Back-of-the-envelope estimation in HLD - System Design Exercise

Design: Back-of-the-envelope Estimation for System Design

Focus on quick, approximate calculations for system scale and performance. Detailed design and implementation are out of scope.

Functional Requirements

FR1: Estimate system capacity quickly with limited data

FR2: Calculate rough resource needs (servers, storage, bandwidth)

FR3: Provide latency and throughput approximations

FR4: Support decision making in early design phases

Non-Functional Requirements

NFR1: Estimates must be done within minutes

NFR2: Accuracy within an order of magnitude is acceptable

NFR3: Use simple math and assumptions

NFR4: No detailed data or simulations required

Think Before You Design

Questions to Ask

❓ Question 1

❓ Question 2

❓ Question 3

❓ Question 4

❓ Question 5

Key Components

User load estimations

Request size and frequency

Network bandwidth

Storage capacity

Compute resources (CPU, memory)

Design Patterns

Load estimation

Capacity planning

Latency and throughput approximation

Resource scaling heuristics

Reference Architecture

No specific architecture diagram needed for estimation; focus on calculation steps.

Components

User Load Estimator

Manual calculation or spreadsheet

Estimate number of concurrent users and requests per second

Data Size Calculator

Manual calculation or spreadsheet

Estimate average data size per request and total data volume

Resource Estimator

Manual calculation or spreadsheet

Estimate CPU, memory, storage, and bandwidth needs

Request Flow

1. 1. Define expected number of users and requests per second.

2. 2. Estimate average data size per request.

3. 3. Calculate total data throughput (requests per second * data size).

4. 4. Estimate storage needs based on data retention policies.

5. 5. Approximate CPU and memory based on request complexity.

6. 6. Check network bandwidth requirements against available capacity.

7. 7. Adjust estimates for peak load and safety margin.

Database Schema

Not applicable for back-of-the-envelope estimation.

Scaling Discussion

Bottlenecks

Underestimating peak traffic leading to resource exhaustion

Ignoring variability in request size or complexity

Not accounting for network latency or failures

Overlooking data growth over time

Solutions

Include safety margins (e.g., 2x peak load) in estimates

Use conservative assumptions for request size and complexity

Plan for horizontal scaling and load balancing

Regularly update estimates with real usage data

Interview Tips

Time: Spend 5 minutes clarifying assumptions, 15 minutes performing rough calculations, 5 minutes discussing results and trade-offs, 5 minutes answering questions.

Clarify assumptions and constraints before estimating

Explain each step of the calculation clearly

Discuss trade-offs between accuracy and speed

Mention how estimates guide design decisions

Highlight importance of revisiting estimates with real data

Practice

1. What is the main purpose of back-of-the-envelope estimation in system design?

easy

A. To quickly estimate system requirements using simple calculations

B. To write detailed code for the system

C. To create a full architecture diagram

D. To perform in-depth performance testing

Solution

1. Step 1: Understand the goal of back-of-the-envelope estimation

   This method is used to quickly guess system needs without detailed work.

2. Step 2: Compare options to the goal

   Only To quickly estimate system requirements using simple calculations matches the quick estimation purpose; others are detailed tasks.

3. Final Answer:

   To quickly estimate system requirements using simple calculations -> Option A

4. Quick Check:

   Quick estimation = To quickly estimate system requirements using simple calculations [OK]

Hint: Focus on quick, simple calculations for early guesses [OK]

Common Mistakes:

• Confusing estimation with detailed design
• Thinking it involves coding or testing
• Assuming it requires full diagrams

2. Which of the following is the correct way to start a back-of-the-envelope estimation for a web service's daily traffic?

easy

A. Calculate exact user behavior with detailed logs

B. Estimate average users per hour and multiply by 24

C. Design the database schema first

D. Write the full API specification

Solution

1. Step 1: Identify the starting point for traffic estimation

   Back-of-the-envelope estimation uses simple averages, not detailed data.

2. Step 2: Evaluate options for simplicity and relevance

   Estimate average users per hour and multiply by 24 uses average users per hour times 24 hours, a simple and effective start.

3. Final Answer:

   Estimate average users per hour and multiply by 24 -> Option B

4. Quick Check:

   Simple average x time = Estimate average users per hour and multiply by 24 [OK]

Hint: Use simple averages and multiply by time units [OK]

Common Mistakes:

• Starting with detailed logs instead of rough estimates
• Jumping to design before estimating traffic
• Confusing estimation with specification writing

3. You estimate a system will have 10,000 users daily, each making 5 requests on average. What is the total number of requests per day?

medium

A. 100,000 requests

B. 2,000 requests

C. 15,000 requests

D. 50,000 requests

Solution

1. Step 1: Multiply users by requests per user

   10,000 users x 5 requests each = 50,000 requests.

2. Step 2: Confirm total requests per day

   The total is simply the product of users and requests per user.

3. Final Answer:

   50,000 requests -> Option D

4. Quick Check:

   Users x requests = 50,000 [OK]

Hint: Multiply users by average requests per user [OK]

Common Mistakes:

• Adding instead of multiplying
• Mixing up users and requests
• Choosing an option too large or too small

4. A designer estimated 1 million requests per day but forgot to consider peak hour traffic. What is the likely problem with this estimation?

medium

A. Ignoring average request size affecting storage needs

B. Overestimating total daily traffic causing wasted resources

C. Underestimating peak load leading to potential system overload

D. Not including user authentication time

Solution

1. Step 1: Understand the impact of ignoring peak traffic

   Peak traffic is often much higher than average, so ignoring it underestimates load.

2. Step 2: Identify the consequence of underestimation

   System may overload during peak times if capacity is based on average only.

3. Final Answer:

   Underestimating peak load leading to potential system overload -> Option C

4. Quick Check:

   Ignoring peak = underestimation risk [OK]

Hint: Always consider peak, not just average, traffic [OK]

Common Mistakes:

• Assuming daily average covers peak needs
• Confusing storage with traffic load
• Focusing on unrelated factors like authentication time

5. You need to estimate the storage required for a photo-sharing app. Each photo is 3MB, and you expect 500,000 uploads per month. What is the approximate monthly storage needed?

hard

A. 1.5 TB

B. 150 GB

C. 15 GB

D. 1.5 GB

Solution

1. Step 1: Calculate total storage in MB

   500,000 photos x 3 MB each = 1,500,000 MB.

2. Step 2: Convert MB to TB

   1,500,000 MB ÷ 1024 ≈ 1465 GB ÷ 1024 ≈ 1.43 TB, approximately 1.5 TB.

3. Final Answer:

   1.5 TB -> Option A

4. Quick Check:

   Uploads x size ≈ 1.5 TB [OK]

Hint: Multiply count by size, then convert units [OK]

Common Mistakes:

• Forgetting to convert MB to GB
• Mixing up MB and GB units
• Using wrong multiplication factors