摘要
马尔科夫链是研究排队系统的主要方法,本文在现有M/M/m排队理论和排队系统仿真理论基础上,利用Matlab建立基于马尔科夫状态转移过程的M/M/m排队模型仿真程序。仿真程序在产生初始化参数设定后,利用时钟推进法来模拟空闲服务台和繁忙服务台情况下的服务流程,最后通过M/M/m模型特征描述的仿真计算,获得平均等待时间(E[W])、平均停机时间(E[DT])、平均排队队长E[Q]、系统中的平均客户数(E[L])和可能延迟的概率(П)5项重要的特征描述。模拟次数设定为20 000次,模拟客户服务率和客户到达率相同,服务台在3～6个的排队系统,并将仿真结果与理论值以及Queue2.0的模拟结果相比较。最终结果显示E[W]、[DT]和Π3项最重要指标的仿真结果和理论值都极为相近,误差范围小,本研究将为优先权排队系统的仿真研究提供理论依据。
Markov chain is the main method for the study of queuing systems. This paper integrates the existing theories of M/M/m queuing system and theories of queuing system simulation, and builds simulation program of M/M/m Queuing Model according to the Markov state transition process using Matlab. The simulation process is as follows. First of all, simulation program initializes the parameter settings, such as service time, the interval of customer arrival, the number of server etc. Secondly, promotes the program used time clock which is based on the arrival time of customers and the end time of service. Thirdly, simulates the free servers and busy servers process when a customer arrived, and recodes the corresponding data. Finally, calculate the M/M/m model＇s characterized de- scriptions, included in the average down time （E[DT]）, the average waiting time （El WJ ）, the average number of queuing customer （E[ Q] ）, the average number of customers in the queuing system（ E[ L] ） and delay probability （17） , based on the simulation formula. Sets the iteration times on 20,000 times, at the same service rate and arrival rate, hut the servers are from 3-6, and runs the simulation program. The results show that the most important indexes （E[ W], E[ DT] and П） are closed to the theoretical value and Queue2.0 simulation resuhs, and it is more comparably accurate than Queue2.0. These studies will provide with theoretical basis for the simulation of priority queuing system.
出处
《重庆师范大学学报（自然科学版）》
CAS
北大核心
2012年第1期61-66,共6页
Journal of Chongqing Normal University:Natural Science
