Question 1 (3+2-5 points) The organizers of a conference in the Houston Conventi

Question

Question 1 (3+2-5 points) The organizers of a conference in the Houston Convention Center are evaluating the possibility of setting up a computer area where attendees can check their e-mail on computers provided by the organization. There will be one common queue for all computers and only one person uses a computer at a time. On average there are 19 attendee arrivals per hour and the average time a person spends on the computer is 14 minutes To ensure that waiting times are not too long, the organizers want to ensure that the utilization of the computers doesn't exceed 80 percent. At least how many computers do they need to have? The organizers of the conference have decided to buy 7 computers. Assume that the standard deviation of arrivals is equal to the average inter-arrival time, and the standard deviation of processing times is equal to the average processing time. What is the average waiting time to check e-mails? a) b)

Explanation / Answer

a) Solution

Arrival rate = 19 persons per hour

Servicing rate = 60 / 14 = 4.29 persons per hour with one computer

Servicing rate with x number of computers =4.29 x per hour

Servicing rate at 80% utilisation =4.29 x (0.80) = 3.43 x per hour

Therefore to service 19 arrivals per hour, we will need x computers = 19/ 3.43 = 4.54

Therefore, the 4.54 can be rounded off to next whole number 5 computers needed.

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