Asymptotic Analysis of N-Model with Static Priority
| Main Authors: | Maltseva, Mariia, Morozov, Evsey |
|---|---|
| Format: | Proceeding eJournal |
| Bahasa: | eng |
| Terbitan: |
FRUCT Oy
, 2020
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/4007428 |
Daftar Isi:
- Inthispaper,westudytheso-called N-modelwhich consists of two pools of servers. Pool 1 contains N1 servers while pool 2 consists of one server, which can be inactive time to time. The 1st pool is fed by a Poisson input of the 1st class customers. Provided all servers of pool 1 are busy and the queue size exceeds a given threshold, a class-1 customer, with a given probability, jumps to server of pool 2, if this server is active. Under exponential assumptions, the number of customers in the 1st pool is a Markov birth-death process. The periods of activity/inactivity constitute initially a transient process which converges to a stationary regime. In this research we deduce stationary distribution of this Markov process in an explicit form. Moreover, we nd conditions when the mentioned convergence of the alternating process of activity/inactivity of the server in the 2nd pool implies convergence of the birth-death process, describing the 1st pool, to stationary regime. Moreover, this convergence is demonstrated by simulation.