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Chapter 4: Problem 44

Some Internet service providers (ISPs) charge companies based on how much bandwidth they use in a month. One method that ISPs use for calculating bandwidth is to find the 95th percentile of a company鈥檚 usage based on samples of hundreds of 5-minute intervals during a month. (a) Explain what 鈥�95th percentile鈥� means in this setting. (b) Which would cost a company more: the 95th percentile method or a similar approach using the 98th percentile? Justify your answer.

Short Answer

Expert verified
The 98th percentile would cost more because it considers higher usage levels.

Step by step solution

01

Understanding Percentiles

In data analysis, a percentile is a measure used to indicate the value below which a given percentage of observations in a dataset falls. In this setting, the 95th percentile represents the bandwidth usage value below which 95% of all sampled 5-minute intervals fall. This means the ISP calculates bandwidth so that 5% of the highest usage intervals exceed this value.
02

95th Percentile Explained

When a company receives a bill based on the 95th percentile of its bandwidth usage, it implies that the ISP is charging them based on a usage level that is greater than what the company uses for 95% of the time. This focuses on the higher end of the company's bandwidth consumption.
03

Understanding 98th Percentile

Like the 95th percentile, the 98th percentile is a point in the dataset below which 98% of the data falls. When bandwidth is calculated based on this percentile, the ISP targets even higher usage values, which means only the top 2% of usage exceeds this value.
04

Comparison of Costs Between Percentiles

The 98th percentile would typically charge based on higher usage values compared to the 95th percentile because it captures higher bandwidth usage intervals. Given the same dataset, the value at the 98th percentile is higher or equal to the value at the 95th percentile.
05

Conclusion on Cost Differences

Since the 98th percentile focuses on a smaller portion of high usage data (2% vs. 5%), it usually results in a higher base for calculating costs, making it more expensive for a company compared to the 95th percentile method.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Bandwidth Billing Methods
When Internet Service Providers (ISPs) bill customers based on bandwidth usage, they often employ methods that calculate usage in terms of percentiles. This method involves analyzing the amount of bandwidth used over specific, regularly sampled intervals. Typically, ISPs will take these usage samples from regular 5-minute intervals over the course of a month to determine a fair billing amount.

The goal of using percentiles in billing is to manage instances of abnormally high bandwidth use without unfairly penalizing the typical usage times. By focusing on percentiles, ISPs aim to create a balance where only the higher moments of usage (those exceeding a certain percentile) are considered for billing purposes, thus preventing momentary spikes from leading to excessive charges.
ISP Pricing Strategies
Internet Service Providers (ISPs) need to have effective pricing strategies to manage their resources and serve clients efficiently. A popular strategy involves using percentiles to determine how much bandwidth a customer has used without charging them based on fleeting high usage. Here's how it works:
  • ISPs collect bandwidth usage data at regular intervals.
  • This data is then analyzed to find high utilizations moments, typically using the 95th or 98th percentiles.
  • The calculated percentile indicates the bandwidth level surpassed only a small percentage of the time.
These strategies allow ISPs to set a pricing structure that scales with bandwidth usage while offering customers a predictable cost structure. This method ensures that occasional peaks in internet activity don't disproportionately skew billing, while also protecting the ISP's network from being overdrawn by sustained high usage.
95th vs 98th Percentile Comparison
Choosing between the 95th and 98th percentile to bill for bandwidth usage can significantly impact the overall costs. The difference between these two percentiles lies in how they measure usage extremes:
  • The 95th percentile means that only the top 5% of usage intervals exceed this level. For most of the time (95%), usage is below this mark.
  • The 98th percentile indicates even higher usage, as it encompasses the top 2% of the highest usage points. This captures more sporadic peaks.
In practical terms, billing based on the 98th percentile means using a higher base bandwidth usage level for billing. Hence, it is generally more expensive since the company is often billed based on the "worst" 2% of its usage times rather than the "worst" 5%. This means higher charges as less of the user's average behavior is taken into account, only focusing on extreme bandwidth spikes.

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