The number of allowed connections to a TimescaleDB service instances is limited to try to make sure the database is able to serve all connections. The Service max_connections setting varies by the plan as follows:
Dev plans: 100
100GB plans: 100
512GB plans: 200
1024GB plans: 400
2048GB plans: 800
4096GB and 10240GB plans: 1000
When there are a lot of clients and/or client threads connecting to the database we recommend using connection pooling to limit the number of actual backend connections. Connection pooling can be configured in the console. Refer to https://kb.timescale.cloud/en/articles/2755154-connection-pools for more information on connection pools.