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hw5sol

# hw5sol - ISE 331 HOMEWORK 5 SOLUTIONS 1 All states...

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ISE 331 HOMEWORK # 5 SOLUTIONS 1. All states communicate There is only one class, and it contains only positive recurrent states. a) None b) None c) {0,1,2,3} d) None, Since P ii 1 for all. e) All states have period 2, since 2. a) b) 3. a) assume demand occurs after the deliveries = 7 . 0 2 . 0 1 . 0 0 0 0 0 4 . 0 3 . 0 2 . 0 1 . 0 0 0 0 0 4 . 0 3 . 0 2 . 0 1 . 0 0 0 0 0 4 . 0 3 . 0 2 . 0 1 . 0 0 0 0 0 4 . 0 3 . 0 2 . 0 1 . 0 0 0 0 0 4 . 0 3 . 0 3 . 0 0 0 0 0 0 4 . 0 6 . 0 P = = = number odd n for P number even n for P n ii n ii 0 0 ) ( ) ( 625 . 0 * 4 / 1 * 3 / 1 1 * 4 / 1 0 * 12 / 1 * 3 / 2 1 * 6 / 1 0 31 31 21 21 31 21 31 = + + + = + + + = a a a a a a a 3 5 . 1 12 / 1 * 3 / 2 1 * 4 / 1 * 3 / 1 5 . 1 * 12 / 1 * 2 / 3 * 4 / 1 * 3 / 1 1 33 32 3 33 33 32 33 33 23 23 32 32 22 32 32 22 22 = + = = + + = + = = + = + + = e e d e e e e e e e e e e e e e e

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b) π P = π π = {0.139,0.139,0.139,0.138,0.141,0.130,0.174} c) The steady probability that a pint of blood is to be discarded = P{D=0}* P{State is in 7} = 0.4*0.174 = 0.0696 d) P{Emergency Deliveries} = P{state 1}* P{D>1} + P{state 2}* P{D>2} = 0.139*(0.2+0.1) + 0.139*0.1 = 0.0556 4. years. 2 5 . 0 1 0 5 . 0 0 5 . 0 firm with the spends partner a that time of length Average 846 . 0 13 / 11 , 3 / 1 5 . 0 2 . 0 7 . 0 1 . 0 15 . 0 35 . 0 5 . 0 partner) - non as leave hired Newly ( 1 0 0 0 0 0 1 0 0 0 5 . 0 0 5 . 0 0 0 0 1 . 0 2 . 0 7 . 0 0 0 5 . 0 0 15 . 0 35 . 0 partner as Leave 5 partner, - non as Leave 4 Partner, 3 Senior, 2 Junior, 1 : 33 33 33 32 32 32 31 31 31 33 14 24 34 34 34 24 24 24 14 14 14 = + = =
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