The repository implements Proximal policy optimization algorithm to optimize N-model control.

The N-model processing network was first proposed in [1]. It is a processing network system with two independent Poisson input arrival flows, two servers, exponential service times, and linear holding costs. We use uniformization to convert the continuous-time control problem to a discrete-time control problem.
The detailed description of the system and its uniformization can be found in Section 5.3 of [2].
File NmodelDynamics.py contains an object describing the N-model. Its method next_state_N1 generates the next state of the system given the current state and the action.

We use Proximal policy optimization algorithm [3] for N-model control optimization. The main file is train.py which starts with hyperparaments selection. File actor_utils.py contains actor-related objects and functions, file value_function.py contains critic-related objects and functions.

File 'value_iteration_Nmodel.py' can be used to find optimal actions for the N-model via the value iteration method. File 'value_iteration_Nmodel.py' should be run separately. File action09.npy contains a numpy array with optimal actions for N-model with load 0.9.

[1] J Michael Harrison. Heavy traffic analysis of a system with parallel servers: asymptotic optimality of discrete-review policies. The Annals of Applied Probability, 8(3):822–848, 1998.
[2] J. G. Dai, Mark Gluzman. Queueing Network Controls via Deep Reinforcement Learning. https://arxiv.org/abs/2008.01644, 2021.
[3] John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. http:https://arxiv.org/abs/1707.06347, 2017