鞅方法下的带有顾客流失的马尔可夫队列

Markovian queues with customers lost based on Martingale method

为研究高负荷条件下带有顾客流失的马尔可夫队列,应用非负下鞅的Doob-Meyer分解定理与计数过程有关的鞅性质,构造了队长过程和其刻画过程的鞅表示,进而运用概率测度收敛和随机过程极限相关理论得到了M/M/n/mn模型队长过程的扩散逼近.

In order to study Markovian queues with customers lost under the condition of heavy traffic,the martingale representations of the queue length process and the scaled queue length process are constructed by using Doob-Meyer decomposition for nonnegative sub-martingales and the martingale properties related to the counting process.According to the correlation theory of stochastic-process limits and convergence of probability measures,the diffusion approximation of the queue length process of the M/M/n/mn model is obtained.