Designing a URL shortening service entails understanding essential functional and non-functional requirements. The primary functionality includes taking a long URL as input and returning a shorter, unique alias. Users should also be able to access the original URL by visiting the short URL.

Non-functional requirements may include low latency for redirection, high availability, scalability to handle a large number of requests, and security to prevent abuse such as generating malicious links. Moreover, the system should allow for analytics such as tracking how many times a URL has been accessed.

For estimating the scale of the service, we can use metrics like the expected number of users and the average number of URLs shortened per user per week. Let's assume a target of 10 million URL shortens per month, resulting in approximately 333,000 requests per day.

Considering a growth rate of 20% per year, we should design for a system that can handle at least double the anticipated load in the early stages. Therefore, we’ll provision infrastructure and storage accordingly, taking into account potential spikes during marketing campaigns or events.

The API will have several endpoints. The primary one would be POST /shorten, which takes a payload of the long URL and returns a shortened version. Another endpoint could be GET /{short-url} for redirection.

For analytics, we can introduce an endpoint like GET /analytics/{short-url} to retrieve access statistics. This lightweight API design will allow for easy integration with various clients while maintaining clean separation of responsibilities.

The database schema will consist of a primary entity representing the URLs. At minimum, we need fields for the original URL, short URL, creation timestamp, and click count. A lookup table could be implemented to maintain unique constraints on short URLs.

For scalability, we might consider NoSQL solutions like DynamoDB for flexibility and speed, or SQL if strong consistency and relationships are required. Caching frequently accessed URLs in a memory store like Redis will enhance performance significantly.

The high-level architecture will feature a client interfacing with a Load Balancer that distributes the requests among multiple servers running the URL shortening service. Each server will interact with the database for both read and write operations.

A caching layer will be employed to store frequently accessed short URLs, minimizing potential database load while improving access speed. Additionally, a job queue can be utilized for tasks like analytics processing that may not require immediate execution.

The request flow begins when a user submits a long URL via the POST /shorten API. The load balancer directs the request to an available service instance. The service checks for existing mappings in the cache before querying the database to persist the new URL mapping.

Upon successful shortening, the system generates a short URL and returns it to the user. For redirection, a GET /{short-url} call retrieves the original URL, incrementing the click count, and redirects the user accordingly.

Key components include the Load Balancer, Web Servers, Database, Cache, and Queue. The Load Balancer ensures high availability and fault tolerance by distributing requests evenly across the servers.

Web Servers host the application logic for handling URL shortening and redirection. The Cache (e.g., Redis) stores the mapping of short and original URLs for fast retrieval, while the Database maintains persistent storage, including traffic analytics.

One trade-off to consider is between consistency and availability. Using distributed databases may lead to eventual consistency issues, while strong consistency can reduce system availability during network partitions.

Another trade-off is minimizing the length of generated short URLs; while shorter URLs are more user-friendly, generating unique short URLs may require more complex algorithms, impacting performance. Balancing between these will be critical during implementation.

Possible failure scenarios include database outages, cache miss handling, and malformed URLs. Implementing fallback systems is crucial; for instance, if the database is down, the service could respond with a cached version of the most recently accessed URLs.

Additionally, malformed URLs should be handled gracefully by validating inputs before attempting to store or redirect to them, returning appropriate error messages to the users.

Future improvements could involve adding user authentication, allowing users to manage their shortened URLs via a dashboard, and providing more advanced analytics.

Further, adding features such as custom short URLs or expiration dates for URLs could appeal to different user needs, while continuous improvements in tracking and performance will ensure the service remains competitive.