【数学建模】基于matlab蒙特卡洛M_M_1排队模型模拟【含Matlab源码 期】.zip

lambda = 0.2:0.1:0.9; mu = 1; numEvents = 10000; avgQueueLength = zeros(length(lambda), 1); avgResponseTime = zeros(length(lambda), 1); for i = 1:length(lambda) arrivalTimes = cumsum(exprnd(1/lambda(i), numEvents, 1)); serviceTimes = exprnd(1/mu, numEvents, 1); departureTimes = zeros(numEvents, 1); for j = 1:numEvents if j == 1 departureTimes(j) = arrivalTimes(j) + serviceTimes(j); else departureTimes(j) = max(arrivalTimes(j), departureTimes(j-1)) + serviceTimes(j); end end responseTimes = departureTimes - arrivalTimes; avgResponseTime(i) = mean(responseTimes); avgQueueLength(i) = lambda(i) * avgResponseTime(i); end % Analytical model rho = lambda / mu; analyticalResponseTime = 1 ./ (mu - lambda); analyticalQueueLength = rho .^ 2 ./ (1 - rho); % Plot figure; subplot(2, 1, 1); plot(lambda, avgResponseTime, 'o-', lambda, analyticalResponseTime, 'x-'); xlabel('λ'); ylabel('Average Response Time'); legend('Simulation', 'Analytical', 'Location', 'Best'); subplot(2, 1, 2); plot(lambda, avgQueueLength, 'o-', lambda, analyticalQueueLength, 'x-'); xlabel('λ'); ylabel('Average Queue Length'); legend('Simulation', 'Analytical', 'Location', 'Best');