A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed （i.i.d.） random variables, that is max{ηi, 1 ≤ i ≤ n}. T...A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed （i.i.d.） random variables, that is max{ηi, 1 ≤ i ≤ n}. The approximating technique is used to obtain the fluid approximation for the queue length, workload and busy time processes. Furthermore, under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate, we prove by the approximating technique that the scaled processes characterizing the queue converge to the corresponding fluid limits with the exponential rate only for large N. Here the scaled processes include the queue length process, workload process and busy time process.展开更多
Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic p...Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence fate are embodied by the queue length, workload, and busy time processes.展开更多
A multi-class single server queue under non-preemptive static buffer priority （SBP） service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length ...A multi-class single server queue under non-preemptive static buffer priority （SBP） service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length and busy time processes. Furthermore, we prove that the convergence rate of the fluid approximation for the queue length and busy time processes is exponential for large N. Additionally, a sufficient condition for stability is obtained.展开更多
Presents information on singularly peturbed two-point boundary value problem of convection-diffusion type. Analysis of the problem; Details of an hp version finite element method on a strongly graded piecewise uniform...Presents information on singularly peturbed two-point boundary value problem of convection-diffusion type. Analysis of the problem; Details of an hp version finite element method on a strongly graded piecewise uniform mesh of Shiskin type; Convergence of the method with respect to the singular perturbation parameter.展开更多
基金Supported by the National Natural Science Foundation of China (No. 10826047 and No.10901023)by the Fundamental Research Funds for the Central Universities under Contract BUPT2009RC0707
文摘A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed （i.i.d.） random variables, that is max{ηi, 1 ≤ i ≤ n}. The approximating technique is used to obtain the fluid approximation for the queue length, workload and busy time processes. Furthermore, under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate, we prove by the approximating technique that the scaled processes characterizing the queue converge to the corresponding fluid limits with the exponential rate only for large N. Here the scaled processes include the queue length process, workload process and busy time process.
文摘Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence fate are embodied by the queue length, workload, and busy time processes.
基金Supported by National Natural Science Foundation of China(Grant No.10901023)the Fundamental Research Funds for the Central Universities(Grant Nos.BUPT2009RC0707 and BUPT2011RC0704)
文摘A multi-class single server queue under non-preemptive static buffer priority （SBP） service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length and busy time processes. Furthermore, we prove that the convergence rate of the fluid approximation for the queue length and busy time processes is exponential for large N. Additionally, a sufficient condition for stability is obtained.
基金the U.S. National Science Foundation through grants DMS-9626193, DMS-0074301, and INT-9605050.
文摘Presents information on singularly peturbed two-point boundary value problem of convection-diffusion type. Analysis of the problem; Details of an hp version finite element method on a strongly graded piecewise uniform mesh of Shiskin type; Convergence of the method with respect to the singular perturbation parameter.
