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Lecture10

# Example contd example contd barber shop problem barber

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Unformatted text preview: Barber Shop Problem Barber Shop Problem Another question to consider: 4. A person who is 30 minutes away wants to know the probability of an immediate service. When calling the shop he is informed that: (a) The shop is currently empty (b) There are currently 2 people in the shop Questions to consider: 1. What is the probability of a customer walking in and getting immediate service? 2. What is the probability of walking In and leaving because the shop is full? 3. What does the barber make on an 8hour day, if the barber makes (after expenses) \$10.00 per haircut? Markov Chains l l l l l Example Modeling Procedures Barber Shop Model Deffne the Epoch to be used in the model Deffne all possible states of the system Determine the transition probabilities for all states to all other states Complete the one-step transition matrix Perform necessary computations to answer questions l l l Deftne the Epoch for the barber shop problem as one 1 Smlnute haircut Let the states of the system be equal to the total number of customers In the barber shop (zero if the shop is empty, thru four If the shop full to capacity) Determine the transition probabllltles transitions occur whenever either a customer arrives or leaves Barber Shop Model Example Transition Matrix Barber Shop Model Cust in shop at time = (t The barber studied the system, counting the customers entering the shop in each l&minute period l The resutts are tabulated below: 5+ 1 2 n 0 3 4 P(n)[ 0.70 0.20 0.07 0.02 0.01 0 l n = number of arriving customers P(n) = probability of n customers arriving 1 2 n 0 P(n)] 0.70 0.20 0.07 EM-602 I QM-710 (NJ) Lecture I.0 Page 10-6 3 0.02 l 16 min) 4 0.01 5+ 0 .’ -- Barber Shop Model Barber Shop Model Transition Matrix Transition Matrix Cust in shop at time = (t n 0 1 2 P(n)1 0.70 0.20 0.07 3 0.02 l 16 min) 4 0.01 Curt in shop at time = (t n 0 1 2 P(n)/ 0.70 0.20 0.07 5+ 0 16 min) l 3 0.02 4 0.01 Barber Shop Model Barber Shop Model Transition Matrix 5+ 0 Transition Matrix Cust in shop at time = (t + 16 min) Cust in shop at time = (t 0 Cud in 0 1 1 0.70 0.20 2 0.07 16 min) l 3 0.02 4 0.011 -- n 0 1 2 3 P(n)1 0.70 0.20 0.07 _ 0.02 a 0.0...
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