A recurrent conjecture in queueing theory is that the functional forms of throughput and response time are concave and convex, respectively. This paper is a first step in the direction of supplying the missing formal proof, by restricting the treatment to single-class, closed, product-form networks.

Since the exact solutions of large queueing network models are often costly, or even infeasible, the results of this paper may be useful in providing some insight into the performance bounds. In this sense, the paper is of value to both theoreticians and the application-oriented audience.