SFWRENG 4E03 Lecture Notes - Lecture 7: Jackson Network, Pedro Winter, Markov Chain
11 Oct 2016
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Put stuff on your cheatsheet you probably don"t need. See previous note: lecture 2015-11-16 (cid:540)node = (cid:540)in,i pin,i. Only 2 are linearly independent, so we can"t substitute the (cid:540)"s for each other. States: (0, 0, 2), (0, 2, 0), (2, 0, 0), (1, 1, 0), (1, 0, 1), (0, 1, 1) P(node 2 is busy) = (0,2,0) + (1,1,0) + (0,1,1) This won"t be able to get (0,2,0) from the previous example; you won"t be able to use it if the question is asking for the arrival rate. Let e[r(m)] denote the expected response time of nodei when there are m jobs in the system. i. => the mean jobs the arriving job sees at node j is. Little"s law: e[ri pi is the probability that an arbitrary arrival to any node is an arrival to node i. Recall that in jackson networks: probabilities are independent of m e. g. 1,2 = 0. 3.
