Markov Birth Research Articles

Performance modeling of the serial processes in refining system of a sugar plant using RAMD analysis

The main objective of this paper is to present a method to identify the critical component of the system. As traditionally, any one parameter among availability, reliability and maintainability parameters is computed to identify the critical component and its effect on performance of the system. In this paper, reliability, availability, maintainability and dependability (RAMD) parameters or indices are computed to identify the critical component of the system. Mathematical modeling of the system based on Markov birth–death process is carried out to derive Chapman–Kolmogorov differential equations. These equations are further solved and RAMD parameters are computed with mean time between failures (MTBF), mean time to repair (MTTR) and dependability ratio parameters for each component of the system. Sensitivity analysis has been conducted for finding the most critical component of the system by varying the failure and repair rates of each subsystem of the system. To show the application of the proposed method, a case of the refining system, a repairable industrial system of sugar plant has been taken for evaluating RAMD indices of the system.

The control safety of airborne local network in the information and calculating system of air cluster

The problem of stability of functioning of aviation airborne networks in the area of air cluster stands especially sharply in connection with the necessity of the absolute providing of safety of flights, exception of flying incidents and pre-conditions to them. This problem is aggravated from the continuous change of network structure are one airplanes as network elements are included in the area of responsibility of air cluster, other go out. This process is substantially non-stationary. For providing of safety of network at presence of external and internal preventing influences it is necessary not simply to promote power and information resources, but apply the optimum methods of control of reconfiguration of network. The mathematical models of Markov birth and death processes with non-stationary probabilities of transition are offered in work, which current status of local aviation airborne network of air cluster is described. The system of the Kolmogorov – Chapman equations for non-stationary probabilities of the state of network is eaten away. The method of Gaussian approximation of distributing of co-ordinates of the system in state space is applied

Mathematical modeling and reliability analysis of the serial processes in feeding system of a sugar plant

In this paper, a numerical method is proposed for the reliability analysis of serial processes in the feeding system of a sugar plant. The feeding system is a complex system and comprises of four repairable sub-systems viz. cutting system, crushing system, bagasse carrying system and heat generating system arranged in series or parallel configurations. Three sub-systems namely cutting system, bagasse carrying system and heat generating system are supported by standby units with perfect switch over devices. Mathematical modeling of the system based on Markov birth–death process is carried out to derive Chapman–Kolmogorov differential equations. These equations are solved by using the proposed method i.e. an adaptive step-size control Runge–Kutta method. The long-run availability, reliability and mean time between failures (MTBF) for the system are computed for performance analysis of the system. These results are presented and discussed with the plant personnel to adopt and practice suitable maintenance policies/strategies to enhance the performance of the feeding system of sugar plant.

The MJO in a Coarse-Resolution GCM with a Stochastic Multicloud Parameterization

Abstract The representation of the Madden–Julian oscillation (MJO) is still a challenge for numerical weather prediction and general circulation models (GCMs) because of the inadequate treatment of convection and the associated interactions across scales by the underlying cumulus parameterizations. One new promising direction is the use of the stochastic multicloud model (SMCM) that has been designed specifically to capture the missing variability due to unresolved processes of convection and their impact on the large-scale flow. The SMCM specifically models the area fractions of the three cloud types (congestus, deep, and stratiform) that characterize organized convective systems on all scales. The SMCM captures the stochastic behavior of these three cloud types via a judiciously constructed Markov birth–death process using a particle interacting lattice model. The SMCM has been successfully applied for convectively coupled waves in a simplified primitive equation model and validated against radar data of tropical precipitation. In this work, the authors use for the first time the SMCM in a GCM. The authors build on previous work of coupling the High-Order Methods Modeling Environment (HOMME) NCAR GCM to a simple multicloud model. The authors tested the new SMCM-HOMME model in the parameter regime considered previously and found that the stochastic model drastically improves the results of the deterministic model. Clear MJO-like structures with many realistic features from nature are reproduced by SMCM-HOMME in the physically relevant parameter regime including wave trains of MJOs that organize intermittently in time. Also one of the caveats of the deterministic simulation of requiring a doubling of the moisture background is not required anymore.

Availability analysis and performance optimization of a butter oil production system: a case study

This paper proposes a method for time dependent system availability (TDSA) analysis of butter oil production system and the performance of the system is optimized using genetic algorithm. The mathematical formulation of the system based on Markov birth–death process is carried out and first order Chapman–Kolmogorov differential equations are developed based on the assumption that the failure and repair rate of each subsystem follows exponential distribution. The proposed method i.e. an adaptive step-size control Runge–Kutta method is used to compute TDSA and mean time between failures for butter oil production system of a dairy plant. The butter oil production system is a complex system and comprises of seven repairable subsystems. The results are presented and discussed with the plant personnel to adopt and practice suitable maintenance policies/strategies to enhance the productivity and quality of butter oil.

Timing of pathogen adaptation to a multicomponent treatment.

The sustainable use of multicomponent treatments such as combination therapies, combination vaccines/chemicals, and plants carrying multigenic resistance requires an understanding of how their population-wide deployment affects the speed of the pathogen adaptation. Here, we develop a stochastic model describing the emergence of a mutant pathogen and its dynamics in a heterogeneous host population split into various types by the management strategy. Based on a multi-type Markov birth and death process, the model can be used to provide a basic understanding of how the life-cycle parameters of the pathogen population, and the controllable parameters of a management strategy affect the speed at which a pathogen adapts to a multicomponent treatment. Our results reveal the importance of coupling stochastic mutation and migration processes, and illustrate how their stochasticity can alter our view of the principles of managing pathogen adaptive dynamics at the population level. In particular, we identify the growth and migration rates that allow pathogens to adapt to a multicomponent treatment even if it is deployed on only small proportions of the host. In contrast to the accepted view, our model suggests that treatment durability should not systematically be identified with mutation cost. We show also that associating a multicomponent treatment with defeated monocomponent treatments can be more durable than associating it with intermediate treatments including only some of the components. We conclude that the explicit modelling of stochastic processes underlying evolutionary dynamics could help to elucidate the principles of the sustainable use of multicomponent treatments in population-wide management strategies intended to impede the evolution of harmful populations.

Performance Optimization for Skim Milk Powder Unit of a Dairy Plant Using Genetic Algorithm

The paper deals with the performance optimization for skim milk powder unit of a dairy plant at National Dairy Research Institute (N. D. R. I.), Karnal using Genetic Algorithm (G. A.). The skim milk powder unit comprises of six subsystems working in series. The failure and repair rates of the subsystems are taken from maintenance history sheets, which follow the exponential distribution. The mathematical formulation is carried out using probabilistic approach and the Markov birth – death process is used to develop the difference differential equations. The steady state availability expression has been derived using normalizing conditions. The optimal values of failure/repai r rates of each subsystem of the skim milk powder unit have been evaluated using Matlab 7.1 G. A. tool. The steady state availability obtained from Markov analysis is also compared with the optimal availability calculated through G. A. tool. So, the findings of the present paper will be highly useful to the plant management for developing proper maintenance strategies which can be implemented in order to enhance system performance.

Demand Side Management With Air Conditioner Loads Based on the Queuing System Model

This paper presents a novel load management technique for the air conditioner loads in large apartment complexes. Through systematic aggregations and load factor controls of the air conditioner loads based on a queuing system model and the Markov birth and death process, the proposed technique can offer effective and convenient load management measures to both the power companies and the customers. The customers' inconveniences or discomforts can be moderated by the aggregations plus the incentives based on the participation levels in the load management. A numerical example using the load data from a large apartment complex shows a good potential for future applications.

Reasonable routing in delay/disruption tolerant networks

Delay/disruption tolerant networking (DTN) is an approach to networking where intermittent connectivity exists: it is often afforded by a store and forward technique. Depending on the capability of intermediary nodes to carry and forward messages, messages can be eventually delivered to their destination by mobile nodes with an appropriate routing protocol. To have achieved a successful delivery, most DTN routing protocols use message duplication methods. Although messages are rapidly transferred to the destination, the redundancy in the number of message copies increases rapidly. This paper presents a new routing scheme based on a stochastic process for epidemic routing. Message redundancy is efficiently reduced and the number of message copies is controlled reasonably. During the contact process of nodes in the network, the number of message copies changes, and according to the variability in the number of copies, we construct a special Markov chain, birth and death process, on the number of message copies then calculate and obtain a stationary distribution of the birth and death process. Comparing the theoretical model with the simulation we have performed we see similar results. Our method improves on time-to-live (TTL) and antipacket methods, in both redundancy and delivery success efficiency.

A Markovian model for the hybrid manufacturing planning and control method ‘Double Speed Single Production Line’

In this paper, the hybrid production planning & control method Double Speed Single Production Line (DSSPL) is presented, modelled and its performances evaluated and compared to classical Production Planning and Control methods (PPC). DSSPL combines JIT/kanban and Material Requirement Planning for the production of different classes of products (A- and B-items based on a market or customer oriented analysis) on one single production line. By the use of a Markovian birth–death queuing model of a single-stage, two-product production system, the performance and the behavior of the basic DSSPL concept are analyzed and compared to the classical MRP concepts. Its capability to cope with limited resources is illustrated with an industrial case study where DSSPL has been implemented to solve coordination problems between a plastic molding feeder shop and the final assembly line of a micromotor producer.

큐잉모델에 기초한 자율 지능 부하 관리 시스템 연구

본 논문은 전력회사와 수용가가 실시간으로 상호 협력하면서 효율적으로 여름철 냉방부하를 관리하여 첨두부하를 저감하기 위한 기법에 대하여 기술한다. 전력회사가 필요 관리량을 수용가 측에 요청하면 부하관리 요청을 받은 수용가, 예를 들면 대규모 아파트 단지의 중앙 지능관리 서버(Central Intelligent Management Server: CIMS)가 자율적인 관리를 통하여 요구받은 관리전력 이내로 부하율을 조정하도록 한다. 부하율을 관리하기 위한 수단으로 CIMS는 필요 관리 부하전력에 따라 냉방기를 가동할 수 있는 권리에 해당하는 적정 수의 토큰(Token)을 발행하고 각 세대내의 냉방기를 제어할 수 있는 다수의 로컬 지능관리 서버(Local Intelligent Management Server: LIMS)들이 각 집안의 상황에 따라 냉방기를 가동하기 원할 경우에 전체 관리 서버에게 냉방기를 가동할 수 있는 권리에 해당하는 토큰을 요청하도록 한다. CIMS는 LIMS들의 토큰 요청을 관리하기 위한 큐(Queue)를 구성하여 관리하고 토큰을 요구한 각 LIMS들은 토큰을 할당받는 대로 자신이 담당하는 세대내의 냉방기를 가동하고 일정조건이 만족되면 자율 또는 타율로 토큰을 반납하여 큐에서 기다리는 다른 LIMS들에게도 토큰이 할당될 수 있도록 한다. 큐 운영 정책에 다양한 냉방기 운용 환경 정보를 반영하고 CIMS와 LIMS간에 원만한 상호 협력을 위하여 지능형 멀티 에이전트(Muti-Agent) 시스템으로 구성하고, 이들을 계층구조의 네트워크로 연결하였다. 제안하는 기법을 서울의 한 아파트단지의 여름철 전력수요 데이터를 예로 하여 예상되는 대기 시간과 지원 받을 수 있는 전력요금 규모를 산정해 보았으며, 비교적 적은 수용가의 불편으로 큰 부하관리 효과를 얻을 수 있는 것을 알 수 있었다.

Functional-integral based perturbation theory for the Malthus-Verhulst process

We apply a functional-integral formalism for Markovian birth and death processes to determine asymptotic corrections to mean-field theory in the Malthus-Verhulst process (MVP). Expanding about the stationary mean-field solution, we identify an expansion parameter that is small in the limit of large mean population, and derive a diagrammatic expansion in powers of this parameter. The series is evaluated to fifth order using computational enumeration of diagrams. Although the MVP has no stationary state, we obtain good agreement with the associated {\it quasi-stationary} values for the moments of the population size, provided the mean population size is not small. We compare our results with those of van Kampen's $\Omega$-expansion, and apply our method to the MVP with input, for which a stationary state does exist.

A general approach to modeling and analysis of species abundance data with extra zeros

A general method for the analysis of ecological count data with extra zeros is presented using a Markov birth process representation of discrete distributions. The method uses a nonparametric formulation of the birth process to model the residual variation and therefore allows the data to play a greater role in determining an appropriate distribution. This enables a more critical assessment of covariate effects and more accurate predictions to be made. The approach is also presented as a useful diagnostic tool for suggesting appropriate parametric models or verifying standard models. As an illustrative example, data describing abundance of a species of possum from the montane ash forests of the central highlands of Victoria, southeast Australia, is considered.

Iterated birth and death process as a model of radiation cell survival

The iterated birth and death process is defined as an n-fold iteration of a stochastic process consisting of the combination of instantaneous random killing of individuals in a certain population with a given survival probability s with a Markov birth and death process describing subsequent population dynamics. A long standing problem of computing the distribution of the number of clonogenic tumor cells surviving a fractionated radiation schedule consisting of n equal doses separated by equal time intervals τ is solved within the framework of iterated birth and death processes. For any initial tumor size i, an explicit formula for the distribution of the number M of surviving clonogens at moment τ after the end of treatment is found. It is shown that if i → ∞ and s → 0 so that is n tends to a finite positive limit, the distribution of random variable M converges to a probability distribution, and a formula for the latter is obtained. This result generalizes the classical theorem about the Poisson limit of a sequence of binomial distributions. The exact and limiting distributions are also found for the number of surviving clonogens immediately after the nth exposure. In this case, the limiting distribution turns out to be a Poisson distribution.

Stochastic Modelling of the Invasion Process of Nematodes in Fly Larvae

SUMMARY Stochastic models based on Markov birth processes are constructed to describe the process of invasion of a fly larva by entomopathogenic nematodes. Various forms for the birth (invasion) rates are proposed. These models are then fitted to data sets describing the observed numbers of nematodes that have invaded a fly larva after a fixed period of time. Non-linear birth-rates are required to achieve good fits to these data, with their precise form leading to different patterns of invasion being identified for three populations of nematodes considered. One of these (Nemasys) showed the greatest propensity for invasion. This form of modelling may be useful more generally for analysing data that show variation which is different from that expected from a binomial distribution.

Divergent growth processes

Here we consider the general Markov birth process X(t), If the birth rate is sufficiently large, such a process may diverge in the sense that P(X(t) = ∞) > 0. Interest then focuses on the size of the population conditional on its remaining finite, We find the asymptotic distribution of the population in these circumstances, enabling us to determine whether the conditional moments are finite or not. These results resolve some conjectures of Roehner (1986).

A non-Markovian birth process with logarithmic growth

I show that the sum of independent random variables converges in distribution when suitably normalised, so long as the Xk satisfy the following two conditions: μ(n)= E |Xn| is comparable with E |Sn| for large n, and Xk/μ(k) converges in distribution. Also I consider the associated birth process X(t) = max{n: Sn ≦ t} when each Xk is positive, and I show that there exists a continuous increasing function v(t) such that for some variable Y with specified distribution, and for almost all u. The function v, satisfies v (t) = A (1 + o (t)) log t. The Markovian birth process with parameters λn = λn, where 0 < λ < 1, is an example of such a process.

A non-Markovian birth process with logarithmic growth

I show that the sumof independent random variables converges in distribution when suitably normalised, so long as theXksatisfy the following two conditions:μ(n)= E |Xn|is comparable withE|Sn| for largen,andXk/μ(k) converges in distribution. Also I consider the associated birth processX(t) = max{n:Sn≦t} when eachXkis positive, and I show that there exists a continuous increasing functionv(t) such thatfor some variableYwith specified distribution, and for almost allu. The functionv, satisfiesv(t) =A(1 +o(t)) logt. The Markovian birth process with parameters λn= λn, where 0 < λ < 1, is an example of such a process.

Modes of growth of counting processes with increasing arrival rates

Jumping processes which grow by unit jumps, with decreasing sojourn times between successive jumps, are studied. Markovian birth processes, non-Markovian branching processes, and some generalizations of these are special cases. Three classes are described, in one of which growth is explosive, in the second asymptotically continuous, and in the third oscillatory. A theorem is proved which gives an explicit functional expression in the asymptotically continuous case, and borderline cases between the classes are investigated.

Modes of growth of counting processes with increasing arrival rates

Jumping processes which grow by unit jumps, with decreasing sojourn times between successive jumps, are studied. Markovian birth processes, non-Markovian branching processes, and some generalizations of these are special cases. Three classes are described, in one of which growth is explosive, in the second asymptotically continuous, and in the third oscillatory. A theorem is proved which gives an explicit functional expression in the asymptotically continuous case, and borderline cases between the classes are investigated.