12516, 00000, "TNS:listener could not find available handler with matching protocol stack"
// *Cause: None of the known and available service handlers for the given
// SERVICE_NAME support the client's protocol stack: transport, session,
// and presentation protocols.
// *Action: Check to make sure that the service handlers (e.g. dispatchers)
// for the given SERVICE_NAME are registered with the listener, are accepting
// connections, and that they are properly configured to support the desired
// protocols.

这个跟连接池大小没什么关系吧？

检查一下服务端的监听状态是否正常，另外自己的连接数据库的ip地址、端口号，服务名/实例名是否正确，或者网络端口是否通

之前遇到过这样的报错，数据库进程数超过参数限制。建议确认下所在实例processes这个参数配置的是不是太小了，并且检查下所在数据库实例在报错时是否存在连接数风暴，控制住数量或者把该参数值调高（需要重启实例）应该可以避免这个错误