A fluid buffer model with Markov modulated input-output rates is considered.When traffic intensity is near its critical value, the system is known as in heavy traffic.It is shown that a suitably scaled sequence of the...A fluid buffer model with Markov modulated input-output rates is considered.When traffic intensity is near its critical value, the system is known as in heavy traffic.It is shown that a suitably scaled sequence of the equilibrium buffer contents has a weakor distributional limit under heavy traffic conditions. This weak limit is a functional of adiffusion process determined by the Markov chain modulating the input and output rates.The first passage time of the reflected process is examined. It is shown that the mean firstpassage time can be obtained via a solution of a Dirichlet problem. Then the transitiondensity of the reflected process is derived by solving the Kolmogorov forward equation witha Neumann boundary condition. Furthermore, when the fast changing part of the generatorof the Markov chain is a constant matrix, the representation of the probability distributionof the reflected process is derived. Upper and lower bounds of the probability distributionare also obtained by means of asymptotic expansions of standard normal distribution.展开更多
This paper is concerned with the stability of multiclass queueing networks of 2 stations and4 buffers under the longest queue first served discipline(LQFS).For this network,the service priority of a customer is determ...This paper is concerned with the stability of multiclass queueing networks of 2 stations and4 buffers under the longest queue first served discipline(LQFS).For this network,the service priority of a customer is determined by the length of the queue that customer resides in at that time.The main result includes two parts.Firstly,the corresponding fluid model is established,and then it is shown that the queueing networks under LQFS are stable whenever the traffic intensity is strictly less than one for each station.展开更多
基金The research of this author was supported in part by the National Science Fundation under grant DMS 0304928.The research of this author was supported in part by a Distinguished Young Investigator Grant from the National Natural Sciences Foundation of Chi
文摘A fluid buffer model with Markov modulated input-output rates is considered.When traffic intensity is near its critical value, the system is known as in heavy traffic.It is shown that a suitably scaled sequence of the equilibrium buffer contents has a weakor distributional limit under heavy traffic conditions. This weak limit is a functional of adiffusion process determined by the Markov chain modulating the input and output rates.The first passage time of the reflected process is examined. It is shown that the mean firstpassage time can be obtained via a solution of a Dirichlet problem. Then the transitiondensity of the reflected process is derived by solving the Kolmogorov forward equation witha Neumann boundary condition. Furthermore, when the fast changing part of the generatorof the Markov chain is a constant matrix, the representation of the probability distributionof the reflected process is derived. Upper and lower bounds of the probability distributionare also obtained by means of asymptotic expansions of standard normal distribution.
基金supported by the National Natural Science Foundation of China under Grant No.11101050
文摘This paper is concerned with the stability of multiclass queueing networks of 2 stations and4 buffers under the longest queue first served discipline(LQFS).For this network,the service priority of a customer is determined by the length of the queue that customer resides in at that time.The main result includes two parts.Firstly,the corresponding fluid model is established,and then it is shown that the queueing networks under LQFS are stable whenever the traffic intensity is strictly less than one for each station.
