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WaitingLineExamples

# WaitingLineExamples - Waiting Line Models Click to edit...

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Click to edit Master subtitle style S. M. Ng, HKUST 11 Waiting Line Models

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S. M. Ng, HKUST 22 Trade-off between Service Capacity and Waiting Line
S. M. Ng, HKUST 33 Queuing System Cost Tradeoff Let: Cw = Cost of waiting per customer per hour Lq = Mean number of waiting customers Cs = Cost of service per server per hour S = Number of servers Total cost per hour = service cost + customer waiting cost = Cs S + Cw Lq Note : Only consider systems where if service rate per server is given. μ λ > S

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S. M. Ng, HKUST 44 Congestion vs. System Utilization 0 1.0 100 10 8 6 4 2 0 For the M/M/1 model, avg. number in the system is: ρ L s 0 0 0.2 0.25 0.5 1 0.8 4 0.9 9 0.99 99 L s ρ ρ ρ = 1 L s ̶
Click to edit Master subtitle style S. M. Ng, HKUST 55 Waiting Line Examples

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S. M. Ng, HKUST 66 Example 1 Students arrive at the ASO at an average of one every 15 minutes and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy, who works 8 hours per day. Assume Poisson arrivals a. What percentage of time is Judy idle? a. How much time, on average, does a student spend waiting in line? a. How long is the (waiting) line on average? a. What is the probability that an arriving student (just before entering the ASO) will find at least one other student waiting in line?
S. M. Ng, HKUST 77 a. What percentage of time is Judy idle?

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