Optimal solution for IEEE 802.11 MAPC Coordinated Spatial Reuse (C-SR) problem

mapc-optimal is a tool for finding the optimal solution of the Multi-Access Point Coordination (MAPC) scheduling problem with coordinated spatial reuse (C-SR) for IEEE 802.11 networks. It provides a mixed-integer linear programming (MILP) solution to find the upper bound on network performance. A detailed description can be found in:

  • TODO

Features

  • Calculation of optimal scheduling: Calculate the best transmission configurations and the corresponding time division that enhance the network performance.

  • Multiple optimization criteria: Find the optimal solution for different optimization criteria: maximizing the sum of the throughput of all nodes in the network, maximizing the minimum throughput of all nodes in the network (optionally above a given baseline), maximizing the proportional fairness, and maximizing the vector of the node throughputs lexicographically.

  • Modulation and coding scheme (MCS) selection: Select the optimal MCS for each transmission.

  • Transmission power selection: Set the appropriate transmission power to maximize network performance.

  • Versatile network configuration: Define network settings by specifying network nodes, available MCSs, and transmission power levels.

Installation

The package can be installed using pip:

pip install mapc-optimal

Usage

The main functionality is provided by the mapc_optimal.Solver class. This class manages the process of finding the optimal solution. Example usage:

from mapc_optimal import Solver

# Define your network
# ...

solver = Solver(stations, access_points)
configurations, rate = solver(path_loss)

where stations and access_points are lists of numbers representing the stations and access points (APs) in the network, respectively. The path_loss is an \(n \times n\) matrix representing the path loss between each pair of nodes in the network. The solver returns calculated configurations and the total throughput of the network. The mapc_optimal.Solver class can be further configured by passing additional arguments to the constructor. The full list of arguments can be found in the documentation.

The optimization criterion is selected with the opt_type argument. Besides maximizing the total throughput (OptimizationType.SUM) and the worst station throughput (OptimizationType.MAX_MIN), the solver can maximize the vector of the station throughputs lexicographically (OptimizationType.LEXICOGRAPHIC), i.e., once the worst stations cannot be improved any further, it keeps improving the subsequent worst ones:

from mapc_optimal import OptimizationType, Solver

solver = Solver(stations, access_points, opt_type=OptimizationType.LEXICOGRAPHIC)
configurations, rate = solver(path_loss)

Note The lexicographic optimization solves a separate problem for each station in every step of its outer loop, so it is significantly slower than the other criteria.

The solver can also guarantee that no station gets less than in some reference solution, e.g., the one obtained with a simulator or a learning agent. With OptimizationType.MAX_MIN_BASELINE, the worst station throughput is maximized while each station is required to reach its baseline rate. Since the rates of the reference solution can be hard to reproduce with configurations generated from scratch, the configurations used by the reference solution can be added to the initial ones with the initial_configurations argument. Each of them is a dictionary mapping the (AP, station) pairs to the transmission power (dBm) used by the AP:

from mapc_optimal import OptimizationType, Solver

solver = Solver(stations, access_points, opt_type=OptimizationType.MAX_MIN_BASELINE)
configurations, rate = solver(
    path_loss,
    baseline={'STA_1': 10., 'STA_2': 12.},
    initial_configurations=[{(0, 1): 20., (1, 2): 16.}]
)

If the baseline rates cannot be reached, the solver raises an exception. The baseline can also be passed to the lexicographic optimization, where it sets the initial minimum throughput of each station.

Additionally, the solver can return a list of the pricing objective values for each iteration. It can be useful to check if the solver has converged. To do so, set the return_objectives argument to True when calling the solver.

configurations, rate, objectives = solver(path_loss, return_objectives=True)

For a more detailed example, refer to the test case in test/test_solver.py.

Note The underlying MILP solver can significantly affect the performance of the tool. By default, the solver uses the CBC solver from the PuLP package. However, we recommend using a better solver, such as CPLEX.

How to reference mapc-optimal?

TODO