排队论单服务台定长服务时间排队模型 C++代码

以下是排队论单服务台定长服务时间排队模型的C++代码实现：

#include <iostream>
#include <queue>
using namespace std;

int main() {
    // 输入参数
    int n, m;
    double lambda, mu;
    cout << "请输入顾客到达率lambda：";
    cin >> lambda;
    cout << "请输入服务率mu：";
    cin >> mu;
    cout << "请输入系统容量n：";
    cin >> n;
    cout << "请输入队列容量m：";
    cin >> m;

    // 计算参数
    double rho = lambda / mu;
    double p0 = 1.0, pn = 0.0;
    for (int i = 1; i <= n; i++) {
        p0 += pow(rho, i) / factorial(i);
    }
    p0 += pow(rho, n + 1) / (factorial(n) * (1 - rho / (n + 1)));
    for (int i = 1; i <= n; i++) {
        pn += pow(rho, i) / factorial(i);
    }
    pn += pow(rho, n + 1) / (factorial(n) * (1 - rho / (n + 1)));

    double Lq = pow(rho, n + 1) * rho / (factorial(n) * pow(1 - rho / (n + 1), 2));
    double Ls = Lq + lambda / mu;
    double Wq = Lq / lambda;
    double Ws = Wq + 1 / mu;

    double p[m + 1] = { 0.0 };
    for (int i = 0; i <= n; i++) {
        p[i] = pow(rho, i) / factorial(i) * p0;
    }
    for (int i = n + 1; i <= m; i++) {
        p[i] = pow(rho, i) / (factorial(n) * pow(n, i - n)) * p0;
    }

    // 输出结果
    cout << "rho = " << rho << endl;
    cout << "p0 = " << p0 << endl;
    cout << "Lq = " << Lq << endl;
    cout << "Ls = " << Ls << endl;
    cout << "Wq = " << Wq << endl;
    cout << "Ws = " << Ws << endl;
    cout << "概率分布：" << endl;
    for (int i = 0; i <= m; i++) {
        cout << "p[" << i << "] = " << p[i] << endl;
    }

    // 模拟队列系统
    int total = 1000000;
    int arrived = 0, served = 0, rejected = 0;
    queue<double> q;
    for (int i = 0; i < total; i++) {
        // 顾客到达
        if ((double)rand() / RAND_MAX < lambda / 60) {
            arrived++;
            if (q.size() < m) {
                q.push((double)rand() / RAND_MAX);
            } else {
                rejected++;
            }
        }
        // 服务结束
        if (!q.empty()) {
            if ((double)rand() / RAND_MAX < mu / 60) {
                served++;
                q.pop();
            }
        }
    }

    // 输出模拟结果
    cout << "模拟结果：" << endl;
    cout << "到达顾客数：" << arrived << endl;
    cout << "服务顾客数：" << served << endl;
    cout << "拒绝顾客数：" << rejected << endl;
    cout << "队列长度期望：" << q.size() << endl;
    cout << "等待时间期望：" << (arrived - served - rejected == 0 ? 0 : (double)q.size() / (arrived - served - rejected) * 60) << "分钟" << endl;

    return 0;
}

其中，`factorial` 函数用于计算阶乘，模拟部分使用了标准库中的队列和随机数生成器。