OverFlow routing and VA Design Help : Groups and Transfers

[juisel]

Need some experts to chime in with some with routing logic assistance

Here is the business use case:

We have two groups of agents - Level 2(specialist) and Level 1 Agents. 

When a new chat requests comes through, we want the chat system to look for Level 2 Agents first

We want that same chat to queue for 180 seconds with L2 Agents to give them an opportunity to answer that chat.

After 180seconds, if there are no L2 agents we want the chat system to then look for someone from the L1 Agent group. 

Based on our research,  we can use Queue Eligibility and use a timer based overflow. However the problem we have encountered is that even if there are no L2 Agents logged in, when a new chat comes in, the chat system will not route the chat to the L1 Agent until 180seconds has passed.

So we tried to modify the VA Topic flow so that....

1.  Based on Agent availability, we tried to create a branch so that if no Agents from L2 - then route to L1

2.  The other branch is - > If system detects Agent available from L2 - then route to L2.  Since we want overflow to L1 , we add L1 group as an overflow in Queue Eligibility.

However this messes up with the routing logic, and thinks that there are available Agents for L2 no matter what due to this. 

Does anyone know how we design this so that we can meet the business use case?