There are a few ways to resolve this issue.
1. If you are using Spring Boot, please see
this article.
2. From the service side, you can upgrade your service instance so that it supports more simultaneous connections. If you are using Pivotal Web Services, many of the free plans only allow up to four simultaneous connections. To get more, you would need to use a paid plan.
3. From the application side, you can define some limits on your DataSource/connection pool. To do this, you'll need to use the manual service configuration option which is described in the documentation
here or
this KB article.