3325p11hs d waiting line

667 note that this is equal to 1 note p0 1 33 444 296

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Unformatted text preview: ystem D – 30 Single-Channel Example Probability of more than k Cars in the System Probability k 0 1 2 3 4 5 6 7 Pn > k = (2/3)k + 1 .667 ← Note that this is equal to 1 Note P0 = 1 - .33 .444 .296 .198 ← Implies that there is a 19.8% .198 Implies chance that more than 3 cars are in the system system .132 .088 .058 .039 D – 31 Single-Channel Economics Customer dissatisfaction and lost goodwill Wq Total arrivals Mechanic’s salary Total hours Total customers spend waiting per day waiting = = $10 per hour = 2/3 hour = 16 per day = $56 per day 2 2 (16) = 10 hours 3 3 Customer waiting-time cost = $10 10 2 3 = $106.67 Total expected costs = $106.67 + $56 = $162.67 D – 32 Multiple-Server Example Queuing Formulas for Model B: Multiple-Server System, also Called M/M/S M = number of servers (channels) open l= average arrival rate µ= average service rate at each server (channel) The probability that there are zero people or units in the system is: 1 P0 = M M −1 n λ ∑ 1 λ ÷ + 1 ÷ M µ n= 0 n ! µ M ! µ M µ − λ for M µ > λ D – 33 Multipl...
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This document was uploaded on 02/19/2014.

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