InClassQueueing.docx - Waiting Line In Class Work Mu rate at which they are processing customers Lambda rate at which customers are coming in Name

InClassQueueing.docx - Waiting Line In Class Work Mu rate...

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Waiting Line - In Class Work Mu: rate at which they are processing customers Lambda: rate at which customers are coming in Name: Example 10.1 Queueing System M/M/1 Facts: 1. λ = 15 customers/hour 2. average service time = 3 mins. We need µ = 20 customers per hour We need to find µ from this information. We reason as follows: 1/µ = 3 mins = 1/20 hour. So µ = 20 customers/hour. Note: λ/µ = 0.75 < 1 as required for stability. Find 1. Utilization of teller. 15/20 = .75 2. Average number in waiting line (queue). L q: =15^2/20x(20-15 )= 2.25 3. Average number in system (i.e., in queue and being served) L s = 15/(20-15)= 3 4. Average waiting time in line. W q = 2.25/15 hrs. = 9 mins 5. Average waiting time in system (i.e., including service). W s = 3/15hrs = 12 mins
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6. The probability that there are no more than 3 customers in the system (ie. P 0 +P 1 +P 2 +P 3 ). P 0 = 1-Lambda/Mu = 1-15/20 = .25 P 1 = .25*(Lambda/Mu^1)= .1875 P 2 = .140625 see excel P 3 = =.105469 see excel 68.36% OF THE TIME THERE ARE 3 OR FEWER IN THE SYSTEM This means that there are more than 3 people for 31.64% of the time 7.
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