This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem ...This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem of finding the closed-loop optimal control can be decomposed into three problems: the deterministic optimal feedback, cautious optimal and probing optimal control problems.展开更多
In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the di...In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.展开更多
This paper studies the bulk-arrival M-x/G/1 queue with single server vacation. By introducing the server busy period and using the Laplace transform, the recursion expression of the Laplace transform of the transient ...This paper studies the bulk-arrival M-x/G/1 queue with single server vacation. By introducing the server busy period and using the Laplace transform, the recursion expression of the Laplace transform of the transient queue-length distribution is derived. Furthermore, the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are obtained. Especially some results for the single-arrival M/G/1 queue with single server vacation and bulk-arrival M-x/G/1 queue but with no server vacation can be derived directly by the results obtained in this paper.展开更多
In this paper, we study an M/M/1 queue with multiple working vacations under following Bernoulli control policy: at the instants of the completion of a service in vacation, the server will interrupt the vacation and e...In this paper, we study an M/M/1 queue with multiple working vacations under following Bernoulli control policy: at the instants of the completion of a service in vacation, the server will interrupt the vacation and enter regular busy period with probability 1 p (if there are customers in the queue) or continue the vacation with probability p. For this model, we drive the analytic expression of the stationary queue length and demonstrate stochastic decomposition structures of the stationary queue length and waiting time, also we obtain the additional queue length and the additional delay of this model. The results we got agree with the corresponding results for working vacation model with or without vacation interruption if we set p = 0 or p = 1, respectively.展开更多
In this paper, we study the M/M/1 queue with working vacations and vacation interruptions. The working vacation is introduced recently, during which the server can still provide service on the original ongoing work at...In this paper, we study the M/M/1 queue with working vacations and vacation interruptions. The working vacation is introduced recently, during which the server can still provide service on the original ongoing work at a lower rate. Meanwhile, we introduce a new policy：, the server can come back from the vacation to the normal working level once some indices of the system, such as the number of customers, achieve a certain value in the vacation period. The server may come back from the vacation without completing the vacation. Such policy is called vacation interruption. We connect the above mentioned two policies and assume that if there are customers in the system after a service completion during the vacation period, the server will come back to the normal working level. In terms of the quasi birth and death process and matrix-geometric solution method, we obtain the distributions and the stochastic decomposition structures for the number of customers and the waiting time and provide some indices of systems.展开更多
This paper considers a discrete-time queue with N-policy and LAS-DA(late arrival system with delayed access) discipline.By using renewal process theory and probability decomposition techniques,the authors derive the r...This paper considers a discrete-time queue with N-policy and LAS-DA(late arrival system with delayed access) discipline.By using renewal process theory and probability decomposition techniques,the authors derive the recursive expressions of the queue-length distributions at epochs n^-,n^+,and n.Furthermore,the authors obtain the stochastic decomposition of the queue length and the relations between the equilibrium distributions of the queue length at different epochs(n^-,n^+,n and departure epoch D_n).展开更多
This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service co...This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service completion, begins a process of search in order to find the following customer to be served with a certain probability, or begins a single vacation process with complementary probability. This paper analyzes the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating functions of the number of customers in the orbit and in the system are also obtained along with the marginal distributions of the orbit size when the server is idle, busy or on vacation. Finally, the author gives two stochastic decomposition laws, and as an application the author gives bounds for the proximity between the system size distributions of the model and the corresponding model without retrials.展开更多
We study an M/PH/1 queue with phase type working vacation and vacation interruption where the vacation time follows a phase type distribution. The server serves the customers at a lower rate in a vacation period. The ...We study an M/PH/1 queue with phase type working vacation and vacation interruption where the vacation time follows a phase type distribution. The server serves the customers at a lower rate in a vacation period. The server comes back to the regular busy period at a service completion without completing the vacation. Such policy is called vacation interruption. In terms of quasi birth and death process and matrix-geometric solution method, we obtain the stationary queue length distribution. Moreover we obtain the conditional stochastic decomposition structures of queue length and waiting time when the service time distribution in the regular busy period is exponential.展开更多
The authors present a new queueing model with （e, d） setup time. Using the quasi-birth-and-death process and matrix-geometric method, the authors obtain the stationary distribution of queue length and the LST of wai...The authors present a new queueing model with （e, d） setup time. Using the quasi-birth-and-death process and matrix-geometric method, the authors obtain the stationary distribution of queue length and the LST of waiting time of a customer in the system. Furthermore, the conditional stochastic decomposition results of queue length and waiting time are given.展开更多
In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matr...In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function（PGF） of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X]/M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.展开更多
In this note, we consider an M/G/1 retrial queue with server vacations, when retrial times, service times and vacation times are arbitrary distributed. The distribution of the number of customers in the system in stat...In this note, we consider an M/G/1 retrial queue with server vacations, when retrial times, service times and vacation times are arbitrary distributed. The distribution of the number of customers in the system in stationary regime is obtained in terms of generating function. Next, we give heavy traffic approximation of such distribution. We show that the system size can be decomposed into two random variables, one of which corresponds to the system size of the ordinary M/G/1 FIFO queue without vacation. Such a stochastic decomposition property is useful for the computation of performance measures of interest. Finally, we solve simple problems of optimal control of vacation and retrial policies.展开更多
This paper considers a leader-following tracking control problem for second-order multiagent systems(MASs) under measurement noises and directed communication channels.It is assumed that each follower-agent can measur...This paper considers a leader-following tracking control problem for second-order multiagent systems(MASs) under measurement noises and directed communication channels.It is assumed that each follower-agent can measure the relative positions and velocities of its neighbors in a noisy environment.Based on a novel velocity decomposition technique,a neighbor-based control law is designed to realize local control strategies for these continuous-time agents.It is shown that the proposed consensus protocol can guarantee that all the follower-agents track the active leader.In addition,this result is extended to a more general case with switching topologies.Finally,a numerical example is given for illustration.展开更多
In this paper,a novel approach for quantifying the parametric uncertainty associated with a stochastic problem output is presented.As with Monte-Carlo and stochastic collocation methods,only point-wise evaluations of ...In this paper,a novel approach for quantifying the parametric uncertainty associated with a stochastic problem output is presented.As with Monte-Carlo and stochastic collocation methods,only point-wise evaluations of the stochastic output response surface are required allowing the use of legacy deterministic codes and precluding the need for any dedicated stochastic code to solve the uncertain problem of interest.The new approach differs from these standard methods in that it is based on ideas directly linked to the recently developed compressed sensing theory.The technique allows the retrieval of the modes that contribute most significantly to the approximation of the solution using a minimal amount of information.The generation of this information,via many solver calls,is almost always the bottle-neck of an uncertainty quantification procedure.If the stochastic model output has a reasonably compressible representation in the retained approximation basis,the proposedmethod makes the best use of the available information and retrieves the dominantmodes.Uncertainty quantification of the solution of both a 2-D and 8-D stochastic Shallow Water problem is used to demonstrate the significant performance improvement of the new method,requiring up to several orders of magnitude fewer solver calls than the usual sparse grid-based Polynomial Chaos(Smolyak scheme)to achieve comparable approximation accuracy.展开更多
文摘This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem of finding the closed-loop optimal control can be decomposed into three problems: the deterministic optimal feedback, cautious optimal and probing optimal control problems.
文摘In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.
基金the National Outstanding Youth Science Foundation !(79725002) the Youth Science Foundation of UEST.
文摘This paper studies the bulk-arrival M-x/G/1 queue with single server vacation. By introducing the server busy period and using the Laplace transform, the recursion expression of the Laplace transform of the transient queue-length distribution is derived. Furthermore, the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are obtained. Especially some results for the single-arrival M/G/1 queue with single server vacation and bulk-arrival M-x/G/1 queue but with no server vacation can be derived directly by the results obtained in this paper.
基金Foundation item： Supported by the National Science Foundation of China（60874083） Supported by the 2011 National Statistical Science Development Funds（2011LY014） Supported by the 2012 Soft Science Devel- opment Funds of Science and Technology Committee of Henan Province（122400450090）
文摘In this paper, we study an M/M/1 queue with multiple working vacations under following Bernoulli control policy: at the instants of the completion of a service in vacation, the server will interrupt the vacation and enter regular busy period with probability 1 p (if there are customers in the queue) or continue the vacation with probability p. For this model, we drive the analytic expression of the stationary queue length and demonstrate stochastic decomposition structures of the stationary queue length and waiting time, also we obtain the additional queue length and the additional delay of this model. The results we got agree with the corresponding results for working vacation model with or without vacation interruption if we set p = 0 or p = 1, respectively.
基金This work was supported in part by National Natural Science Foundation of China under Grant No. 10671170.5. Acknowledgment The authors thank to the anonymous referees for their insightful comments and suggestions, which are very helpful to improve the presentations of the paper.
文摘In this paper, we study the M/M/1 queue with working vacations and vacation interruptions. The working vacation is introduced recently, during which the server can still provide service on the original ongoing work at a lower rate. Meanwhile, we introduce a new policy：, the server can come back from the vacation to the normal working level once some indices of the system, such as the number of customers, achieve a certain value in the vacation period. The server may come back from the vacation without completing the vacation. Such policy is called vacation interruption. We connect the above mentioned two policies and assume that if there are customers in the system after a service completion during the vacation period, the server will come back to the normal working level. In terms of the quasi birth and death process and matrix-geometric solution method, we obtain the distributions and the stochastic decomposition structures for the number of customers and the waiting time and provide some indices of systems.
基金supported by the National Natural Science Foundation of China under Grant No.70871084The Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 200806360001a grant from the "project 211(PhaseⅢ)" of the Southwestern University of Finance and Economics, Scientific Research Fund of Southwestern University of Finance and Economics
文摘This paper considers a discrete-time queue with N-policy and LAS-DA(late arrival system with delayed access) discipline.By using renewal process theory and probability decomposition techniques,the authors derive the recursive expressions of the queue-length distributions at epochs n^-,n^+,and n.Furthermore,the authors obtain the stochastic decomposition of the queue length and the relations between the equilibrium distributions of the queue length at different epochs(n^-,n^+,n and departure epoch D_n).
基金supported by the National Natural Science Foundation of China under Grant No.11171019the Fundamental Research Funds for the Central Universities under Grant No.2011JBZ012the Program for New Century Excellent Talents in University under Grant No.NCET-11-0568
文摘This paper considers a discrete-time Geo/G/1 retrial queue where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy. It is assumed that the server, after each service completion, begins a process of search in order to find the following customer to be served with a certain probability, or begins a single vacation process with complementary probability. This paper analyzes the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating functions of the number of customers in the orbit and in the system are also obtained along with the marginal distributions of the orbit size when the server is idle, busy or on vacation. Finally, the author gives two stochastic decomposition laws, and as an application the author gives bounds for the proximity between the system size distributions of the model and the corresponding model without retrials.
文摘We study an M/PH/1 queue with phase type working vacation and vacation interruption where the vacation time follows a phase type distribution. The server serves the customers at a lower rate in a vacation period. The server comes back to the regular busy period at a service completion without completing the vacation. Such policy is called vacation interruption. In terms of quasi birth and death process and matrix-geometric solution method, we obtain the stationary queue length distribution. Moreover we obtain the conditional stochastic decomposition structures of queue length and waiting time when the service time distribution in the regular busy period is exponential.
基金the National Natural Science Foundation of China under Grant No.10671170the Doctorial Foundation of Yanshan University under Grant No.B228.
文摘The authors present a new queueing model with （e, d） setup time. Using the quasi-birth-and-death process and matrix-geometric method, the authors obtain the stationary distribution of queue length and the LST of waiting time of a customer in the system. Furthermore, the conditional stochastic decomposition results of queue length and waiting time are given.
基金supported by National Natural Science Foundation of China(No. 10671170)Natural Science Foundation of Hebei Province(No. F2008000864)
文摘In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function（PGF） of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X]/M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.
基金supported in parts by the Ministry of universities,Algeria,through grant CNEPRU B~*00220060089.
文摘In this note, we consider an M/G/1 retrial queue with server vacations, when retrial times, service times and vacation times are arbitrary distributed. The distribution of the number of customers in the system in stationary regime is obtained in terms of generating function. Next, we give heavy traffic approximation of such distribution. We show that the system size can be decomposed into two random variables, one of which corresponds to the system size of the ordinary M/G/1 FIFO queue without vacation. Such a stochastic decomposition property is useful for the computation of performance measures of interest. Finally, we solve simple problems of optimal control of vacation and retrial policies.
基金supported by the National Natural Science Foundation of China under Grant No.61174070the Specialized Research Found for the Doctoral Program under Grant No.20110172110033
文摘This paper considers a leader-following tracking control problem for second-order multiagent systems(MASs) under measurement noises and directed communication channels.It is assumed that each follower-agent can measure the relative positions and velocities of its neighbors in a noisy environment.Based on a novel velocity decomposition technique,a neighbor-based control law is designed to realize local control strategies for these continuous-time agents.It is shown that the proposed consensus protocol can guarantee that all the follower-agents track the active leader.In addition,this result is extended to a more general case with switching topologies.Finally,a numerical example is given for illustration.
基金supported by the French National Agency for Research(ANR)under projects ASRMEI JC08#375619 and CORMORED ANR-08-BLAN-0115 and by GdR Mo-MaS.
文摘In this paper,a novel approach for quantifying the parametric uncertainty associated with a stochastic problem output is presented.As with Monte-Carlo and stochastic collocation methods,only point-wise evaluations of the stochastic output response surface are required allowing the use of legacy deterministic codes and precluding the need for any dedicated stochastic code to solve the uncertain problem of interest.The new approach differs from these standard methods in that it is based on ideas directly linked to the recently developed compressed sensing theory.The technique allows the retrieval of the modes that contribute most significantly to the approximation of the solution using a minimal amount of information.The generation of this information,via many solver calls,is almost always the bottle-neck of an uncertainty quantification procedure.If the stochastic model output has a reasonably compressible representation in the retained approximation basis,the proposedmethod makes the best use of the available information and retrieves the dominantmodes.Uncertainty quantification of the solution of both a 2-D and 8-D stochastic Shallow Water problem is used to demonstrate the significant performance improvement of the new method,requiring up to several orders of magnitude fewer solver calls than the usual sparse grid-based Polynomial Chaos(Smolyak scheme)to achieve comparable approximation accuracy.
