scholarly journals Analysis of Queueing System MMPP/M/K/K with Delayed Feedback

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1128 ◽  
Author(s):  
Agassi Melikov ◽  
Sevinj Aliyeva ◽  
Janos Sztrik
Keyword(s):  
Numerical Experiments ◽  
Queueing System ◽  
Three Dimensional ◽  
Delayed Feedback ◽  
State Dependent ◽  
Repeated Calls ◽  
Markov Modulated Poisson Process ◽  
Markov Modulated ◽  
Steady State Probabilities ◽  
Dependent Probability

The model of multi-channel queuing system with Markov modulated Poisson process (MMPP) flow and delayed feedback is considered. After the customer is served completely, they will decide either to join the retrial group again for another service (feedback) with some state-dependent probability or to leave the system forever with complimentary probability. Feedback calls organize an orbit of repeated calls (r-calls). If upon arrival of an r-call all the channels of the system are busy, then it either leaves the system with some state-dependent probability or with a complementary probability returns to orbit. Methods to calculate the steady-state probabilities of the appropriate three-dimensional Markov chain as well as performance measures of investigated system are developed. Results of numerical experiments are demonstrated.

scholarly journals Retrial Queues with Unreliable Servers and Delayed Feedback

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2415
Author(s):  
Agassi Melikov ◽  
Sevinj Aliyeva ◽  
Janos Sztrik
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Delayed Feedback ◽  
Retrial Queues ◽  
Bernoulli Feedback ◽  
Bernoulli Scheme ◽  
Multi Server ◽  
Steady State Probabilities

In this paper, models of unreliable multi-server retrial queues with delayed feedback are examined. The Bernoulli retrial is allowed upon the arrival of both primary (from outside) and feedback customers (from orbit), as well as the Bernoulli feedback that may occur after each service in this system. Servers can break down both during the service of customers and when they are idle. If a server breaks down during the service of a customer, then the interrupted customer, in accordance with the Bernoulli scheme, decides either to leave the system or join a common orbit of retrial and feedback customers. An approximate method, based on the space merging approach of three-dimensional Markov chains, is proposed for the calculation of the steady-state probabilities, as well as performance measures of the system. The results of the numerical experiments are demonstrated.

scholarly journals Analysis of Instantaneous Feedback Queue with Heterogeneous Servers

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2186
Author(s):  
Agassi Melikov ◽  
Sevinj Aliyeva ◽  
János Sztrik
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Threshold Value ◽  
High Accuracy ◽  
Approximate Algorithms ◽  
Heterogeneous Servers ◽  
Bernoulli Scheme ◽  
Markov Modulated ◽  
Steady State Probabilities ◽  
Feedback Queue

A system with heterogeneous servers, Markov Modulated Poisson flow and instantaneous feedback is studied. The primary call is serviced on a high-speed server, and after it is serviced, each call, according to the Bernoulli scheme, either leaves the system or requires re-servicing. After the completion of servicing of a call in a slow server, according to the Bernoulli scheme, it also either leaves the system or requires re-servicing. If upon arrival of a primary call the queue length of such calls exceeds a certain threshold value and the slow server is free, then the incoming primary call, according to the Bernoulli scheme, is either sent to the slow server or joins its own queue. A mathematical model of the studied system is constructed in the form of a three-dimensional Markov chain. Approximate algorithms for calculating the steady-state probabilities of the models with finite and infinite queues are proposed and their high accuracy is shown. The results of numerical experiments are presented.

scholarly journals A bivariate two-state Markov modulated Poisson process for failure modeling

2021 ◽  
Vol 208 ◽  
pp. 107318
Author(s):  
Yoel G. Yera ◽  
Rosa E. Lillo ◽  
Bo F. Nielsen ◽  
Pepa Ramírez-Cobo ◽  
Fabrizio Ruggeri
Keyword(s):  
Poisson Process ◽  
Failure Modeling ◽  
Markov Modulated Poisson Process ◽  
Markov Modulated

Continuous-time mean-variance portfolio selection with regime-switching financial market: Time-consistent solution

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishak Alia ◽  
Farid Chighoub
Keyword(s):  
Portfolio Selection ◽  
Regime Switching ◽  
Optimal Time ◽  
Uniqueness Results ◽  
State Dependent ◽  
Consistent Solution ◽  
Game Theoretic ◽  
Markov Modulated ◽  
Mean Variance Portfolio ◽  
Mean Variance

Abstract This paper studies optimal time-consistent strategies for the mean-variance portfolio selection problem. Especially, we assume that the price processes of risky stocks are described by regime-switching SDEs. We consider a Markov-modulated state-dependent risk aversion and we formulate the problem in the game theoretic framework. Then, by solving a flow of forward-backward stochastic differential equations, an explicit representation as well as uniqueness results of an equilibrium solution are obtained.

Acceleration of the EM-like reconstruction method for diffuse optical tomography with ordered-subsets method

2014 ◽  
Vol 22 (3) ◽  
Author(s):  
Caifang Wang
Keyword(s):  
Numerical Experiments ◽  
Imaging Modality ◽  
Random Medium ◽  
Optical Tomography ◽  
Back Propagation ◽  
Three Dimensional ◽  
Diffuse Optical Tomography ◽  
Optical Parameters ◽  
Reconstruction Method ◽  
Boundary Measurements

Abstract.Diffuse optical tomography (DOT) is an optical imaging modality, which provides the spatial distribution of the optical parameters inside a random medium. A propagation back-propagation method named EM-like reconstruction method for stationary DOT problem has been proposed yet. This method is really time consuming. Hence the ordered-subsets (OS) technique for this reconstruction method is studied in this paper. The boundary measurements of DOT are grouped into nonoverlapping and overlapping ordered sequence of subsets with random partition, sequential partition and periodic partition, respectively. The performance of OS methods is compared with the standard EM-like reconstruction method with two-dimensional and three-dimensional numerical experiments. The numerical experiments indicate that reconstruction of nonoverlapping subsets with periodic partition, overlapping subsets with periodic partition and standard EM-like method provide very similar acceptable reconstruction results. However, reconstruction of nonoverlapping subsets with periodic partition spends a minimum of time to get proper results.

Reconstruction of the Reservoir Fine Structure by Using Scattering Attributes

2021 ◽  
Author(s):  
Vladimir Cheverda ◽  
Vadim Lisitsa ◽  
Maksim Protasov ◽  
Galina Reshetova ◽  
Andrey Ledyaev ◽  
...  
Keyword(s):  
Seismic Data ◽  
Numerical Experiments ◽  
Seismic Waves ◽  
Fractured Reservoirs ◽  
Three Dimensional ◽  
Geological Structure ◽  
Discrete Elements ◽  
Digital Twin ◽  
The North ◽  
Slip Surfaces

Abstract To develop the optimal strategy for developing a hydrocarbon field, one should know in fine detail its geological structure. More and more attention has been paid to cavernous-fractured reservoirs within the carbonate environment in the last decades. This article presents a technology for three-dimensional computing images of such reservoirs using scattered seismic waves. To verify it, we built a particular synthetic model, a digital twin of one of the licensed objects in the north of Eastern Siberia. One distinctive feature of this digital twin is the representation of faults not as some ideal slip surfaces but as three-dimensional geological bodies filled with tectonic breccias. To simulate such breccias and the geometry of these bodies, we performed a series of numerical experiments based on the discrete elements technique. The purpose of these experiments is the simulation of the geomechanical processes of fault formation. For the digital twin constructed, we performed full-scale 3D seismic modeling, which made it possible to conduct fully controlled numerical experiments on the construction of wave images and, on this basis, to propose an optimal seismic data processing graph.

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