### ?

## Research and optimization of semi-Markov queueing models

Optimization: A Journal of Mathematical Programming and Operations Research. 2018. Vol. 67. No. 6. P. 921-941.

Kondrashova E. V., Kashtanov V.

Algorithmization of the quality of queueing systems is carried out in oder to optimize the work, constructing the revenue functional on the trajectories of a managed semi-Markov process while managing the system's structure. In particular, we consider both semi-Markov and Markoqueueing systems with control of several parameters chaaractirestics of the system). The task is to find the optimal management strategy.

Lazarev A. A., Kvaratskhelia A., Доклады Академии наук 2010 Т. 432 № 6 С. 746-749

Одним из актуальных вопросов разработки математической теории расписаний является построение метрик, которые можно использовать при разработке точных и приближенных алгоритмов решения задач. Введение метрических пространств для $NP$-трудных задач теории расписаний позволяет применять общие математические подходы к нахождению приближенного решения с гарантированной абсолютной погрешностью. Ранее для $NP$-трудных задач с критерием минимизации максимального временн\'ого смещения $\{P,R,Q\}|prec,r_j|\{L_{\max},C_{\max}\}$ была ...

Added: November 23, 2012

Lazarev A. A., Gafarov E., Автоматика и телемеханика 2008 № 12 С. 86-104

Consideration was given to the resource-constrained project scheduling problem and its special cases. The existing lower estimates of the objective function—minimization of the project time—were compared. It was hypothesized that the optimal value of the objective function of the nonpreemptive resource-constrained project scheduling problem is at most twice as great as that of the objective ...

Added: November 23, 2012

Pardalos P. M., Rassias T. undefined., Springer, 2014

The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional ...

Added: May 30, 2014

Gafarov E., Lazarev A. A., Werner F., A Polynomial Time Graphical Algorithm for Maximizing Total Tardiness on a Single Machine / Otto-von-Guericke Universitaet. 2010. No. 12.

In this paper, we consider the problem of maximizing total tardiness on a single machine, where the first job starts at time zero and idle times between the processing of jobs are not allowed. We present a modification of an exact pseudo-polynomial algorithm based on a graphical approach, which has a polynomial running time. ...

Added: March 4, 2013

Lazarev A. A., Kvaratskhelia A., Gafarov E., Доклады Академии наук 2007 Т. 412 № 6 С. 739-742

27.47.19 Исследование операций
28.15.19 Нелинейные детерминированные системы
28.19.15 Оптимальные системы
28.29.15 Методы исследования операций ...

Added: November 23, 2012

Gafarov E., Lazarev A. A., Werner F., Автоматика и телемеханика 2010 № 10 С. 63-79

In this paper, we consider two scheduling problems on a single machine, where a specific objective function has to be maximized in contrast to usual minimization problems. We propose exact algorithms for the single machine problem of maximizing total tardiness 1‖max-ΣT j and for the problem of maximizing the number of tardy jobs ...

Added: November 24, 2012

Gafarov E., Lazarev A. A., Werner F., Mathematical Social Sciences 2011 No. 62 P. 7-13

We consider single machine scheduling problems with a non-renewable resource. These types of problems have not been intensively investigated in the literature so far. For several problems of these types with standard objective functions (namely the minimization of makespan, total tardiness, number of tardy jobs, total completion time and maximum lateness), we present some complexity ...

Added: November 24, 2012

Gafarov E., Lazarev A. A., Werner F., Single Machine Scheduling With a Generalized Total Tardiness Objective Function / Otto-von-Guericke Universitaet. 2010. No. 10.

In this note, we consider a single machine scheduling problem with generalized total tardiness objective function. An NP-hardness proof and a pseudo-polynomial time solution algorithm are proposed for a special case of this problem. Moreover, we present a new graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted ...

Added: March 4, 2013

Lazarev A. A., Gafarov E., Доклады Академии наук 2008 Т. 424 № 1 С. 7-9

27.47.19 Исследование операций
28.15.19 Нелинейные детерминированные системы
28.19.15 Оптимальные системы
28.29.15 Методы исследования операций ...

Added: November 23, 2012

Lazarev A. A., Kvaratskhelia A., Автоматика и телемеханика 2010 № 10 С. 80-89

In this paper, we consider the minimizing total weighted completion time in preemptive equal-length job with release dates scheduling problem on a single machine. This problem is known to be open. Here, we give some properties of optimal schedules for the problem and its special cases. ...

Added: November 24, 2012

Springer, 2015

This book offers a wealth of interdisciplinary approaches to urbanization strategies in architecture centered on growing concerns about the future of cities and their impacts on essential elements of architectural optimization, livability, energy consumption and sustainability. It portrays the urban condition in architectural terms, as well as the living condition in human terms, both of ...

Added: April 13, 2015

Кибзун А. И., Panarin S. I., Вестник компьютерных и информационных технологий 2010 № 12 С. 31-40

The stochastic model is provided. Using the model, redesign of distance learning system CLASS.NET is done by solving the stochastic optimization problem. ...

Added: December 5, 2013

Werner F., Lazarev A. A., Automation and Remote Control 2010 Vol. 71 No. 10 P. 2019-2020

Foreword to the thematical issue devoted to the seventieth anniversary of Academician V.S. Tanaev ...

Added: November 23, 2012

Lazarev A. A., Werner F., A Graphical Approach for Solving NP-Hard Combinatorial Problems / Otto-von-Guericke Universitaet. 2008. No. 15.

In this paper we consider a graphical realization of dynamic programming. The concept is discussed on the partition and knapsack problems. In contrast to dynamic programming, the new algorithm can also treat problems with non-integer data without necessary transformations of the corresponding problem. We compare the proposed method with existing algorithms for these problems on ...

Added: March 4, 2013

Gafarov E., Lazarev A. A., Information Processing Letters 2012 Т. 112 № 3 С. 72-76

In this note, we consider a single machine scheduling problem with generalized total tardiness objective function.
A pseudo-polynomial time solution algorithm is proposed for a special case of this problem. Moreover, we present a new
graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted number
of tardy jobs on a single ...

Added: November 24, 2012

Afanaseva L., Grishunina S., Queueing Systems 2020 Vol. 94 No. 3 P. 213-241

We study the stability conditions of the multiserver queueing system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and service times of a given customer are independent at the occupied servers. The service time has an exponential, phase-type or hyper-exponential distribution. We ...

Added: April 22, 2018

Gafarov E., Lazarev A. A., Werner F., Annals of Operations Research 2012 Vol. 196 No. 1 P. 247-261

We consider the problem of maximizing total tardiness on a single machine, where the first job starts at time zero and idle times between the processing of jobs are not allowed.We present a modification of an exact pseudo-polynomial algorithm based on a graphical approach, which has a polynomial running time. This result settles the complexity ...

Added: November 24, 2012

Lazarev A. A., Журнал вычислительной математики и математической физики 2007 Т. 47 № 6 С. 1087-1099

The classical NP-hard (in the ordinary sense) problem of scheduling jobs in order to minimize the total tardiness for a single machine 1‖ΣT j is considered. An NP-hard instance of the problem is completely analyzed. A procedure for partitioning the initial set of jobs into subsets is proposed. Algorithms are constructed for finding ...

Added: November 23, 2012

Stepanov E., Buttazzo G., Pratelli A. et al., Berlin : Springer, 2009

Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and ...

Added: December 12, 2018

M. : [б.и.], 2018

Book include abstracts of reports presented at the IX International Conference on Optimization Methods and Applications "Optimization and applications" (OPTIMA-2018) held in Petrovac, Montenegro, October 1 - October 5, 2018. ...

Added: October 9, 2018

A.Yu. Golubin, Gridin V. N., Automation and Remote Control 2012 Vol. 73 No. 9 P. 1529-1538

We find optimal (from the insurer’s point of view) strategies for insurance and reinsurance
in a controllable Cramer–Lundberg risk process that describes the capital dynamics of
an insurance company over an infinite time interval. As the optimality criterion being minimized,
we use the stationary variation coefficient, taking into account additional constraints
on residual risks for both insurers and reinsurer. ...

Added: February 20, 2014

Pardalos P. M., Rassias T. undefined., Springer, 2014

This volume consists of chapters written by eminent scientists and engineers from the international community and presents significant advances in several theories, and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, and Discrete Mathematics and Geometry, as well as several ...

Added: May 30, 2014

Yu. Grishunina, L. Manita, Lobachevskii Journal of Mathematics 2017 Vol. 38 No. 5 P. 906-909

We propose a new mathematical model of virus spreading over local area networks. We
define a cost functional and consider a maximization problem for the average income given by the
computer network per unit time. ...

Added: September 2, 2017

Lazarev A. A., Werner F., Algorithms for Special Single Machine Total Tardiness Problems / Otto-von-Guericke Universitaet. 2008. No. 12.

The scheduling problem of minimizing total tardiness on a single machine is knownto be NP-hard in the ordinary sense. In this paper, we consider the special case of the problem when the processing times $p_j$ and the due dates $d_j$ of the jobs $j, \, j \in N = \{ 1, 2, \ldots, n \}$, ...

Added: March 4, 2013