An iterative approximation scheme for repetitive Markov processes
Journal of Applied Probability, cilt.36, sa.3, ss.654-667, 1999 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 36 Sayı: 3
- Basım Tarihi: 1999
- Doi Numarası: 10.1017/s0021900200017472
- Dergi Adı: Journal of Applied Probability
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.654-667
- Anahtar Kelimeler: Approximate solutions, Numerical algorithms, Quasi-birth-and-death processes
- Boğaziçi Üniversitesi Adresli: Hayır
Özet
Repetitive Markov processes form a class of processes where the generator matrix has a particular repeating form. Many queueing models fall in this category such as M / M / 1 queues, quasi-birth-and-death processes, and processes with M / G / 1 or GI / M / 1 generator matrices. In this paper, a new iterative scheme is proposed for computing the stationary probabilities of such processes. An infinite state process is approximated by a finite state process by lumping an infinite number of states into a super-state. What we call the feedback rate, the conditional expected rate of flow from the super-state to the remaining states, given the process is in the super-state, is approximated simultaneously with the steady state probabilities. The method is theoretically developed and numerically tested for quasi-birth-and-death processes. It turns out that the new concept of the feedback rate can be effectively used in computing the stationary probabilities.