Event-based optimization of admission control in open queueing networks

In this paper, we use the event-based optimization framework to study the admission control problem in an open Jackson network. The external arriving customers are controlled by an admission controller. The controller makes decision only at the epoch when an event of customer arrival happens. Every customer in the network obtains a fixed reward for each service completion and pays a cost with a fixed rate during its sojourn time (including waiting time and service time). The complete information of the system state is not available for the controller. The controller can observe only the number of total customers in the network. Based on the property of closed form solution of Jackson networks, we prove that the system performance is monotonic with respect to the admission probabilities and the optimal control policy has a threshold form. That is, when the number of total customers is smaller than a threshold, all of the arriving customers are admitted; otherwise, all are rejected. The sufficient condition and necessary condition of optimal policy are also derived. Furthermore, we develop an iterative algorithm to find the optimal policy. The algorithm can be executed based on a single sample path, which makes the algorithm online implementable. Simulation experiments are conducted to demonstrate the effectiveness of our approach.