ADM 3301 Lecture Notes - Lecture 14: Capacity Utilization

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> similarly, when a second customer arrives, and the server is busy, there is an 80% chance that someone else is in the queue, or a 16% chance that they are second in line. > when a job enters the system, there is a 41% chance of 4 or more jobs waiting! Now suppose =15 and =30 , and only one server again (s=1): > avg. no. of customers in system: l=1. > avg. no. waiting in the queue: lq = 0. 5. > avg waiting time in system: w = 1/15 hours [= 4 minutes] > avg. waiting time in queue wq = 1/30 hours [= 2 minutes] > t = time in queue plus avg. service time = 1/30 + 1/30 = 1/15 hours [= 4 minutes] > now you have a system that woks very efficiently (notice little"s law) > thus there is an unavoidable trade-off between keeping waiting times low and wasting resource capacity.

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