On diffusion approximation of controlled queueing processes (Q790785)

The author considered a queueing system that can be controlled by switching service rates. When there is the switching cost besides the holding and operating cost, the control problem is to choose an optimal strategy \(\{\) s(k), u(k)\(\}\), \(k=1,2,...\), where s(k) is the k-th switching time and u(k) the service rate used at s(k). The author showed that, under heavy traffic, a sequence of rescaled queueing processes converges weakly to a diffusion. Moreover, the optimal cost functions to control rescaled queueing processes tend to those of corresponding diffusions.