基于现代通信网络的具有广播服务机制的多服务器排队系统研究

Based on the problem of queue of the running process of modern communication networks with TCP/IP protocol,we are studying multi-server queueing system with the following disciplines.One discipline suggests that the arriving customer who meets several idel servers at its arrival epoch is copied and each replica of the customer is served by one server independently of other copies of the customer. The second discipline suggests that the arriving customer who meets m, m>1, idel servers at its arrival epoch is split into m equal parts each of which is considered as an independent customer and is served by the corresponding server with the rate m times higher than the nominal rate of the service of an arbitrary customer by a single server. We will refer to the first discipline as BC (Broadcasting with Copying) discipline and to the second one as BS (Broadcasting with Spliting) discipline. BC discipline can be used in many real-life systems (police and ambulance emergence service,broker-dealer operations,etc.) where speed is a critical factor and customers try to get service using different path or different channels in the hope that one of them get faster than others and a priori one can not tell which one will. BS discipline is a reasonal approximation to real-world strategies in current software systems, e.g. web servers. The purpose of the subject is to design algorithms for computing the stationary distribution of the number of customers and sojourn or waiting time, as well as derivation of expression for the performance measures of queueing system with broadcasting service discipline and to optimize the quality of service of communication networks.

基于采用TCP/IP协议的现代通信网络的运行过程中出现的排队问题,我们研究如下服务机制的多服务器排队系统:将顾客的服务请求根据它到达时刻空闲服务器的数量复制若干份,这些空闲服务器同时启动为该顾客服务;或将服务请求根据它到达时刻空闲服务器的数量分割为大小相同的若干片,这些空闲服务器分别独立地为它的每个片段服务,两个服务机制分别称为BC(Broadcasting with Copying)和BS(Broadcasting with Splitting)服务机制。广播服务机制可以描述许多现实生活中的系统(警察和紧急救护服务等),这些系统中请求的响应时间是关键因素。本项目以现代通信网运行过程中出现的某些排队问题为研究对象,利用概率论、排队论及矩阵分析等工具,建立相应的数学模型,计算系统中顾客数量的稳态概率分布及等待(逗留)时间等各项重要性能指标,以所研究数学模型为指导,优化通信网络的服务质量。

基于采用TCP/IP协议的现代通信网络的运行过程中出现的排队问题，我们研究了如下服务机制的多服务器排队系统：将顾客的服务请求根据它到达时刻空闲服务器的数量复制若干份，这些空闲服务器同时启动为该顾客服务；或将服务请求根据它到达时刻空闲服务器的数量分割为大小相同的若干片，这些空闲服务器分别独立地为它的每个片段服务，两个服务机制分别称为BC(Broadcasting with Coping) 和BS(Broadcasting with Splitting)服务机制。广播服务机制可以描述许多现实生活中的系统,这些系统中请求的响应时间是关键因素。项目研究内容包括：1）具有BC服务机制和服务器预热的MAP/PH/ N型多服务器排队系统；2）具有BC服务机制和灾难马尔柯夫输入的MAP/PH/N型多服务器排队系统；3）具有BC服务机制和不稳定服务器的SM/PH/N型多服务器排队系统。本研究利用概率论、排队论及矩阵分析等数学工具，为每个所研究的系统建立相应的数学模型，计算系统中顾客数量的稳态概率分布及等待（逗留）时间等各项重要性能指标，以所研究数学模型为指导，优化通信网络的服务质量。依托该项目已经发表了EI收录期刊论文一篇、EI收录会议论文一篇，正在审稿的SCI收录期刊论文三篇。项目的研究成果在实际应用方面可以有效提高通信网络的服务质量。