In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a...In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.展开更多
In this paper we study a Geo/T-IPH/1 queue model,where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states.The queue model can be described by a quas...In this paper we study a Geo/T-IPH/1 queue model,where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states.The queue model can be described by a quasi-birth-anddeath(QBD)process with countably phases.Using the operator-geometric solution method,we first give the expression of the operator and the joint stationary distribution.Then we obtain the probability generating function(PGF)for stationary queue length distribution and sojourn time distribution,respectively.展开更多
This paper presents a review of methodologies for analyzing stochastic manufacturing and service systems. On the basis of the scale and level of details of operations, we can study stochastic systems using micro-,meso...This paper presents a review of methodologies for analyzing stochastic manufacturing and service systems. On the basis of the scale and level of details of operations, we can study stochastic systems using micro-,meso-, and macro-scopic models. Such a classification unifies stochastic modeling theory. For each model type,we highlight the advantages and disadvantages and the applicable situations. Micro-scopic models are based on quasi-birth-and-death process because of the phase-type distributed service times and/or Markov arrival processes.Such models are appropriate for modeling the detailed operations of a manufacturing system with relatively small number of servers(production facilities). By contrast,meso-scopic and macro-scopic models are based on the functional central limit theorem(FCLT) and functional strong law of large numbers(FSLLN), respectively, under heavy-traffic regimes. These high-level models are appropriate for modeling large-scale service systems with many servers, such as call centers or large service networks. This review will help practitioners select the appropriate level of modeling to enhance their understanding of the dynamic behavior of manufacturing or service systems. Enhanced understanding will ensure that optimal policies can be designed to improve system performance. Researchers in operation analytics and optimization of manufacturing and logistics also benefit from such a review.展开更多
基金Supported by the National Natural Science Foundation of China(11571372,11771452)the Innovation Program of Central South University(10900-50601010)
文摘In this paper, we show that a positive recurrent ?uid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a ?uid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.
基金This work was supported by the National Natural Science Foundation of China(No.61174160)Post-Doctoral Science Foundation of Central South University(No.125011)The authors are grateful to the three anonymous referees and the editor for their careful reading and invaluable comments and suggestions,which are helpful to improve the paper.This research completed when the first author was a post-doctoral fellow in School of Mathematics,Central South University。
文摘In this paper we study a Geo/T-IPH/1 queue model,where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states.The queue model can be described by a quasi-birth-anddeath(QBD)process with countably phases.Using the operator-geometric solution method,we first give the expression of the operator and the joint stationary distribution.Then we obtain the probability generating function(PGF)for stationary queue length distribution and sojourn time distribution,respectively.
文摘This paper presents a review of methodologies for analyzing stochastic manufacturing and service systems. On the basis of the scale and level of details of operations, we can study stochastic systems using micro-,meso-, and macro-scopic models. Such a classification unifies stochastic modeling theory. For each model type,we highlight the advantages and disadvantages and the applicable situations. Micro-scopic models are based on quasi-birth-and-death process because of the phase-type distributed service times and/or Markov arrival processes.Such models are appropriate for modeling the detailed operations of a manufacturing system with relatively small number of servers(production facilities). By contrast,meso-scopic and macro-scopic models are based on the functional central limit theorem(FCLT) and functional strong law of large numbers(FSLLN), respectively, under heavy-traffic regimes. These high-level models are appropriate for modeling large-scale service systems with many servers, such as call centers or large service networks. This review will help practitioners select the appropriate level of modeling to enhance their understanding of the dynamic behavior of manufacturing or service systems. Enhanced understanding will ensure that optimal policies can be designed to improve system performance. Researchers in operation analytics and optimization of manufacturing and logistics also benefit from such a review.
