# ans4-6 - INWK6211 – Mathematics for Internetworking...

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Unformatted text preview: INWK6211 – Mathematics for Internetworking Spring 2010 Tutorial Problem Answers For Chapters 4 to 6 1) 3 13 2) a) For a clear day being state 1 and a rainy day being state 2: P ≈ = bracketleftBigg . 9 . 1 . 3 . 7 bracketrightBigg b) π 1 = 0 . 75, π 2 = 0 . 25 c) P (3) 11 = 0 . 804 d) f (2) 12 = 0 . 09 e) μ 22 = 4 days. 3) If state 1 is a zero, and state 2 is a one, then P ≈ = bracketleftBigg p 1 − p 1 − p p bracketrightBigg and the steady-state probabilities are π 1 = 0 . 5 π 2 = 0 . 5 4) This is a 4-server problem with maximum number in system of 4. For this problem, we must solve the balance equations. a) The fraction of time idle is π = 0 . 5355. b) The fraction of users lost is π 4 = 0 . 003405. 5) We can approximate this as an infinite server problem (see Higgins and McNulty, pg 315 for the results relating to this problem), in which case r = λt = arrival rate service rate = 60 / 9 1 / 5 = 100 3 Since the mean number of users is r = 100 / 3 = 33 . 3 << 150, the assumption of an infinite server model is...
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ans4-6 - INWK6211 – Mathematics for Internetworking...

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