The M/M/1 Queue with Randomly Varying Arrival and Service Rates: A Phase Substitution Solution
提出一种计算M/M/1队列稳态概率向量的新方法，利用连续时间马尔可夫链的生成元结构，在随机环境下高效求解，计算时间短且受流量强度影响小。
This paper presents an alternative procedure for computing the steady state probability vector of an M/M/1 queue with randomly varying arrival and service rates. By exploiting the structure of the infinitesimal generator of the underlying continuous-time Markov chain, the approach represents an efficient adaptation of the state reduction method introduced by Grassmann for solving problems involving M/M/1 queues under a random environment. We compare computational requirements of the proposed approach with the method of Neuts and block elimination under different rush-hour congestion patterns while keeping the overall traffic intensity constant as well as under different traffic intensities. We demonstrate that the proposed method requires minimal computing time to reach convergence and moreover the time requirement does not change much when traffic intensity increases.