A symptotic analysis of large heterogeneous queueing systems

As a simple example of a large heterogeneous queueing system, we consider a single queue with many servers with differing service rates. In the limit of infinitely many servers, we identify a queue control policy that minimizes the average system delay. When there are only two possible server speeds, we can analyze the convergence of this policy to optimality. Based on this result, we propose policies for large but finite systems with a general distribution of server speeds.