318 lines
12 KiB
Python
318 lines
12 KiB
Python
import random
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import os
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import time
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from heapq import heappush, heappop
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import matplotlib.pyplot as plt
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from scipy.stats import t
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import numpy as np
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from multiprocessing import Pool
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class Event:
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def __init__(self, event_type, request):
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self.event_type = event_type # 'request', 'router_finish', 'process_finish'
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self.request = request
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class Request:
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def __init__(self, category, arrival_time):
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self.category = category
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self.arrival_time = arrival_time
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class Simulation:
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def __init__(self, C, lambda_val):
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# C clusters of K servers
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self.C = C
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self.K = 12 // C
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self.occupied_servers = [0] * self.C
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# service rate exponential distribution parameter
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service_rates = {1: 4/20, 2:7/20, 3:10/20, 6:14/20}
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self.service_rate = service_rates[C]
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# router request processing time
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self.router_processing_time = (C - 1) / C
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# λ
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self.lambda_val = lambda_val
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self.router_state = 'idle' # 'idle', 'processing', 'blocked'
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self.event_queue = [] # (time, Event)
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self.current_time = 0.0
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self.router_queue = []
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self.total_requests = 0
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self.lost_requests = 0
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self.loss_rate = 0
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self.response_times = []
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def next_request(self):
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# exponential distribution, parameter λ
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interval = random.expovariate(self.lambda_val)
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new_time = self.current_time + interval
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arrival_time = new_time
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category = random.randint(0, self.C-1) if self.C>1 else 0
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request = Request(category, arrival_time)
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request_event = Event("request", request)
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heappush(self.event_queue, (arrival_time, request_event))
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def handle_request(self, request, max_loss_value):
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self.total_requests += 1
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if len(self.router_queue) == 0 and self.router_state == "idle":
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self.router_process(request)
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elif ((len(self.router_queue) + (self.router_state == "processing")) < 100):
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self.router_queue.append(request)
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else:
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self.lost_requests += 1
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self.loss_rate = self.lost_requests / self.total_requests
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if self.loss_rate > max_loss_value :
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raise ValueError("lossrate too high")
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def router_process(self, request):
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if self.router_state == "idle":
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self.router_state = 'processing'
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router_finish = Event("router_finish", request)
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finish_time = self.current_time + self.router_processing_time
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heappush(self.event_queue, (finish_time, router_finish))
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else:
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raise RuntimeError("shouldn't reach this branch")
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def router_process_finish(self, request):
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# send the request to a free server
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if self.occupied_servers[request.category] < self.K:
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self.router_state = "idle"
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self.occupied_servers[request.category] += 1
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self.process_request(request)
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else:
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self.router_state = "blocked"
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self.router_queue.insert(0, request)
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# router process next request
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self.router_process_next()
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def router_process_next(self):
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if (len(self.router_queue) > 0) and (self.router_state == "idle"):
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self.router_process(self.router_queue.pop(0))
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def process_request(self, request):
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interval = random.expovariate(self.service_rate)
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finish_time = self.current_time + interval
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process_finish = Event("process_finish", request)
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heappush(self.event_queue, (finish_time, process_finish))
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def process_request_finish(self, request):
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self.response_times.append(self.current_time - request.arrival_time)
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self.occupied_servers[request.category] -= 1
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if (self.router_state == "blocked") and (request.category == self.router_queue[0].category):
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self.process_request(self.router_queue.pop(0))
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self.occupied_servers[request.category] += 1
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self.router_state = "idle"
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self.router_process_next()
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def run(self, max_time, max_loss_value):
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# first request
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self.next_request()
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while (self.current_time <= max_time):
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current_event = heappop(self.event_queue)
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self.current_time = current_event[0]
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match current_event[1].event_type:
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case "request":
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self.next_request()
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self.handle_request(current_event[1].request, max_loss_value)
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case "router_finish":
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self.router_process_finish(current_event[1].request)
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case "process_finish":
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self.process_request_finish(current_event[1].request)
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case _ :
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raise RuntimeError("shouldn't reach this branch")
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def run_single_simulation(args):
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c, lambda_val, simulation_time, max_loss_value = args
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# for different seed in each process
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random.seed(time.time() + os.getpid())
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try:
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sim = Simulation(c, lambda_val)
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sim.run(simulation_time, max_loss_value)
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if len(sim.response_times) > 0:
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run_mean = sum(sim.response_times) / len(sim.response_times)
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loss_rate = sim.loss_rate
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return (run_mean, loss_rate)
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else:
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return None
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except ValueError: # Loss rate too high
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return None
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def simulation_wrapper1(simulation_time, num_runs, min_runs, confidence_level, lambda_vals, ax_rt):
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C_values = [1, 2, 3, 6]
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mean_at_lambda1 = {}
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loss_data = {}
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with Pool() as pool: # pool of workers
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for c in C_values:
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lambda_points = []
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means = []
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ci_lower = []
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ci_upper = []
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losses = []
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print(f"\nProcessing C={c}")
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for lambda_val in lambda_vals:
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# run num_runs simulation for each lambda
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args_list = [(c, lambda_val, simulation_time, 0.05) for _ in range(num_runs)]
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results = pool.map(run_single_simulation, args_list)
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# collect results from successful simulations
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successful_results = [res for res in results if res is not None]
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run_results = [res[0] for res in successful_results]
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loss_rates = [res[1] for res in successful_results]
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n = len(run_results)
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# reject if not enough successful run
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if n >= min_runs:
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# statistics
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mean_rt = np.mean(run_results)
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std_dev = np.std(run_results, ddof=1)
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# confidence interval
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t_value = t.ppf((1 + confidence_level)/2, n-1)
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ci = t_value * std_dev / np.sqrt(n)
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# loss rate
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mean_loss = np.mean(loss_rates)
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# store results
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lambda_points.append(lambda_val)
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means.append(mean_rt)
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ci_lower.append(mean_rt - ci)
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ci_upper.append(mean_rt + ci)
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losses.append(mean_loss)
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print(f"C={c}, λ={lambda_val:.2f}, Mean RT={mean_rt:.2f} ± {ci:.2f}, Mean Loss Rate={mean_loss:.2%}")
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elif n > 0:
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print(f"λ={lambda_val:.2f} skipped - only {n} successful run(s)")
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continue
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else:
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print(f"Stopped at λ={lambda_val:.2f} - no successful run")
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break
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ax_rt.plot(lambda_points, means, label=f'C={c}')
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ax_rt.fill_between(lambda_points, ci_lower, ci_upper, alpha=0.2)
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# store response time for lamba = 1
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if 1 in lambda_points:
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idx = lambda_points.index(1)
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mean_at_lambda1[c] = (means[idx], ci_lower[idx], ci_upper[idx])
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loss_data[c] = (np.array(lambda_points), np.array(losses))
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# plot curves
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if len(lambda_vals)>1:
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ax_rt.set_xlim(left=0)
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ax_rt.set_xlabel('Arrival Rate (λ)')
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ax_rt.set_ylabel('Mean Response Time')
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ax_rt.set_title(f'Mean Response Time vs Arrival Rate ({num_runs} runs, {int(confidence_level*100)}% CI)')
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ax_rt.legend()
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ax_rt.grid(True)
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return loss_data, mean_at_lambda1
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def simulation_wrapper2(simulation_time, num_runs, min_runs, confidence_level, lambda_vals, max_loss_value=0.1):
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fig, (ax_rt, ax_loss) = plt.subplots(2,1, figsize=(12,10), gridspec_kw={'height_ratios': [4, 3], 'hspace': 0.4}, sharex=False)
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loss_data, mean_at_lambda1 = simulation_wrapper1(simulation_time, num_runs, min_runs, confidence_level, lambda_vals, ax_rt)
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if len(lambda_vals) > 1:
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for c, (lams, losses) in loss_data.items():
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lambda_vals2 = []
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if len(lams)==0:
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print(f"C={c}: no data at all.")
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continue
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pos_idx = np.where(losses > 0)[0]
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if pos_idx.size > 0:
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first_lambda = lams[pos_idx[0]]
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else:
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first_lambda = None
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last_lambda = lams[-1]
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print(f"C={c:>1} first λ with loss > 0: "
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f"{first_lambda if first_lambda is not None else 'never'}; "
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f" last λ with data: {last_lambda}")
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lambda_vals2.extend([last_lambda + i/1000 for i in range(-100,51)])
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lambda_points = []
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losses = []
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ci_lower = []
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ci_upper = []
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print(f"\nProcessing C={c}")
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with Pool() as pool:
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for lambda_val in lambda_vals2:
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args_list = [(c, lambda_val, simulation_time, max_loss_value) for _ in range(num_runs)]
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results = pool.map(run_single_simulation, args_list)
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successful_results = [res for res in results if res is not None]
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loss_rates = [res[1] for res in successful_results]
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n = len(loss_rates)
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if n >= min_runs:
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# statistics
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mean_loss = np.mean(loss_rates)
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std_dev = np.std(loss_rates, ddof=1)
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# confidence interval
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t_value = t.ppf((1 + confidence_level)/2, n-1)
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ci = t_value * std_dev / np.sqrt(n)
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# store results
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lambda_points.append(lambda_val)
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losses.append(mean_loss)
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ci_lower.append(mean_loss - ci)
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ci_upper.append(mean_loss + ci)
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print(f"C={c}, λ={lambda_val:.4f}, Mean Loss Rate={mean_loss:.2%} ± {ci:.2f}")
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elif n > 0:
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print(f"λ={lambda_val:.4f} skipped - only {n} successful run(s)")
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continue
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else:
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print(f"Stopped at λ={lambda_val:.4f} - no successful run")
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break
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ax_loss.plot(lambda_points, losses, label=f'C={c}')
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ax_loss.fill_between(lambda_points, ci_lower, ci_upper, alpha=0.2)
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# determine optimal C for lamba = 1
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if mean_at_lambda1:
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sorted_C = sorted(mean_at_lambda1.items(), key=lambda item: item[1][0])
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(best_C, (mean1, lower1, upper1)), (_, (_, lower2, _)) = sorted_C[:2]
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if upper1 < lower2:
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print(f"Optimal C at λ=1 is {best_C} with Mean RT = {mean1:.2f} (non-overlapping CIs)")
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else:
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print("Confidence intervals overlap between the two best C.")
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else:
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print("\nNo valid λ=1 data for any C.")
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#plot curves
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if len(lambda_vals) > 1:
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ax_loss.set_xlim(left=2)
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ax_loss.set_xlabel('Arrival Rate (λ)')
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ax_loss.set_ylabel('Mean Loss Rate')
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ax_loss.set_title(f'Mean Loss Rate vs Arrival Rate ({num_runs} runs, {int(confidence_level*100)}% CI)')
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ax_loss.legend()
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ax_loss.grid(True)
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plt.show()
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