SOLUTIONS MANUAL for Stochastic Modeling: Analysis and ...

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14. Case 6.3
S n represents the destination of the nth rider
M = {1, 2,...,m} one state for each region of the city
p ij ≡ probability a rider picked up in region i has destination in region j
p i ≡ probability driver starts the day in region i
Case 6.4
S n represents the nth key typed
⎧
⎫
⎪⎨
⎪⎬
M = 1, 2,...,26 27, 28,...,36 37, 38,...,42 43,...
} {{ } } {{ } } {{ } } {{ }
⎪⎩
⎪⎭
letters numbers punctuation space and others
≡{A,B,...,Z,0, 1,...,9, ; , ·, “, ‘, ?, ′, space,...}
p ij ≡ probability next key typed is j given last one was i
p i ≡ probability first letter typed is i
Case 6.5
S n represents the brand of the nth toothpaste purchase
M = {1, 2, 3, 4,...,m} where each state represents a brand of toothpaste
p ij ≡ probability a consumer next purchases brand j given they currently use i
p i ≡ probability a consumer uses brand i at the beginning of the study
Case 6.6
S n represents the high temperature on the nth day
M = {−20, −19, −18,...,109, 110} is temperature in Fahrenheit
p ij ≡ probability high temperature tomorrow is j given today’s high is i
p i ≡ probability temperature is i on the first day of the study
Case 6.7
S n represents the task type of the nth task
M = {1, 2,...,m} where each state represents a task such as “move,” “place,”
“change tool,” etc.
p ij ≡ probability next task is j given current task is i
p i ≡ probability first task is type i