This paper investigates the stability of switched systems with time-varying delay and all unstable subsystems. According to the stable convex combination, we design a state-dependent switching rule. By employing Wirti...This paper investigates the stability of switched systems with time-varying delay and all unstable subsystems. According to the stable convex combination, we design a state-dependent switching rule. By employing Wirtinger integral inequality and Leibniz-Newton formula, the stability results of nonlinear delayed switched systems whose nonlinear terms satisfy Lipschitz condition under the designed state-dependent switching rule are established for different assumptions on time delay. Moreover,some new stability results for linear delayed switched systems are also presented. The effectiveness of the proposed results is validated by three typical numerical examples.展开更多
This paper considers a single server retrial queue in which a state-dependent service policy is adopted to control the service rate. Customers arrive in the system according to a Poisson process and the service times ...This paper considers a single server retrial queue in which a state-dependent service policy is adopted to control the service rate. Customers arrive in the system according to a Poisson process and the service times and inter-retrial times are all exponentially distributed. If the number of customers in orbit is equal to or less than a certain threshold, the service rate is set in a low value and it also can be switched to a high value once this number exceeds the threshold. The stationary distribution and two performance measures are obtained through the partial generating functions. It is shown that this state-dependent service policy degenerates into a classic retrial queueing system without control policy under some conditions. In order to achieve the social optimal strategies, a new reward-cost function is established and the global numerical solutions, obtained by Canonical Particle Swarm Optimization algorithm, demonstrate that the managers can get more benefits if applying this state-dependent service policy compared with the classic model.展开更多
基金supported by the National Natural Science Foundation of China(61503052,61503050,61603065)the Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJQN201801120,KJQN201801104,KJ1709206)+1 种基金the Opening Foundation of Hubei Key Laboratory of Applied Mathematics(Hubei University)(HBAM201805)Chongqing Science and Technology Commission Technology Innovation and Application Demonstration(Social Livelihood General)Project(cstc2018jscx-msyb X0049)。
文摘This paper investigates the stability of switched systems with time-varying delay and all unstable subsystems. According to the stable convex combination, we design a state-dependent switching rule. By employing Wirtinger integral inequality and Leibniz-Newton formula, the stability results of nonlinear delayed switched systems whose nonlinear terms satisfy Lipschitz condition under the designed state-dependent switching rule are established for different assumptions on time delay. Moreover,some new stability results for linear delayed switched systems are also presented. The effectiveness of the proposed results is validated by three typical numerical examples.
基金supported by the National Natural Science Foundation of China under Grant Nos.71571014 and 71390334
文摘This paper considers a single server retrial queue in which a state-dependent service policy is adopted to control the service rate. Customers arrive in the system according to a Poisson process and the service times and inter-retrial times are all exponentially distributed. If the number of customers in orbit is equal to or less than a certain threshold, the service rate is set in a low value and it also can be switched to a high value once this number exceeds the threshold. The stationary distribution and two performance measures are obtained through the partial generating functions. It is shown that this state-dependent service policy degenerates into a classic retrial queueing system without control policy under some conditions. In order to achieve the social optimal strategies, a new reward-cost function is established and the global numerical solutions, obtained by Canonical Particle Swarm Optimization algorithm, demonstrate that the managers can get more benefits if applying this state-dependent service policy compared with the classic model.
