks (jobs) by the second station is temporarily suspended (blocking factor) and tasks must wait on the first station until the transmission process is resumed. Any new task that finds all service lines at the first station occupied is turned away and is lost (loss factor). Initially, in this document, a Markov model of the loss tandem with blocking is investigated. Here, a two-dimensional state graph is constructed and a set of steady-state equations is created. These equations allow the calculation of state probabilities for each graph state. A special algorithm for transforming the Markov model into a semi-Markov process is presented. This approach allows calculating steady-state probabilities in the semi-Markov model. In the next part of the paper, the algorithms for calculation of the main measures of effectiveness in the semi-Markov model are presented. Finally, the numerical part of this paper contains an investigation of some special semi-Markov models, where the results are presented of the calculation of the quality of service (QoS) parameters and the main measures of effectiveness.

On the entropy for semi-Markov processes

2003 ◽  
Vol 40 (4) ◽  
pp. 1060-1068 ◽  
Author(s):  
Valerie Girardin ◽  
Nikolaos Limnios
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Relative Entropy ◽  
Continuous Time ◽  
Entropy Rate ◽  
Renewal Processes ◽  
Semi Markov Process ◽  
Continuous Time Processes ◽  
Semi Markov Processes ◽  
Jump Markov Processes

The aim of this paper is to define the entropy of a finite semi-Markov process. We define the entropy of the finite distributions of the process, and obtain explicitly its entropy rate by extending the Shannon–McMillan–Breiman theorem to this class of nonstationary continuous-time processes. The particular cases of pure jump Markov processes and renewal processes are considered. The relative entropy rate between two semi-Markov processes is also defined.

Redundancy Allocation for Multistate Systems With Component Dependencies and Load Sharing

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Jing Wang ◽  
Mian Li
Keyword(s):  
Markov Process ◽  
Process Model ◽  
Load Sharing ◽  
Two Component System ◽  
System Availability ◽  
Redundancy Allocation ◽  
Markov Process Model ◽  
Dependent Failures ◽  
Binary State ◽  
Semi Markov Process

Binary-state and component independent assumptions will lead to doubtful and misleading redundancy allocation schemes which may not satisfy the reliability requirements for real engineering applications. Most published works proposed methods to remove the first assumption by studying the degradation cases where multiple states of a component are from the best state to the degradation states then to the completely failed state. Fewer works focused on removing the second assumption and they only discussed dependent failures which are only a special case of component dependency. This work uses the Semi-Markov process to describe a two-component system for redundancy allocation. In this work, multiple states of a component are represented by multiple output levels, which are beyond the scope of degradation, and the component dependency is not limited to failure dependency only. The load sharing is also taken care of in the proposed work. The optimal redundancy allocation scheme is obtained by solving the corresponding redundancy allocation optimization problem with the reliability measure, the system availability, obtained through the Semi-Markov process model being constraint. Two case studies are presented, demonstrating the applicability of the propose method.

scholarly journals Semi-Markov-Based Approach for the Analysis of Open Tandem Networks with Blocking and Truncation

2009 ◽  
Vol 19 (1) ◽  
pp. 151-164 ◽  
Author(s):  
Walenty Oniszczuk
Keyword(s):  
Steady State ◽  
Markov Process ◽  
Markov Model ◽  
Markov Models ◽  
Network Models ◽  
State Graph ◽  
State Equations ◽  
Semi Markov Process ◽  
Tandem Networks ◽  
Measures Of Effectiveness

Semi-Markov-Based Approach for the Analysis of Open Tandem Networks with Blocking and TruncationThis paper describes an analytical study of open two-node (tandem) network models with blocking and truncation. The study is based on semi-Markov process theory, and network models assume that multiple servers serve each queue. Tasks arrive at the tandem in a Poisson fashion at the rate λ, and the service times at the first and the second node are non-exponentially distributed with meanssAandsB, respectively. Both nodes have buffers with finite capacities. In this type of network, if the second buffer is full, the accumulation of new tasks by the second node is temporarily suspended (a blocking factor) and tasks must wait on the first node until the transmission process is resumed. All new tasks that find the first buffer full are turned away and are lost (a truncation factor). First, a Markov model of the tandem is investigated. Here, a two-dimensional state graph is constructed and a set of steady-state equations is created. These equations allow calculating state probabilities for each graph state. A special algorithm for transforming the Markov model into a semi-Markov process is presented. This approach allows calculating steady-state probabilities in the semi-Markov model. Next, the algorithms for calculating the main measures of effectiveness in the semi-Markov model are presented. In the numerical part of this paper, the author investigates examples of several semi-Markov models. Finally, the results of calculating both the main measures of effectiveness and quality of service (QoS) parameters are presented.

On the entropy for semi-Markov processes

2003 ◽  
Vol 40 (04) ◽  
pp. 1060-1068 ◽  
Author(s):  
Valerie Girardin ◽  
Nikolaos Limnios
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Relative Entropy ◽  
Continuous Time ◽  
Entropy Rate ◽  
Renewal Processes ◽  
Semi Markov Process ◽  
Continuous Time Processes ◽  
Semi Markov Processes ◽  
Jump Markov Processes

The aim of this paper is to define the entropy of a finite semi-Markov process. We define the entropy of the finite distributions of the process, and obtain explicitly its entropy rate by extending the Shannon–McMillan–Breiman theorem to this class of nonstationary continuous-time processes. The particular cases of pure jump Markov processes and renewal processes are considered. The relative entropy rate between two semi-Markov processes is also defined.

Quasi-steady-state performance of a heat pipe subjected to transient acceleration loadings

10.2514/3.895 ◽  
1997 ◽  
Vol 11 ◽  
pp. 306-309 ◽  
Author(s):  
Edwin H. Olmstead ◽  
Edward S. Taylor ◽  
Meng Wang ◽  
Parviz Moin ◽  
Scott K. Thomas ◽  
...  
Keyword(s):  
Steady State ◽  
Heat Pipe ◽  
Quasi Steady State ◽  
Steady State Performance
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