Monotonicity and Continuity of Stochastic Discrete Event Systems

Monotonicity and continuity are important qualitative properties of stochastic discrete event systems, such as networks of queues. Questions of monotonicity arise in comparing the performance of different systems: stochastic monotonicity results make it possible to determine which system is 'better' without evaluating performance quantitatively, which can be difficult. Continuity is an important precondition for the use of stochastic derivatives for real-time parametric control.