User zoltan - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T16:06:59Z http://mathoverflow.net/feeds/user/4976 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/22440/markov-chain-alternative-from-the-perspective-of-feedback Markov-chain alternative (from the perspective of "feedback") Zoltan 2010-04-24T17:19:20Z 2010-04-24T17:19:20Z <p>First of all, I'm not quiet sure the "feedback" word is used in this context. Let's say we have a simple M/M/1 queue. Markov-chains are used to describe such entities, for example taking the number of people in the queue as a state.</p> <p>What if we introduce feedback into the picture? What if there's a chance at each state that if the number of people in the queue are larger than a fixed number, then we add an other queue to the picture - essentially transforming the underlying structure?</p> <p>The same question arises if we say that at state $k$, there's an $A_{k}$ chance that $f(k)$ number of people arrive - we don't know the exact number of states.</p> <p>Is there a way to describe this kind of situation?</p> http://mathoverflow.net/questions/21839/induced-arrivals-in-an-m-m-1-queue "Induced" arrivals in an M/M/1 queue? Zoltan 2010-04-19T14:10:29Z 2010-04-20T16:37:30Z <p>I'm a newcomer to the realm of queueing theory, so please bear with me :)</p> <p>I'd like to model web server traffic with a modified M/M/1 queue. In the simple case we have two parameters - $\lambda$ for the arrival rate and $\mu$ for the departure (or service) rate.</p> <p>If I understand correclty, the general way to get the performance evaluation equations (average number of requests in the queue, for example) is to draw a flow diagram, and solve the equlibrium equation system, namely for the M/M/1 model:</p> <p>$0 = -\lambda p_{0}$ + $\mu p_{1}$</p> <p>$0 = \lambda p_{n-1} - (\lambda + \mu) p_{n} +\mu p_{n+1}$, n = 1, 2, ...</p> <p>I don't know how I could extend the model the fit the real-world scenario the most. Each normal request induces a number of image requests, for example, let it be $u$ on average, and let it's service rate be $\sigma$. How can I factor these into the equations?</p> http://mathoverflow.net/questions/22440/markov-chain-alternative-from-the-perspective-of-feedback Comment by Zoltan Zoltan 2010-04-24T20:06:53Z 2010-04-24T20:06:53Z I don't see how a future event in the chain (like reaching a limit) could alter the behaviour at a previous state (to &quot;fork&quot; a new server). And this seems to go against the definiton of a Markov-chain.. http://mathoverflow.net/questions/21839/induced-arrivals-in-an-m-m-1-queue/21845#21845 Comment by Zoltan Zoltan 2010-04-20T10:52:51Z 2010-04-20T10:52:51Z Okay, I get the general idea, thanks. What is a bit misleading is that I don't need two &quot;stages&quot;: the induces/generated requests should be the same &quot;type&quot; as a newly arrived one. if I undestand correctly, you used p_{n}(1) and p_{n}(2) to essentially split it into two queues.