A meticulous, well-researched budget is the cornerstone of any successful venture – this holds true even for something as seemingly mundane as pool cleaning. Pool maintenance is a cyclical, consistent requirement that necessitates a careful allocation of financial resources to ensure an inviting, sparkling aquatic oasis year-round. Therefore, we delve into the intricate aspects of creating a comprehensive budget for your pool cleaning needs.

The first point of consideration is the frequency of pool usage. It is axiomatic that a frequently used pool demands more regular cleaning and maintenance. The increased volume of external contaminants like body oils, lotions, and sunscreen necessitate a higher frequency of chemical treatments, filter changes, and overall upkeep. Therefore, gauging the usage of your pool and quantifying it into your budget is a crucial aspect.

Pool size is also a significant determinant in the budgeting process. According to the Euclidean geometry principle, the cleaning effort and resources exponentially increase with the enlargement of area, thus, larger pools will naturally require more cleaning supplies and possibly professional assistance. Consequently, pool size will play a pivotal role in your budgeting.

The choice between an automatic pool cleaner or hiring professional pool cleaning services is not one to be made lightly. Automatic pool cleaners, though they have a higher upfront cost, are beneficial in the long run as they cut down on labor costs and time. Many of these cleaners use advanced technologies like gyroscopes and sensors to ensure comprehensive cleaning. Alternatively, professional pool cleaning services, while they may seem cost-effective initially, can add up over time. This tradeoff between labor and capital, akin to the economic theory propounded by John Maynard Keynes, should be made taking into consideration the frequency and magnitude of the cleaning task.

The type of pool—saltwater or chlorinated—also affects the budget. Saltwater pools require specific equipment for maintenance, such as saltwater chlorinators, and the cost of salt can add up. In contrast, chlorinated pools necessitate regular purchases of chlorine tablets, algaecides, pH balancers, and other chemicals. It's a bit like comparing the operational costs of a diesel versus a petrol automobile: each has its unique costs associated with maintenance and running.

Understanding the seasonal changes in your location is vital in pool maintenance budgeting. During colder months, pools may require less frequent cleaning but may need winterizing products and methods to protect them from harsh conditions. Analogous to the concept of entropy in thermodynamics, neglecting the pool during these periods can lead to disorder or damage, leading to higher costs in the long run.

Finally, the age and condition of your pool play a substantial role in determining your pool cleaning budget. Older pools may require more frequent equipment repairs or replacements and potentially more chemicals to maintain water balance. It's not dissimilar to the 'Law of Diminishing Returns' in economics; as a pool ages, the cost of maintaining it in pristine condition can increase.

The creation of a pool cleaning budget thus requires a comprehensive understanding of multiple factors, each with its own weightage. The unequivocal objective is to ensure your pool remains a refreshing, aesthetically pleasing haven, without causing financial strain. This necessitates a delicate balance between various conflicting demands – a task that requires planning, foresight, and meticulous adherence to the budget set out at the beginning of each season.

Remember, the key to successful budgeting is regular review and adjustment. Economic conditions fluctuate, technologies advance, and pool usage patterns change, all of which necessitate budget revisions. In this way, your pool maintenance budget becomes a living, evolving entity, much like the shimmering, ever-changing waters it serves to maintain.

Consider this budgeting exercise not as a mundane task, but as an opportunity to engage in a thought-provoking, intellectually stimulating endeavor that employs principles from mathematics, economics, and science, all with the aim of achieving the very tangible, very enjoyable result of a well-maintained pool.