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Stabilty Conditions for Some Multiqueue Distributed Systems: Buffered Random Access Systems
| Content Provider | Semantic Scholar |
|---|---|
| Author | Szpankowski, Wojciech |
| Copyright Year | 1992 |
| Abstract | Assessing stability of multidimensional systems is notoriously difficult. We consider the standard discrete-time slotted ALOHA system with a finite number of buffered users. Stability study of such a system was initiated in 1979 by Tsybakov and Mikhailov. Several bounds on the stability region have been established up-to-date, however, the exact stability region is known only for the symmetric system and two users ALOHA. This paper proves necessary and sufficient condltions for stability of the ALOHA system, hence solves the problem posed by Tsybakov and Mikhailov. We accomplish this by means of a novel technique based on three simple observations. Namely, isolating single queue from the system, applying Loynes' stability criteria for such an isolated queue, and using stochastic dominance and mathematical induction to verify the required stationarity assumptions in the Loynes' criterion. We also point out that our technique can be used to assess stability regions for other multidimensional systems. We illustrate it by providing also the stability region for a buffered system with conflict resolution algorithms. In another paper (Georgiadis and Szpankowski (1992)) we have used a similar technique to establish stability criteria for the token passing ring system. ·This research \Vas supported in part by the NSF grants CCR-8900305 and NCR-87021l5, by AFOSR grant 90-0107, and by grant ROl LM05118 from the National Library of Medicine. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1950&context=cstech |
| Alternate Webpage(s) | https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1950&context=cstech |
| Alternate Webpage(s) | https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1950&context=cstech&httpsredir=1&referer= |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
