Analysing performance-based contract for manufacturing systems using absorbing state Markov chain

2017 ◽  
Vol 9 (1) ◽  
pp. 37
Author(s):  
Pradipta Patra ◽  
U. Dinesh Kumar
Keyword(s):  
Markov Chain ◽  
Manufacturing Systems ◽  
Absorbing State

On the age distribution of a Markov chain

1978 ◽  
Vol 15 (1) ◽  
pp. 65-77 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Limit Theorems ◽  
Age Distribution ◽  
Weak Limit ◽  
Absorbing State ◽  
Absorbing Markov Chain ◽  
Continuous Random Walk ◽  
A Chain ◽  
Watson Process

This paper develops the notion of the limiting age of an absorbing Markov chain, conditional on the present state. Chains with a single absorbing state {0} are considered and with such a chain can be associated a return chain, obtained by restarting the original chain at a fixed state after each absorption. The limiting age, A(j), is the weak limit of the time given Xn = j (n → ∞).A criterion for the existence of this limit is given and this is shown to be fulfilled in the case of the return chains constructed from the Galton–Watson process and the left-continuous random walk. Limit theorems for A (J) (J → ∞) are given for these examples.

On the age distribution of a Markov chain

1978 ◽  
Vol 15 (01) ◽  
pp. 65-77 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Limit Theorems ◽  
Age Distribution ◽  
Weak Limit ◽  
Absorbing State ◽  
Absorbing Markov Chain ◽  
Continuous Random Walk ◽  
A Chain ◽  
Watson Process

This paper develops the notion of the limiting age of an absorbing Markov chain, conditional on the present state. Chains with a single absorbing state {0} are considered and with such a chain can be associated a return chain,obtained by restarting the original chain at a fixed state after each absorption. The limiting age,A(j), is the weak limit of the timegivenXn=j(n → ∞).A criterion for the existence of this limit is given and this is shown to be fulfilled in the case of the return chains constructed from the Galton–Watson process and the left-continuous random walk. Limit theorems forA(J) (J →∞) are given for these examples.

FUNDAMENTAL MATRIX OF TRANSIENT QBD GENERATOR WITH FINITE STATES AND LEVEL DEPENDENT TRANSITIONS

2009 ◽  
Vol 26 (05) ◽  
pp. 697-714 ◽  
Author(s):  
YANG WOO SHIN
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Fundamental Matrix ◽  
Transient State ◽  
Matrix Product ◽  
Absorbing State ◽  
Finite State ◽  
Qbd Process ◽  
Characteristic Values ◽  
Absorption Probabilities

Fundamental matrix plays an important role in a finite-state Markov chain to find many characteristic values such as stationary distribution, expected amount of time spent in the transient state, absorption probabilities. In this paper, the fundamental matrix of the finite-state quasi-birth-and-death (QBD) process with absorbing state and level dependent transitions is considered. We show that each block component of the fundamental matrix can be expressed as a matrix product form and present an algorithm for computing the fundamental matrix. Some applications with numerical results are also presented.

Effect of Failure Rate on the Availability Analysis of Nestle CERELAC Plant Using Markov Chain Method

2018 ◽  
pp. 121-127
Author(s):  
Gurbinder Singh ◽  
Rakesh Kumar
Keyword(s):  
Markov Chain ◽  
Manufacturing Systems ◽  
Production Systems ◽  
Research Work ◽  
Automated Production ◽  
Availability Analysis ◽  
Long Run ◽  
Machine Reliability ◽  
Markov Chain Method

In the performance analysis of production systems by using the traditional methods of engineering the knowledge of machine reliability factors is assumed to be precisely known. The current study entitled performance evaluation of food industry in India. To analyze and determine the availability of plant a case study has been undertaken from Moga Nestle food private limited industry in India. Various studies evaluating the performance of automated production systems with the help of modeling and simulation and analytical methods have always given priority to steady state performance as compared to transient performance. Production systems in which such kind of situations arises include systems with dysfunctional states and deadlocks, not stable queuing systems. This research work presents an approach for analyzing the performance of unreliable manufacturing systems that take care of uncertain machine factor estimates. The method that is being proposed is on the basis of Markov chain and probability density function discretization techniques for studying manufacture lines consist unreliable machines. To determine the performance of plant, important information has been collected from different systems and subsystems to find out long run availability of whole system.

Stochastic Approach for Determining Stable Coalition Structure

2015 ◽  
Vol 17 (04) ◽  
pp. 1550009 ◽  
Author(s):  
Elena Parilina ◽  
Artem Sedakov
Keyword(s):  
Markov Chain ◽  
Nash Equilibrium ◽  
Special Form ◽  
Stochastic Game ◽  
Coalition Structure ◽  
Stochastic Approach ◽  
Tu Games ◽  
Absorbing State ◽  
Stable Coalition ◽  
Definition Of

In this paper, we study TU-games with coalition structure and propose an approach for determining a stable coalition structure solving a stochastic game of a special form. Using a Nash equilibrium in this game, we draw an analogy between the stable coalition structure and an absorbing state in a Markov chain. In addition, we consider a case of restricted coalitions assuming that not all coalitions are feasible and extend the definition of the stable coalition structure to this case.

scholarly journals Analysis of Closed Queueing Networks with Batch Service

2020 ◽  
Vol 20 (4) ◽  
pp. 527-533
Author(s):  
Elena P. Stankevich ◽  
◽  
Igor E. Tananko ◽  
Vitalii I. Dolgov ◽  
◽  
...  
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Queueing Networks ◽  
Manufacturing Systems ◽  
Queueing Network ◽  
Transport Systems ◽  
Batch Service ◽  
Single Server ◽  
Closed Queueing Networks ◽  
Number Of Customers

We consider a closed queuing network with batch service and movements of customers in continuous time. Each node in the queueing network is an infinite capacity single server queueing system under a RANDOM discipline. Customers move among the nodes following a routing matrix. Customers are served in batches of a fixed size. If a number of customers in a node is less than the size, the server of the system is idle until the required number of customers arrive at the node. An arriving at a node customer is placed in the queue if the server is busy. The batсh service time is exponentially distributed. After a batсh finishes its execution at a node, each customer of the batch, regardless of other customers of the batch, immediately moves to another node in accordance with the routing probability. This article presents an analysis of the queueing network using a Markov chain with continuous time. The qenerator matrix is constructed for the underlying Markov chain. We obtain expressions for the performance measures. Some numerical examples are provided. The results can be used for the performance analysis manufacturing systems, passenger and freight transport systems, as well as information and computing systems with parallel processing and transmission of information.

scholarly journals Stochastic analysis of a single server unreliable queue with balking and general retrial time

2020 ◽  
Vol 28 (4) ◽  
pp. 319-326
Author(s):  
Mohamed Boualem
Keyword(s):  
Markov Chain ◽  
Cognitive Radio ◽  
Stochastic Analysis ◽  
Manufacturing Systems ◽  
Cognitive Radio Network ◽  
Stochastic Orders ◽  
Embedded Markov Chain ◽  
Single Server ◽  
Radio Network ◽  
If Current

In this investigation, we consider an M/G/1 queue with general retrial times allowing balking and server subject to breakdowns and repairs. In addition, the customer whose service is interrupted can stay at the server waiting for repair or leave and return while the server is being repaired. The server is not allowed to begin service on other customers until the current customer has completed service, even if current customer is temporarily absent. This model has a potential application in various fields, such as in the cognitive radio network and the manufacturing systems, etc. The methodology is strongly based on the general theory of stochastic orders. Particularly, we derive insensitive bounds for the stationary distribution of the embedded Markov chain of the considered system.

Application of Model Predictive Control to Control Transient Behavior in Stochastic Manufacturing System Models

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Alireza Fazlirad ◽  
Theodor Freiheit
Keyword(s):  
Optimal Control ◽  
Markov Chain ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Manufacturing Systems ◽  
Manufacturing System ◽  
Transient Behavior ◽  
Research Area ◽  
State Planning ◽  
Expected Performance

Increasing complexity in manufacturing strategies and swift changes in market and consumer requirements have driven recent studies of manufacturing systems, with transient behavior being identified as a key research area. Till date, satisfying consumer demand has focused on steady-state planning of production, mostly using stochastic or deterministic optimal control methods. Due to the difficulty of obtaining optimal control for many practical situations, as well as in evaluating performance under optimal control, these studies have not been conducive to the analysis or control of transient behavior. This paper bridges this gap by applying model predictive control to a manufacturing system modeled as a discrete-time Markov chain. By modifying the initiation of production as probabilities within the Markov chain, a method is proposed to directly control the system to specific expected performance levels and improve its stochastic transient behavior.

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