Article ID: | iaor1989343 |
Country: | United States |
Volume: | 35 |
Issue: | 5 |
Start Page Number: | 561 |
End Page Number: | 570 |
Publication Date: | May 1989 |
Journal: | Management Science |
Authors: | Kao Edward P.C., Lin Chiunsin |
Keywords: | computational analysis, markov processes |
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. The authors 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. They 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.