I don't know how to classify this queue. I am going to try and describe it thoroughly. I have a multi server queue with servers having constant efficiencies (the service times are modeled as exponential distributions with constant means with respect to time, maybe different for different servers). The requests arrive in accordance to a Poisson point process with a constant arrival rate. Each request has two stages, with different sets of servers (say, roles) catering to the stages.
At each request arrival, the request is assigned/routed to two servers who have the least number of requests assigned to them. What sort of queue is this?