服务时间分布为H2*的带有顾客流失的高负荷极限

Heavy-traffic limits for H2* service time distribution with customers loss

研究服务时间分布服从H2*的带有顾客流失的队列模型。探讨等待空间有限的单服务台G/H2*/1/k队列模型,得到队长和流失人数的极限表达;将该模型推广至到达率随时间变化的多服务台Gt/H2*/m/k队列模型,应用连续映射等方法对极限进行研究。结合随机过程极限对分裂过程和叠加到达过程的相应队列模型进行分析,得到队长和流失人数的高负荷极限。

The queue model with customers lost in service time distribution obeyed by H*2 is studied.Firstly,the queue model of single server with finite waiting space was studied,and the limit expression of queue length and the number of customers lost was obtained.Secondly,it extended model into the multi-service queues with time-varying arrival rate,using continuous mapping method to get the limit of queue length and the number of people lost.Finally,the split processes and superposition arrival process were analyzed by combining the limit of stochastic process,and then the heavy-traffic limit of queue length and the number of customers lost was obtained.