Question

. 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 15 attendee arrivals per hour and the average time a person spends on the computer is 10 minutes. To ensure that waiting times are not too long, the organizers want to ensure that the utilization of the computers doesn’t exceed 90 percent. At least how many computers do they need to have?

Answer 1

Arrival ratio = 15 peoples / hour

Servicing proportion = 60 / 10 = 6 people / hour with one workstation

Servicing proportion with x amount of workstations = 6x / hour

Servicing proportion at 90% consumption = 6x (90%) = 5.40x / hour

Thus, to facility 13 arrivals / hour, the requirement will be x workstations = 15 / 5.40 = 2.78

With 2 workstations, the service capability might be 12 / hour and the consumption might be 15/12 = 1.25, which outstrips the manager’s regular of 90% consumption.

With 3 workstations, the service capability rises to 18 / hour. If 13 peoples reach, the consumption proportion might be 15 / 18 = 0.8333, Moreover, below the essential extreme of 90% consumption.

Hence, the 2.78 might be rounded off to subsequent whole digit, which is 3 workstations

Answer 2

They would need to have at least 3 computers

Step-by-step explanation:

According to the given data we have the following:

Arrival rate = 15 persons per hour

Servicing rate = 60 / 10 = 6 persons per hour with one computer

Servicing rate with x number of computers = 6x per hour

Servicing rate at 90% utilisation = 6x (0.90) = 5.40x per hour

Therefore to service 13 arrivals per hour, we will need x computers = 15/ 5.40 = 2.78

With 2 computers, the service capacity will be 12 per hour and the utilisation will be 15/12 = 125%, which exceeds the organiser’s standard of 90% utilization.

With 3 computers, the service capacity increases to 18 persons per hour. If only 13 persons arrive, the utilisation rate will be 15 / 18 = 83.33%, below the required maximum of 90% utilisation.

Therefore, the 2.78 can be rounded off to next whole number 3 computers