SFWRENG 4E03 Lecture Notes - Lecture 8: Jackson Network, Markov Chain, Mathtype

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Jackson networks 1 e. g. 1) 1. Usra summer project: info session: nov 12th 2-4pm cibc hall. External arrival rates can be modelled by the poisson processes. Service times at each node are exponential. Probabilistic routing e. g. 1) r (cid:314) ] (1) (cid:313)0. 25(cid:314)0. 75 ] (2) |(cid:314)0. 25 (cid:313)_________________(cid:315) (cid:541)1 = 3 (cid:541)2 = 1. 5. Solve (cid:540)5 (cid:540)1 = r + 0. 75 (cid:540)2 (cid:540)2 = 0. 75. As r(cid:314) , jobs in system(cid:314) r is dependent on the rate of clearing jobs. = 1. 71 r: rite (cid:540)2 in terms of r, ensure 2 < 1, (cid:540)2/(cid:541)2 < 1. ___0. 5_______ (cid:315) (cid:314)]((cid:541)1) (cid:314) ]((cid:541)2) (cid:313) (cid:313)0. 5 | Traffic equations: equations of stuff going in and out of each node with (cid:540)s and stuff. Methods: jackson network, simulate with numbers, ctmc. Ctmc (n1, n2), i. e. (jobs at node1, jobs at node2) (0, 2) (cid:314) (0, 2) 0. 7(cid:541)1, but doesn"t affect the ctmc balance equations, so ignore (0. 3 (cid:541)1 + (cid:541)2) 1,1= (cid:541)2 0,2 + 0. 3(cid:541)1 2,0.

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