从概率统计看限流阈值问题

package com.cainiao.hyena;
import java.math.BigDecimal;
import java.math.RoundingMode;
/**
 * [Poisson分布概率计算工具]
 *
 * @author jianping.pjp created on 2020/12/8 下午11:29
 * Copyright 2020 (C) <Alibaba Global>
 */
public class PoissonTest {
    //在指定QPS平均值的前提下，我们猜测实际最大能打到的QPS，可根据实际跑出的结果来调整，这个值是和平均值正相关的
    private static final int MAX_K = 40;
    public static void main(String[] args) {
        int m = 10;
        BigDecimal p = new BigDecimal(0);
        for (int k = 0; k < MAX_K; k++) {
            BigDecimal x = p2(m, k);
            p = p.add(x);
            System.out.println(k + "," + p.setScale(10, RoundingMode.DOWN).doubleValue());
        }
    }
    private static BigDecimal p2(int m, int k) {
        BigDecimal a = new BigDecimal(1);
        if (k == 0) {
            return new BigDecimal(Math.exp(-m));
        }
        BigDecimal r = new BigDecimal(-m).divide(new BigDecimal(k), 100, RoundingMode.DOWN);
        BigDecimal b = new BigDecimal(Math.exp(r.doubleValue()));
        for (int n = 1; n <= k; n++) {
            BigDecimal an = new BigDecimal(m).divide(new BigDecimal(n), 100, RoundingMode.DOWN).multiply(b);
            a = a.multiply(an);
        }
        return a;
    }
}

package com.cainiao.hyena;
import java.util.HashMap;
import java.util.Map;
import java.util.Random;
/**
 * [模拟QPS实现验证]
 *
 * @author jianping.pjp created on 2020/12/10 下午1:07
 * Copyright 2020 (C) <Alibaba Global>
 */
public class PoissonVerification {
    //在指定QPS平均值的前提下，我们猜测实际最大能打到的QPS，可根据实际跑出的结果来调整，这个值是和平均值正相关的
    private final static int MAX_K = 40;
    public static void main(String [] args){
        Random r = new Random();
        //每次实验打到指定机器的实际QPS
        Map<Integer,Integer> map = new HashMap<>();
        //模拟QPS平均值
        int qps = 10;
        //实现次数
        int experimentsTimes = 1000000;
        for(int i=0;i<qps*experimentsTimes;i++){
            int n = r.nextInt(experimentsTimes);
            Integer c= map.get(n);
            if(c==null){
                c = 0;
            }
            c++;
            map.put(n,c);
        }
        for(int k=0;k<MAX_K;k++){
            //实际QPS不超过K的实验次数
            int lk = 0;
            for(int i=0;i<experimentsTimes;i++){
                Integer c = map.get(i);
                if(null ==c || c<=k){
                    lk++;
                }
            }
            double ratio = (double)lk/experimentsTimes;
            System.out.println(k+","+ratio);
        }
    }
}