在排队论中，M/M/C 模型表示到达过程和服务过程都符合泊松分布，且有 C 个服务台。若要实现具有优先级的 M/M/C 算法，可结合优先队列来处理不同优先级的顾客。下面是一个简单的 Python 实现示例，使用`heapq`模块来实现优先队列： ```python import heapq import numpy as np # 定义顾客类 class Customer: def __init__(self, arrival_time, service_time, priority): self.arrival_time = arrival_time self.service_time = service_time self.priority = priority self.start_time = None self.departure_time = None def __lt__(self, other): return self.priority < other.priority # 实现具有优先级的 M/M/C 算法 def priority_mmc(lambda_, mu, c, total_time, priorities): # 初始化变量 time = 0 next_arrival = np.random.exponential(1 / lambda_) servers = [0] * c queue = [] customers = [] while time < total_time: # 处理下一个事件：到达或离开 if len(queue) == 0: next_departure = float('inf') else: next_departure = min(servers) if next_arrival < next_departure: # 处理顾客到达 time = next_arrival priority = np.random.choice(priorities) service_time = np.random.exponential(1 / mu) customer = Customer(time, service_time, priority) heapq.heappush(queue, customer) next_arrival = time + np.random.exponential(1 / lambda_) else: # 处理顾客离开 time = next_departure server_index = servers.index(next_departure) departing_customer = heapq.heappop(queue) departing_customer.start_time = max(time, departing_customer.arrival_time) departing_customer.departure_time = departing_customer.start_time + departing_customer.service_time servers[server_index] = departing_customer.departure_time customers.append(departing_customer) return customers # 参数设置 lambda_ = 2 # 到达率 mu = 3 # 服务率 c = 2 # 服务台数量 total_time = 100 # 模拟总时间 priorities = [1, 2, 3] # 优先级列表 # 运行模拟 customers = priority_mmc(lambda_, mu, c, total_time, priorities) # 输出结果 for customer in customers: print(f"Arrival: {customer.arrival_time}, Start: {customer.start_time}, Departure: {customer.departure_time}, Priority: {customer.priority}") ``` 在上述代码中，`Customer`类表示顾客，包含到达时间、服务时间和优先级等属性。`priority_mmc`函数实现了具有优先级的 M/M/C 算法，使用`heapq`模块来维护优先队列。模拟过程中，根据到达时间和离开时间处理顾客的到达和离开事件。