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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
If that isn't an option a good package to look into is spatie/period (https://github.com/spatie/period). By converting your allTimeSlots data and your booking data into periods you should be able to get the information you want.
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Related posts
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Are there any packages that handle fetching according to periods (for example, fetch users created last month)
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How can I check if the current date is between the start and end date of my sale?
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How can I check if a booking lies, overlaps or "eats up" already existing bookings?
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Availability Calendar / Livewire?
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I've released a brand new major version of spatie/period today, it might be a useful package if you're working with date ranges