Question

CPU on demand offers real time high performance computing services. CPUD owns 1 super computer that can be accessed through the internet. Their customers send jobs that arrive on average every 4 hours. The standard deviation of the interarrival times is 7 hours. Executing each job takes on average 2 hours on the supercomputer and the standard deviation of the processing time is 3.5 hours.

How long does a customer have to wait to have a job completed

Answer 1

Arrival rate = 4 hours

Standard deviation of arrival = 7 hours

Activity processing time = 2 hours

Standard deviation of processing = 3.5 hours

Utilization =Activity time/ Arrival rate 2/4 = 0.5

CVa = 4/7

CVp =2/3.5

Expected waiting time Tq= (activity time)*(utilization/ (1-utilization))*((CVa² + CVp²)/2)

Tq = (2)*(0.5/(1-0.5))*(((4/7)² +(2/3.5)²)/2) = 0.653061 hours

Total time customer will have to wait to have a job completed = Expected waiting time +Activity processing time = 2 + 0.653061

= 2.653061 or 2.65 hours (round off)

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