What is the total utilization of a circuit-switched network, accommodating five users with equal bandwidth share, and the following properties:

Three users each using 60% of their bandwidth share
Two users each using 5% of their bandwidth share

Give answer in percent, with one decimal place (normal rounding) and no percentage sign (e.g. for 49.15% you would enter "49.2" without the quotes).

Question

What is the total utilization of a circuit-switched network, accommodating five users with equal bandwidth share, and the following properties:

Three users each using 60% of their bandwidth share
Two users each using 5% of their bandwidth share

Give answer in percent, with one decimal place (normal rounding) and no percentage sign (e.g. for 49.15% you would enter "49.2" without the quotes).

BlackTom AI · Accepted Answer

We start by identifying that there are five users sharing the circuit equally, so each user has a bandwidth share of 1/5 (or 20%).

Now, evaluate each group of users based on how much of their share they use:
- Three users each using 60% of their share: each contributes 0.60 × 1/5 = 0.60 × 0.20 = 0.12 (which is 12% of the total network capacity). For three users, total contribution = 3 × 0.12 = 0.36 (36%).
- Two users each using 5% of their share: each contributes 0.05 × 1/5 = 0.05 × 0.20 = 0.01 (which is 1% of the total). For two users, total contribution = 2 × 0.01 = 0.02 (2%).

Add the contributions from both groups to get the overall utilization: 0.36 + 0.02 = 0.38, which corresponds to 38.0% when expressed as a percentage.

Expressed as a decimal, the total utilization is 0.38, and when converted to a percentage with one decimal place (normal rounding), it remains 38.0. Note that no percent sign is required in the final numeric answer.

INTRO TO COMPUTER NETWORKS (CS_372_400_U2025) Midterm Exam

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