基于M/G/1排队模型的业务流性能研究

Study of Business Flow Performance Based on M/G/1 Queuing Model

针对无线传感器网络可能存在的拥塞问题,提出了一种新的业务流性能刻画方法.利用M/G/1排队模型建立了一步转移概率矩阵,在先来先服务策略的基础上推导了业务流的队列长度和等待时间的数学表达式,通过仿真实验分析了当服务源分别服从定长分布和k阶Erlang分布时,系统的等待时间与服务率、到达率之间的关系.结果表明,等待时间与到达率成正相关,与服务率成负相关,并且对k阶Erlang分布的影响更大.

As wireless sensor networks may have congestion problem, a new performance characterization method was proposed which first used M/G/1 queuing model to establish one-step transition probability ma- trix and derived the mathematic formulas of queue length and delay time for business flow based on First Come First Served policy. A simulation was conducted to study the relationship between waiting time of the system and service rate as well as arrival rate when service source respectively obeyed fixed-length distribu- tion and k-Erlang distribution. The results show that waiting time has positive relationship with arrival rate and negative relationship with service rate and has much impact on k-Erlang distribution.