Oracle - Should processes limit be lower than sessions parameter SQL&gt; select * from v$resource_limit;

RESOURCE_NAME   CURRENT_UTILIZATION MAX_UTILIZATION INITIAL_ALLOCATION LIMIT_VALUE
-------------   ------------------- --------------- ------------------ -----------
processes       88                  150             150                150
sessions        100                 174             248                248

Assuming that all the sessions are active and doesn't share processes with each other, is it okay to keep the processes limit significantly lower than sessions limit? In all the resources I've read, it's suggested / calculated to keep sessions as processes * 1.5. But what if the active processes reaches its limit and sessions could not able to assign a process to it?
We faced an exception intermittently while establishing a database connection on a successfully running application.
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |  java.sql.SQLException: Listener refused the connection with the following error:
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 | ORA-12519, TNS:no appropriate service handler found
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |  
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |     at oracle.jdbc.driver.T4CConnection.logon(T4CConnection.java:458)
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |     at oracle.bc.driver.PhysicalConnection.&lt;init&gt;(PhysicalCoConnection.java:546)
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |     at oracle.jdbc.driver.T4CConnection.&lt;init&gt;(T4CConnection.java:236)
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |     at oracle.jdbc.driver.T4CDriverExtension.getConnection(T4CDriverExtension.java:32)
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |     at oracle.jdbc.driver.OracleDriver.connect(OracleDriver.java:521)
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |     ...
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 | Caused by: oracle.net.ns.NetException: Listener refused the connection with the following error:
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 | ORA-12519, TNS:no appropriate service handler found
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |  
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |     at oracle.net.ns.NSProtocol.connect(NSProtocol.java:395)
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |     at oracle.jdbc.driver.T4CConnection.connect(T4CConnection.java:1102)
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |     at oracle.jdbc.driver.T4CConnection.logon(T4CConnection.java:320)
INFO   | jvm 1    | main    | 2020/07/30 13:35:13 |     ... 54 more

Considering that the MAX_UTILIZATION of processes reached its limit of 150 at some point (and sessions reached upto 174), I am suspecting that there isn't enough processes to assign it to a session which led me to think that processes should always be higher than or equal to sessions parameter.
SQL&gt; select * from v$version;

BANNER
--------------------------------------------------------------------------------
Oracle Database 11g Release 11.2.0.3.0 - 64bit Production
PL/SQL Release 11.2.0.3.0 - Production
CORE    11.2.0.3.0  Production
TNS for Linux: Version 11.2.0.3.0 - Production
NLSRTL Version 11.2.0.3.0 - Production
The value of sessions can not be lower than processes by definition. Even if you try to set it, the database will just ignore it:
SESSIONS

Default value Derived: (1.5 * PROCESSES) + 22
Oracle uses the default value of this parameter as its minimum. Values
between 1 and the default do not trigger errors, but Oracle ignores
them and uses the default instead.

You simply hit the process limit for that instance. Increase the limit accordingly, or investigate what application opened/opens these sessions.
Also the number of sessions for users should be limited by their profile, not the instance level sessions parameter.
CREATE PROFILE - look for SESSIONS_PER_USER.