matlab 排队论mm1代码

MATLAB是一款非常强大的数学软件，可以用来进行各种科学计算和数据分析。排队论是MATLAB中的一个重要应用领域，可以用来模拟和分析各种排队系统，如MM1排队系统。

以下是一个简单的MATLAB代码示例，用于模拟MM1排队系统：

% MM1 Queue Simulation

% Number of customers to simulate
numCustomers = 100;

% Inter-arrival times (exponential distribution)
interArrivalTimes = exprnd(5, 1, numCustomers);

% Service times (exponential distribution)
serviceTimes = exprnd(4, 1, numCustomers);

% Arrival times
arrivalTimes = zeros(1, numCustomers);
for i = 2:numCustomers
    arrivalTimes(i) = arrivalTimes(i-1) + interArrivalTimes(i);
end

% Service start times
serviceStartTimes = zeros(1, numCustomers);
for i = 2:numCustomers
    serviceStartTimes(i) = max(arrivalTimes(i), serviceStartTimes(i-1) + serviceTimes(i-1));
end

% Service end times
serviceEndTimes = serviceStartTimes + serviceTimes;

% Waiting times
waitingTimes = serviceStartTimes - arrivalTimes;

% Total time in system
totalTimes = serviceEndTimes - arrivalTimes;

% Average waiting time
avgWaitingTime = mean(waitingTimes);

% Average total time in system
avgTotalTime = mean(totalTimes);

disp(['Average waiting time: ' num2str(avgWaitingTime)]);
disp(['Average total time in system: ' num2str(avgTotalTime)]);

该代码可以模拟一个包含100个顾客的MM1排队系统，并计算平均等待时间和平均总时间。具体实现过程可以参考代码注释。