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Equilibrium Arrivals to Preemptive Queueing System with Fixed and Random Population Size

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Journal of the Operations Research Society of China 2024年第1期12卷 77-92页

作者： Julia Chirkova Vladimir Mazalov Institute of Applied Mathematical Research Karelian Research Centre of RASPetrozavodsk185910Russia school of mathematics and Statistics Qingdao UniversityQingdao266071ShandongChina

A single-server queueing system with preemptive access is considered.Each customer has one attempt to enter the system at its working interval[0,T].As soon as the customer request enters the system,the server immediately starts the service.But when the next request arrives in the system,the previous one leaves the system even he has not finished his service yet.We study a non-cooperative game in which the customers wish to maximize their probability of obtaining service within a certain period of time.We characterize the Nash equilibrium and the price of anarchy,which is defined as the ratio between the optimal and equilibrium social utility.Two models are considered.In the first model the number of players is fixed,while in the second it is random and obeys the Poisson distribution.We demonstrate that there exists a unique symmetric equilibrium for both models.Finally,we calculate the price of anarchy for both models and show that the price of anarchy is not monotone with respect to the number of customers.

关键词： Service system Preemptive priorities Strategic users Random number of players Optimal arrivals Kolmogorov backward equations Nash equilibrium Price of anarchy

STRONG CONVERGENCE OF JUMP-ADAPTED IMPLICIT MILSTEIN METHOD FOR A CLASS OF NONLINEAR JUMP-DIFFUSION PROBLEMS

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Journal of Computational mathematics 2024年第1期42卷 248-270页

作者： Xu Yang Weidong Zhao school of mathematics China University of Mining and TechnologyXuzhou 221116China school of mathematics Shandong UniversityJinan 250100China

In this paper,we study the strong convergence of a jump-adapted implicit Milstein method for a class of jump-diffusion stochastic differential equations with non-globally Lipschitz drift coefficients.Compared with the regular methods,the jump-adapted methods can significantly reduce the complexity of higher order methods,which makes them easily implementable for scenario simulation.However,due to the fact that jump-adapted time discretization is path dependent and the stepsize is not uniform,this makes the numerical analysis of jump-adapted methods much more involved,especially in the non-globally Lipschitz setting.We provide a rigorous strong convergence analysis of the considered jump-adapted implicit Milstein method by developing some novel analysis techniques and optimal rate with order one is also successfully recovered.Numerical experiments are carried out to verify the theoretical findings.

关键词： Jump-diffusion Jump-adapted implicit Milstein method Poisson jumps Strong convergence rate Non-Lipschitz coefficients

Non-symmetric differentially subordinate martingales and sharp weak-type bounds for Fourier multipliers

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Science China mathematics 2024年第8期67卷 1807-1826页

作者： Meryem Akboudj Yong Jiao Adam Os?kowski school of mathematics and Statistics Hunan Key Laboratory of Analytical Mathematics and ApplicationsCentral South University Faculty of mathematics Informatics and MechanicsUniversity of Warsaw

Let p>2 be a given exponent. In this paper, we prove, with the best constant, the weak-type(p, p)inequality ■ for a large class of non-symmetric Fourier multipliers Tm obtained via modulation of jumps of certain Lévy processes. In particular, the estimate holds for appropriate linear combinations of second-order Riesz transforms and skew versions of the Beurling-Ahlfors operator on the complex plane. The proof rests on a novel probabilistic bound for Hilbert-space-valued martingales satisfying a certain non-symmetric subordination principle. Further applications to harmonic functions and Riesz systems on Euclidean domains are indicated.

关键词： weak-type bound Fourier multiplier martingale differential subordination laminate

Time-inconsistent stochastic linear-quadratic control problem with indefinite control weight costs

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Science China mathematics 2024年第1期67卷 211-236页

作者： Qi Lü Bowen Ma school of mathematics Sichuan UniversityChengdu 610064China

A time-inconsistent linear-quadratic optimal control problem for stochastic differential equations is studied.We introduce conditions where the control cost weighting matrix is possibly singular.Under such conditions,we obtain a family of closed-loop equilibrium strategies via multi-person differential games.This result extends Yong’s work(2017) in the case of stochastic differential equations,where a unique closed-loop equilibrium strategy can be derived under standard conditions(namely,the control cost weighting matrix is uniformly positive definite,and the other weighting coefficients are positive semidefinite).

关键词： linear-quadratic optimal control problem time-inconsistent cost functional generalized Riccati equation indefinite control weight cost closed-loop equilibrium strategy

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Preface: The Special Issue on Dynamic and Networking Games

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Journal of the Operations Research Society of China 2024年第1期12卷 1-3页

作者： Hong-Wei Gao Vladimir Mazalov school of mathematics and Statistics Qingdao University266071QingdaoShandongChina Institute of Applied Mathematical Research Karelian Research Centre of RAS185910PetrozavodskRussia

Numerous game theory-based techniques to characterize agent behavior haveemerged in response to the swift advancements in technology,communications,indus-trial organization,economic integration,and international trade.There is a huge varietyof mathematical techniques used in game theory.The application of dynamic and net-working game techniques is the main topic of this special issue.Studying strategicinteractions between many decision-makers with dynamic and varied connections isthe focus of research in the game theory discipline of dynamic and networking games.This field of study examines how agents or people make choices in dynamic circum-stances and how those choices impact their overall outcomes and payoffs.

关键词： agent strategic advancement

Distributed Heterogeneous Multi-Agent Optimization with Stochastic Sub-Gradient

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Journal of Systems Science & Complexity 2024年第4期37卷 1470-1487页

作者： HU Haokun MO Lipo CAO Xianbing school of mathematics and Statistics Central South University school of mathematics and Statistics Beijing Technology and Business University Research centre for Agri-Product Quality Traceability Beijing Technology and Business University school of Computer and Artificial Intelligence Beijing Technology and Business University China Food Flavor and Nutrition Health Innovation Center Beijing Technology and Business University

This paper studies the optimization problem of heterogeneous networks under a timevarying topology. Each agent only accesses to one local objective function, which is nonsmooth. An improved algorithm with noisy measurement of local objective functions' sub-gradients and additive noises among information exchanging between each pair of agents is designed to minimize the sum of objective functions of all agents. To weaken the effect of these noises, two step sizes are introduced in the control protocol. By graph theory, stochastic analysis and martingale convergence theory, it is proved that if the sub-gradients are uniformly bounded, the sequence of digraphs is balanced and the union graph of all digraphs is joint strongly connected, then the designed control protocol can force all agents to find the global optimal point almost surely. At last, the authors give some numerical examples to verify the effectiveness of the stochastic sub-gradient algorithms.

关键词： Communication noises distributed stochastic optimization heterogeneous networks sub-gradient measurement noises

THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR differential equations

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Acta Mathematica Scientia 2024年第1期44卷 103-114页

作者：刘慧芳毛志强 school of mathematics and Statistics Jiangxi Normal UniversityNanchang330022China school of mathematics and Computer Jiangxi Science and Technology Normal UniversityNanchang330038China

We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.

关键词： Nevanlinna theory nonlinear differential equations meromorphic functions entire functions

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Vaccination effect on a stochastic epidemic model with healing and relapse

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International Journal of Biomathematics 2024年第1期17卷 29-59页

作者： M.M.Abdeslami L.Basri M.El Fatini I.Sekkak R.Taki Laboratory of Partial differential equations Spectral Algebra and Geometry Department of mathematics Faculty of Sciences Ibn Tofail UniversityBP 133KénitraMorocco centre de Recherche en Sante Publique Montréal(Québec)H3N 1X9 Canada Departement de Medecine Sociale et Preventive Ecole de SantéPublique de I'Universitéde Montreal 101Avenue du ParcMontréal(Quebec)H3N 1X9Canada EST Sidi Bennour Chouaib Doukkali UniversityEl JadidaMorocco

In this work,we consider a stochastic epidemic model with vaccination,healing and relapse.We prove the existence and the uniqueness of the positive solution.We establish sufficient conditions for the extinction and the persistence in mean of the stochastic system.Moreover,we also establish sufficient conditions for the existence of ergodic stationary distribution to the model,which reveals that the infectious disease will persist.The graphical illustrations of the approximate solutions of the stochastic epidemic model have been performed.

关键词： Stochastic epidemic model with relapse and healing vaccination extinction persistence in mean Markov semigroup stationary distribution

differential Game Model of Resource Extraction with Continuous and Dynamic Updating

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Journal of the Operations Research Society of China 2024年第1期12卷 51-75页

作者： Ovanes Petrosian Tihomirov Denis Jiang-Jing Zhou Hong-Wei Gao school of mathematics Harbin Institute of TechnologyHarbin150001HeilongjiangChina school of Automation Qingdao UniversityQingdao266071ShandongChina Faculty of Applied mathematics and Control Processes Saint-Petersburg State UniversitySaint PetersburgRussia National Research University"High school of Economics" Saint-PetersburgRussia school of mathematics and Statistics Qingdao UniversityQingdao266071ShandongChina

This paper is devoted to a new class of differential games with continuous and dynamic updating.The direct application of resource extraction in a case of dynamic and continuous updating is considered.It is proved that the optimal control(cooperative strategies)and feedback Nash equilibrium strategies uniformly converge to the corresponding strategies in the game model with continuous updating as the number of updating instants converges to infinity.Similar results are presented for an optimal trajectory(cooperative trajectory),equilibrium trajectory and corresponding payoffs.

关键词： differential games Dynamic updating Continuous updating Optimal control Feedback Nash equilibrium