Question

At the low end, the telephone system is star shaped, with all the local loops in a neighborhood converging on an end office. In contrast, cable television consists of a single long cable snaking its way past all the houses in the same neighborhood. Suppose that a future TV cable were 10-Gbps fiber instead of copper. Could it be used to simulate the telephone model of everybody having their own private line to the end office? If so, how many one-telephone houses could be hooked up to a single fiber?

Short answer

A 10-Gbps fiber can support about 156,250 simultaneous telephone calls.

Step-by-step solution

Understand the problem statement

We are asked to determine if a 10-Gbps fiber cable can be used to simulate the telephone model, where each house has its own dedicated line. We need to calculate how many such lines can fit on this fiber cable.

Analyze the bandwidth requirements

Determine the typical bandwidth required for a single voice telephone call. Typically, a standard telephone call requires 64 kbps of bandwidth in a digital form using Pulse Code Modulation (PCM).

Calculate the number of simultaneous calls

Since the fiber has a capacity of 10 Gbps, we need to find out how many 64 kbps channels can fit into this capacity. Use the formula: \[ \text{Number of Calls} = \frac{\text{Total Fiber Capacity (in bps)}}{\text{Bandwidth per Call (in bps)}} \]

Substitute and calculate

Substitute the given values into the formula from Step 3:\[ \text{Number of Calls} = \frac{10 \, \text{Gbps} \times 10^9}{64 \, \text{kbps} \times 10^3} = \frac{10,000,000,000}{64,000} \] Simplifying this gives approximately 156,250.

Conclusion

Therefore, the 10-Gbps fiber can support approximately 156,250 simultaneous one-telephone houses, simulating the private line model of a telephone system.

Key concepts

Telephone System Model

The telephone system model is a fascinating concept highlighting the infrastructure of traditional telecommunication. In this model, each household is typically connected to a central point known as an end office or central office through an individual line. This is often referred to as the "star network model" because the end office serves as the hub, and each household as the endpoint of a star-like structure.
Unlike a distributed system where connections might form a web or a mesh, the star model is great for maintaining dedicated lines, making it reliable for services like voice calls. But, laying individual lines involves substantial infrastructure costs, which is a limitation of this model.

• Each home is directly linked to an end office.
• Reliability in maintaining dedicated communication paths.
• Higher cost due to dedicated infrastructure.

This model is still in use today, though modern systems may employ more robust solutions to accommodate data and multimedia services beyond voice.

10-Gbps Fiber Cable

Fiber optics have revolutionized telecommunications by providing massive bandwidth capabilities. A 10-Gbps (Gigabits per second) fiber cable can carry an immense amount of data over great distances with minimal loss, making it significantly more efficient than traditional copper cables.
The 10-Gbps specification refers to how much data can be transmitted across the fiber optic line every second. This high capacity is crucial for meeting modern telecommunication demands, particularly in areas with high internet and communication traffic.

• High data capacity: Suitable for both internet and telecommunication.
• Low loss over long distances: More efficient than copper.
• Ideal for densely populated areas needing robust communication lines.

By switching to a high-bandwidth fiber, the potential to handle many simultaneous communications increases dramatically, a key attribute in upgrading local and global networks.

Bandwidth Calculation

Calculating bandwidth, or the data rate available for communication, is essential when assessing how many concurrent communications can be supported by a given system. When thinking about a 10-Gbps fiber, the goal is to determine how effectively this bandwidth can be partitioned for various uses, such as simulating the telephone model.
When we talk about bandwidth for a phone system, each call requires a specified amount of data rate—often 64 kbps using PCM. To calculate the number of concurrent calls, we use:
\[ \text{Number of Calls} = \frac{\text{Total Fiber Capacity (in bps)}}{\text{Bandwidth per Call (in bps)}} \]
This formula helps us understand the efficiency of the fiber optic technology by determining that approximately 156,250 calls can occur simultaneously on a single 10-Gbps fiber, illustrating the cable's capacity to handle substantial communication loads.

Pulse Code Modulation (PCM)

Pulse Code Modulation (PCM) is a method to digitally represent sampled analog signals. It is one of the most common ways telephone systems digitize audio signals, making communication more reliable and clear in digital networks.
PCM operates by sampling an analog signal at regular intervals—often 8000 times per second for telephone audio—and then quantizing these samples into discrete numerical values. It generates 64,000 bits per second (64 kbps) per telephone call, which is standard in digital telecommunication systems.

• Audio is sampled at regular intervals for digital clarity.
• 64 kbps required per call in standard telephone applications.
• PCM is integral to modern telecommunication as it facilitates digital transmission and storage.

Understanding PCM is crucial for grasping how voice bandwidth is calculated and applied in telecommunication models, acting as the backbone for digital voice communication.