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Lecture10

# A person who is 30 minutes away wants to know the

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Unformatted text preview: shop currently has 2 customers l 30 minute travel time = 2 epochs l Immediate service implies that the barber chair and all waiting chairs are empty l This condition only exists at state 0 Absolute probability vector of a system after 2 time periods is given by: AC’, = AWPW For part (a), I shop is initially at state 0 [email protected]) = [1 0 0 0 0 ] AC’) = AlWpC’h [1 0 0 0 0 ] p(2) For part (b), if shop is initially in state 2 [email protected]) = [0 0 1 0 0 ] AU, = AWpC’k [O 0 1 0 0 ] pC’) EM-602 / QM-710 (NJ) Lecture 10 Page 10-8 Question #4 (b) Question #4 (a) Barber Shop Problem l Sarber Shop Problem Part (a) Shop is currently empty *Part (b) Shop now has 2 customers r.63 .229 .091 .0339 .01611 Ao)= up 1 .63 229 .091 .0339 .0161/ =[I) 0 1 0 0 I A9 .28 .138 AM3 .029 ) 0 A9 .28 .159 .071 1 0 0 A9 .35 .16 J r.63 .229 .091 .0339 .01611 A”‘= A’W’O) ’I*63 .229 .091 .0339 .0161 1 =[l 0 0 0 0 ! A9 .28 .138 .063 .029 ) 1 I 0 0 A9 0 .28 A9 =[.63 .229 .091 .0339 .0161] l .159 .35 .071 .16 J = [A9 .28 .138 A63 i.e. a 63% chance of immediate service *i.e. a 49% chance of immediate service Homework Problem #2 Lecture 10 l l l l l l .029] Consider the barber shop problem Suppose the customer phoned the shop from a location 45 minutes away What is the probability of immediate service if: (a) the barber shop is currently empty (b) the barber shop is currently full (c) the barber doesn’t answer the phone, from which you infer only that he is busy EM-602 / QM-710 (NJ) Lecture 10 Page 10-9...
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