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’) EM602 / QM710 (NJ) Lecture 10
Page 108 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 EM602 / QM710 (NJ) Lecture 10
Page 109...
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 Spring '94
 DonaldC.Johnson
 Probability theory, barber shop, Barber Shop Model, barber shop problem

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