We first show that the expectation of convex increasing functions of the workload (or waiting time) in (max, +) linear systems, under a single input sequence, is multi-modular. This is done using a coupling argument and a vectorial version of Lindley's equation. Next, we use this result and the optimization theory based on multi-modular 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.
['Eitan Altman', 'Bruno Gaujal', 'Arie Hordijk']
Admission control in stochastic event graphs