real_heu_sim.m

function [tdr_heu_sim] = real_heu_sim()
% Simulate the proposed heuristic scheme (realistic)
% Declare global variables
% See main_without_retran.m
global N D lambda sigma NE

% Run independent numerical experiments
success = zeros(1, NE);

parfor ne = 1:NE
    % Simulate the packet arrival
    % status: 0 (inactive), 1 (active)
    status = rand(1, N) < lambda;
    % Consider an arbitrary node as the tagged node
    tagged_node = randi([1 N]);
    % Initialize the approximation on the activity belief
    approx_belief = [N - 1, lambda];
    
    for t = 1:D
        if status(tagged_node) > 0
            % Determine the value of transmission probability
            M = approx_belief(1);
            a = approx_belief(2);
            if M * a + 1 > D - t + 1 || t == D
                p = min(1 / (M * a + a), 1);
            else
                p = 1 / (D - t + 1);
            end
            % Simulate the random access
            access = (rand(1, N) < p) .* (status > 0);
            status = status - access;
            if access(tagged_node) * sum(access) == 1 && rand < sigma
                success(ne) = 1;
            end
            % Update the approximation on the activity belief
            if sum(access) == 0
                % case 1: observation = idle
                approx_belief = [M, (a - a * p) / (1 - a * p)];
            else
                % case 2: observation = busy
                approx_belief = [M - 1, 1];
                if approx_belief(1) > 0
                    approx_belief(2) = ...
                        M * (a - a * p) * (1 - (1 - a * p)^(M - 1)) / ((M - 1) * (1 - (1 - a * p)^M));
                end
            end
        else
            break
        end
    end
    
end

% Compute the TDR performance
tdr_heu_sim = sum(success) / NE / lambda;

% Print the TDR performance
fprintf("tdr_heu_sim (real) = %.4f\n", tdr_heu_sim);