I am having difficulties to get all MMCQ Validation tests passed. Here are the snippet of the output. Please help me how to fix the MATLAB Code so that The p_state calculates all p_states which needs to account for users waiting in the queue AND users begin served. You are only accounting for users waiting. Users being served are not waiting but they are still in the system. rho should be lambda/mu . Lq calculation is wrong. lambda_loss, Lq and p_drop) also need to be adjusted for the correct number of states. % MMCQ model calculation function [Ws, Wq, c_util, p_drop, p_state] = MMCQ(lambda, mu, c, Nwait) rho = lambda / mu; % rho = traffic intensity % p0: the probability of zero customers in the system against the number of servers p0_denom = sum((c * rho).^(0:(c - 1)) / factorial(0:(c - 1))) + (c * rho)^c / factorial(c) / (1 - rho); p0 = 1 / p0_denom; % p_state: the steady-state probabilities of the system states (0 to Nwait customers in the system) %Nwait: the average number of customers in the queue p_state = zeros(1, Nwait + 1); p_state(1) = p0; for i = 1:Nwait ci = min(i, c); if i <= c p_state(i + 1) = ci / c * p_state(i) * rho / factorial(i); else p_state(i + 1) = c^ci / factorial(ci) * p_state(i) * rho^i / factorial(c); end end p_state = p_state / sum(p_state); % pN = p_state(Nwait + 1); P0 = (1 - rho) / (1 - rho^(c+1)); PN = rho^c * P0; fprintf('The probability of having %d customers in the system is %.2f ', c, PN); lambda_loss = lambda * p_state(Nwait + 1); lambda_eff = lambda - lambda_loss; Lq = sum((0:Nwait) .* p_state); Ls = Lq + lambda_eff / mu; c_bar = Ls - Lq; c_util = c_bar / c; p_drop = p_state(Nwait + 1); Ws = Ls / lambda_eff; Wq = Lq / lambda_eff; end % Run this test case to check your code % Test and validation code lambda = 2; % Arrival rate: 2 calls per minute mu =0.1; % Service rate: 0.1 calls per minute per agent % Assuming an initial number of agents for the calculation c = 4; % Placeholder, needs adjustment based on system requirements Nwait = 10; % Nwait Maximum number of customers waiting in the queue. Placeholder, needs adjustment based on system requirements % Call the MMCQ function with the given parameters % The function MMCQ calculates the performance metrics of a multi-server queue (M/M/c queue) with a finite waiting room. % [Ws, Wq, c_util, p_drop, p_state] = MMCQ(lambda, mu, c, Nwait); % Run this test case to check your code [Ws, Wq, c_util, p_drop, p_state] = MMCQ(1, 0.5, 14, 10); rel_error = @(x,y) abs(x - y)/y; if rel_error(Ws, 2.1557) < 0.005 fprintf('Ws = %6.3f PASS ', Ws); else fprintf('Ws = %6.3f FAIL ', Ws); end if rel_error(Wq, 0.1557) < 0.005 fprintf('Wq = %6.3f PASS ', Wq); else fprintf('Wq = %6.3f FAIL ', Wq); end if rel_error(c_util, 0.4986) < 0.005 fprintf('c_util = %6.3f PASS ', c_util); else fprintf('c_util = %6.3f FAIL ', c_util); end if rel_error(p_drop, 0.00272) < 0.005 fprintf('p_drop = %8.5f PASS ', p_drop); else fprintf('p_drop = %8.5f FAIL ', p_drop); end % Extra Tests disp(['p_state: ', num2str(p_state)]); if abs(sum(p_state) - 1) < 1e-5 disp('The probabilities sum to 1. Test PASSED.'); else disp('The probabilities do not sum to 1. Test FAILED.'); end % Display state probabilities fprintf('State probabilities: '); for i = 0:Nwait fprintf('State %d probability: %f ', i, p_state(i + 1)); end The probability of having 14 customers in the system is 0.50 Ws = 2.162 PASS Wq = 0.162 FAIL c_util = 0.143 FAIL p_drop = 0.00000 FAIL p_state: 0.85855 0.12265 0.017521 0.0012515 2.9798e-05 1.7737e-07 2.1116e-10 4.1896e-14 1.1875e-18 4.2075e-24 1.6564e-30 The probabilities sum to 1. Test PASSED. State probabilities: State 0 probability: 0.858547 State 1 probability: 0.122650 State 2 probability: 0.017521 State 3 probability: 0.001252 State 4 probability: 0.000030 State 5 probability: 0.000000 State 6 probability: 0.000000 State 7 probability: 0.000000 State 8 probability: 0.000000 State 9 probability: 0.000000 State 10 probability: 0.000000