3325p11hs d waiting line

0041 0003 hrs 1 second time in queue d 40 constant

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Unformatted text preview: ER OF SERVERS M NUMBER IN QUEUE 1 window 1 8.1 .45 hrs, 27 minutes 2 windows 2 .2285 .0127 hrs, ¾ minute 3 windows 3 .03 .0017 hrs, 6 seconds 4 windows 4 .0041 .0003 hrs, 1 second TIME IN QUEUE D – 40 Constant-Service Model Average length of queue λ2 Lq = 2µ(µ – λ) 2µ(µ Average waiting time in queue Wq = Average number of Average customers in system Ls = Lq + Average time Average in the system in λ 2µ(µ – λ) 2µ(µ W s = Wq + λ µ 1 µ D – 41 Constant-Service Example Trucks currently wait 15 minutes on average Truck and driver cost $60 per hour Automated compactor service rate (µ) = 12 trucks per hour Arrival rate (λ ) = 8 per hour Compactor costs $3 per truck Current waiting cost per trip = (1/4 hr)($60) = $15 /trip 1 8 Wq = = hour 12 2(12)(12 – 8) 2(12)(12 Waiting cost/trip with compactor = (1/12 hr wait)($60/hr cost) Savings with = $15 (current) – $5(new) $15 new equipment /trip /trip Cost of new equipment amortized Net savings = $ 5 /trip = $10 $10 = $ 3 /trip = $ 7 /trip D – 42 Little’s Law A queuing system in steady state L = λW (which is the same as W = L/λ Lq = λWq (which is the same as Wq = Lq/λ Once one of these parameters is known, the other can be easily found It makes no assumptions about the probability distribution of arrival and service times Applies to all queuing models except the limited population model D – 43 Limited-Population Model T T+U Average number running: J = NF(1 - X) Average NF(1 Service factor: X =...
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