Question

A cable company decides to provide Internet access over cable in a neighborhood consisting of 5000 houses. The company uses a coaxial cable and spectrum allocation allowing \(100 \mathrm{Mbps}\) downstream bandwidth per cable. To attract customers, the company decides to guarantee at least 2 Mbps downstream bandwidth to each house at any time. Describe what the cable company needs to do to provide this guarantee.

Short answer

100 cables are needed, each serving 50 houses.

Step-by-step solution

Calculate Total Required Bandwidth

First, determine the total bandwidth required to fulfill the company's promise of at least 2 Mbps per house. With 5000 houses, each needing 2 Mbps, the total required bandwidth is \( 5000 \times 2 = 10,000 \) Mbps, or equivalently 10 Gbps.

Analyze the Current Bandwidth Setup

The company currently has a downstream bandwidth of 100 Mbps allocated per cable. This is based on their spectrum allocation on a coaxial cable. Compare this to the total bandwidth requirement calculated in the previous step.

Determine the Number of Cables Needed

To fulfill the bandwidth requirement of 10,000 Mbps, calculate how many 100 Mbps cables are necessary. Divide the total required bandwidth by the bandwidth per cable: \( \frac{10,000}{100} = 100 \) cables needed.

Recommendation for Implementation

The company should install 100 separate coaxial cables to provide the guaranteed 2 Mbps to each house. Each cable will support 50 houses (because \( \frac{100}{2} = 50\)), totaling to the service of 5000 houses with the necessary 100 cables.

Key concepts

Bandwidth Calculation

When providing internet access, especially via cable, understanding bandwidth calculation is crucial. Bandwidth refers to the maximum rate at which data can be transferred over a network channel. In our scenario, the promise is a minimum of 2 Mbps per household. To find the total required bandwidth for a neighborhood of 5000 houses, you multiply the number of houses by the bandwidth each house is guaranteed:

• Each house requires 2 Mbps.
• Total number of houses: 5000.

This results in a total bandwidth requirement of 10,000 Mbps or 10 Gbps. Accurate bandwidth calculation ensures that every household receives the promised internet speed without disruption even during peak usage times.

Coaxial Cable

Coaxial cables are a common medium used by cable companies to provide internet services. These cables consist of a core conductor, usually copper, surrounded by an insulating layer, a metallic shield, and an outer insulating layer. Coaxial cables are chosen for their ability to efficiently transmit high-frequency signals over long distances with minimal interference. This makes them ideal for delivering high-speed internet and television services to multiple homes in a neighborhood. In the case of our exercise, the cable company uses coaxial cable to allocate 100 Mbps of downstream bandwidth per cable. This technology's reliability and performance make it suitable for ensuring stable internet connections.

Spectrum Allocation

Spectrum allocation is the process of assigning specific frequency bands for particular uses by cable companies. In the context of internet delivery, these frequencies are used to carry internet data. Proper spectrum allocation enables the efficient use of the electromagnetic spectrum to maximize the data capacity of each coaxial cable. In our situation, by allocating 100 Mbps to each cable, the company ensures that the transmission is optimized to handle the required bandwidth for the served houses. Effective spectrum allocation is essential for maximizing the use of available bandwidth, reducing congestion, and ensuring reliable internet service to multiple subscribers.

Guaranteed Bandwidth

Guaranteed bandwidth refers to the minimum level of data transmission speed that a service provider promises to its customers. In many contracts, this is stated as a "minimum speed" and helps ensure that subscribers receive consistent and reliable internet service. To provide a guaranteed 2 Mbps to each of the 5000 houses, the cable company should install sufficient infrastructure to meet demand. This includes implementing 100 separate coaxial cables, each supporting a segment of 50 houses. Providing guaranteed bandwidth requires strategic planning and infrastructure investment to ensure each customer's service remains uninterrupted and operates at the expected speed.