Consider a user types a document with a speed of 100 words
per minute. Assume that an average word consists of 5 letters and ends
by a break which can be a space, new line, TAB, or punctuation, and an
average sentence consists of 20 words. Assume that a spell-check thread
is only activated when a word break is detected, and it will finish its
task within 1 millisecond. Similarly, a grammar-check thread is only
activated when a sentence break, a period, is detected, and it needs 1.5
millisecond to finish its task. Assume that context switch overhead is 0.1
millisecond. What’s the maximum number of word processing users can
be admitted if the human eye refreshing rate is 1/20 second.
To find the maximum number of word processing users that can be admitted, we need to consider the time it takes for each task and the refresh rate of the human eye. Here's how we can calculate it step-by-step:
1. Calculate the time it takes to process each word:
- Average word length = 5 letters + 1 break = 6 characters
- Time to process a word = 6 characters / 100 characters per minute = 0.06 minutes per word = 60 milliseconds per word
2. Calculate the time it takes to process each sentence:
- Average sentence length = 20 words
- Time to process a sentence = 20 words * 60 milliseconds per word = 1200 milliseconds per sentence
3. Calculate the time it takes for context switching:
- Context switch overhead = 0.1 milliseconds
4. Calculate the time it takes for spell-check thread:
- Time for spell-check thread = 1 millisecond
5. Calculate the time it takes for grammar-check thread:
- Time for grammar-check thread = 1.5 milliseconds
6. Calculate the total time per sentence:
- Total time per sentence = Time to process a sentence + Context switch overhead + Time for grammar-check thread
7. Calculate the total time per word processing task:
- Total time per word processing task = Time to process a word + Context switch overhead + Time for spell-check thread
8. Calculate the maximum number of users that can be admitted:
- Refresh rate of human eye = 1/20 seconds = 50 milliseconds
- Maximum number of users = Refresh rate of human eye / (Total time per sentence + Total time per word processing task)
Let's substitute the values into the formula and calculate:
Total time per sentence = 1200 milliseconds + 0.1 milliseconds + 1.5 milliseconds = 1201.6 milliseconds
Total time per word processing task = 60 milliseconds + 0.1 milliseconds + 1 millisecond = 61.1 milliseconds
Refresh rate of human eye = 50 milliseconds
Maximum number of users = 50 milliseconds / (1201.6 milliseconds + 61.1 milliseconds) = 50 milliseconds / 1262.7 milliseconds ≈ 0.04
Therefore, the maximum number of word processing users that can be admitted is approximately 0.04, which means less than one user can be admitted based on the given constraints.
To determine the maximum number of word processing users that can be admitted, we need to consider the time it takes to process each word, including the spell-check and grammar-check threads, as well as the time required for context switching.
Given:
- User typing speed: 100 words per minute.
- Average word length: 5 letters.
- Average sentence length: 20 words.
- Spell-check thread time: 1 millisecond per word break.
- Grammar-check thread time: 1.5 milliseconds per sentence break (period).
- Context switch overhead: 0.1 millisecond.
- Human eye refresh rate: 1/20 second.
Let's calculate the time it takes to process each word:
- Time to process a word: (5 letters / average word length) * (1/100) minute per word = 0.05 minutes per word.
- Time to process a word: 0.05 minutes per word * 60 seconds per minute = 3 seconds per word.
Now let's calculate the time it takes to process each sentence:
- Time to process a sentence: 20 words * 3 seconds per word = 60 seconds per sentence.
Considering the spell-check and grammar-check threads, we need to account for the time it takes to process each word break and sentence break:
- Time for spell-check thread: 1 millisecond per word break.
- Time for grammar-check thread: 1.5 milliseconds per sentence break.
Next, let's calculate the total time required for each word processing user:
- Total time for a word: Time to process the word + Time for spell-check thread = 3 seconds + 1 millisecond = 3001 milliseconds.
- Total time for a sentence: Time to process the sentence + Time for spell-check thread + Time for grammar-check thread = 60 seconds + 1 millisecond + 1.5 milliseconds = 60001.5 milliseconds.
Considering the context switch overhead, the total time required per user would be:
- Total time per user: Total time for a sentence + Context switch overhead = 60001.5 milliseconds + 0.1 millisecond = 60001.6 milliseconds.
Now, let's calculate the maximum number of users that can be admitted within the human eye refreshing rate of 1/20 second:
- Refreshing rate time: 1/20 second = 50 milliseconds.
The maximum number of users can be calculated as:
Maximum Number of Users = Refreshing rate time / Total time per user
= 50 milliseconds / 60001.6 milliseconds
Calculating this value gives us the maximum number of word processing users that can be admitted within the human eye refreshing rate.