Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures.Diferent from standard batch arrival retrial queues with starting failures,we assume that each cu...Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures.Diferent from standard batch arrival retrial queues with starting failures,we assume that each customer after service either immediately returns to the orbit for another service with probabilityθor leaves the system forever with probability 1θ（0≤θ〈1）.On the other hand,if the server is started unsuccessfully by a customer（external or repeated）,the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 q（0≤q〈1）.Firstly,we introduce an embedded Markov chain and obtain the necessary and sufcient condition for ergodicity of this embedded Markov chain.Secondly,we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary time.We also derive a stochastic decomposition law.In the special case of individual arrivals,we develop recursive formulae for calculating the steady-state distribution of the orbit size.Besides,we investigate the relation between our discrete-time system and its continuous counterpart.Finally,some numerical examples show the influence of the parameters on the mean orbit size.展开更多
In this article, we study the locally distributed feedback stabilization problem of a nonuniform Euler-Bernoulli beam. Firstly, using the semi-group theory, we establish the wellposedness of the associated closed loop...In this article, we study the locally distributed feedback stabilization problem of a nonuniform Euler-Bernoulli beam. Firstly, using the semi-group theory, we establish the wellposedness of the associated closed loop system. Then by proving the uniqueness of the solution to a related ordinary differential equation, we derive the asymptotic stability of the closed loop system. Finally, by means of the piecewise multiplier method, we prove that, by either one distributed force feedback or a distributed moment feedback control, the closed loop system can be exponentially stabilized.展开更多
基金Supported by the National Natural Science Foundation of China(Nos.11171019,11171179,and 11271373)Program for New Century Excellent Talents in University(No.NCET-11-0568)+2 种基金the Fundamental Research Funds for the Central Universities(No.2011JBZ012)Tianyuan Fund for Mathematics(Nos.11226200 and 11226251)Program for Science Research of Fuyang Normal College(2013FSKJ01ZD)
文摘Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures.Diferent from standard batch arrival retrial queues with starting failures,we assume that each customer after service either immediately returns to the orbit for another service with probabilityθor leaves the system forever with probability 1θ（0≤θ〈1）.On the other hand,if the server is started unsuccessfully by a customer（external or repeated）,the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 q（0≤q〈1）.Firstly,we introduce an embedded Markov chain and obtain the necessary and sufcient condition for ergodicity of this embedded Markov chain.Secondly,we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary time.We also derive a stochastic decomposition law.In the special case of individual arrivals,we develop recursive formulae for calculating the steady-state distribution of the orbit size.Besides,we investigate the relation between our discrete-time system and its continuous counterpart.Finally,some numerical examples show the influence of the parameters on the mean orbit size.
文摘In this article, we study the locally distributed feedback stabilization problem of a nonuniform Euler-Bernoulli beam. Firstly, using the semi-group theory, we establish the wellposedness of the associated closed loop system. Then by proving the uniqueness of the solution to a related ordinary differential equation, we derive the asymptotic stability of the closed loop system. Finally, by means of the piecewise multiplier method, we prove that, by either one distributed force feedback or a distributed moment feedback control, the closed loop system can be exponentially stabilized.
