Admission control in stochastic event graphs

In this paper, we first show that the expectation of convex increasing func tions of the workload (or waiting time) in (max, +) linear systems, under a single input sequence, is multimodular. This is done using a coupling argu ment and a vectorial version of Lindley's equation. In the second part of t he paper, we use this result and the optimization theory based on multimodu lar costs to construct the optimal open-loop admission control in general ( max, +) linear systems under admission rate constraints. This optimization result only requires stationarity assumptions on the arrival process and on the service times of the servers in the system.