Erlang arrivals joining the shorter queue

We consider a system in which customers join upon arrival the shortest of two single-server queues. The interarrival times between customers are Erlang distributed and the service times of both servers are exponentially distributed. Under these assumptions, this system gives rise to a Markov chain on a multi-layered quarter plane. For this Markov chain we derive the equilibrium distribution using the compensation approach. The obtained expression for the equilibrium distribution matches and re??nes heavy-traffic approximations and tail asymptotics obtained earlier in the literature. Keywords: random walks in the quarter plane, compensation approach, join the shorter queue, tail asymptotics