3325p11hs d waiting line

m p 20 the average time a unit spends in the waiting

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Unformatted text preview: e-Server Example Queuing Formulas for Model B: Multiple-Server System, also Called M/M/S The number of people or units in theMsystem is: LS = λµ ( λ / µ ) ( M − 1) !( M µ − λ ) P+ 20 λ µ The average time a unit spends in the waiting line and being serviced (namely, in the system) is: µ ( λ / µ) M 1 LS WS = P+ = 20 µλ M −1 ! Mµ − λ ( )( ) D – 34 Multiple-Server Example Queuing Formulas for Model B: Multiple-Server System, also Called M/M/S The average number of people or units in line waiting for service is: λ Lq = LS − µ The average time a person or unit spends in the queue waiting for service is: 1 Lq Wq = WS − = µλ D – 35 Multiple-Server Example λ=2 µ=3 P0 = 1 M=2 2 1 n 2 2(3) ∑ 1 2 ÷ + 1 ÷ n=0 n! 3 2! 3 2(3) − 2 1 1 1 = = = 212 2 1 4 6 1+ + 1+ + ÷ ÷ 33 3 2 9 6 − 2 = .5 probability of zero cars in the system D – 36 Multiple-Server Example LS ( ) = ( 1) !( 2(3) − 2) (2)(3) 2 / 3 2 1 2 8 / 3 1 2 3 += ÷+ = 2 ÷ 2 3 16 2 3 4 = .75 average numb...
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