⏳ 延迟效应

# 延迟建模：SaaS 用户增长模拟 import numpy as np class SaaSGrowthModel: def __init__(self, marketing_delay=4, feature_delay=12, churn_delay=2): """ marketing_delay: 营销投入到新用户到达的延迟(周) feature_delay: 功能开发到影响留存的延迟(周) churn_delay: 用户不满到实际流失的延迟(周) """ self.marketing_queue = [0] * marketing_delay self.feature_queue = [0] * feature_delay self.churn_queue = [0] * churn_delay self.users = 1000 self.mrr = 10000 def step(self, marketing_spend, feature_investment): # 营销延迟：今天的投入，N周后才有新用户 new_users = self.marketing_queue.pop(0) self.marketing_queue.append(marketing_spend * 0.5) # 转化率50% # 功能延迟：今天的开发，N周后才影响留存 retention_boost = self.feature_queue.pop(0) self.feature_queue.append(feature_investment * 0.1) # 流失延迟：用户不满不会立刻走 churn = self.churn_queue.pop(0) self.churn_queue.append(max(0, 50 - retention_boost)) # 更新状态 self.users = self.users + new_users - churn self.mrr = self.users * 10 return self.users, self.mrr # 模拟：连续加大营销投入会发生什么？ model = SaaSGrowthModel(marketing_delay=4) for week in range(52): # 第10-30周加大投入 spend = 200 if 10 <= week <= 30 else 50 users, mrr = model.step(spend, 10) # 注意：投入停止后，新用户还会继续来4周（管道效应）