From 47a304c1297ce72504d1c2e70ded488c9ff3bab4 Mon Sep 17 00:00:00 2001
From: Andreas Tsouchlos <an.tsouchlos@gmail.com>
Date: Thu, 29 May 2025 23:22:20 -0400
Subject: [PATCH] Add approximate_response_time.py

---
 scripts/approximate_response_time.py | 88 ++++++++++++++++++++++++++++
 1 file changed, 88 insertions(+)
 create mode 100644 scripts/approximate_response_time.py

diff --git a/scripts/approximate_response_time.py b/scripts/approximate_response_time.py
new file mode 100644
index 0000000..ae14bd5
--- /dev/null
+++ b/scripts/approximate_response_time.py
@@ -0,0 +1,88 @@
+import pandas as pd
+import numpy as np
+
+
+filename_participants = "res/full_participant_measurement.csv"
+
+filename_left = "res/flowrate_left.csv"
+filename_right = "res/flowrate_right.csv"
+filename_both = "res/flowrate_both.csv"
+
+arrival_rate = 1 / 36.66  # Measured
+
+
+def get_response_time_and_utilization(S, arrival_rate):
+    df = pd.read_csv(filename_participants)
+
+    E_S = S.mean()
+    E_S2 = (S**2).mean()
+
+    utilization = arrival_rate * E_S
+
+    W = E_S + (arrival_rate * E_S2) / 2*(1 - utilization)
+
+    return W, utilization
+
+
+def print_response_time():
+    df = pd.read_csv(filename_participants)
+    S = df["time"]
+
+    W, rho = get_response_time_and_utilization(S, arrival_rate)
+
+    print(f"//")
+    print(f"// Response time")
+    print(f"// ")
+    print(f"    E{{S}} = {S.mean():.3f} s")
+    print(f"1/lambda = {1/arrival_rate:.3f} s")
+    print(f"     rho = {rho:.3f}")
+    print(f"       W = {W:.3f} s")
+
+
+def print_best_achievable_response_time():
+    # Get mean flowrates
+
+    df_left = pd.read_csv(filename_left)
+    df_right = pd.read_csv(filename_right)
+    df_both = pd.read_csv(filename_both)
+
+    flowrate_left = np.mean(np.array(df_left["flowrate"]))
+    flowrate_right = np.mean(np.array(df_right["flowrate"]))
+    flowrate_both = np.mean(np.array(df_both["flowrate"]))
+
+    # Convert service times to what they would be with the best strategy
+
+    df_part = pd.read_csv(filename_participants)
+
+    times_left = np.array(df_part[df_part["button"] == "left"]["time"])
+    times_right = np.array(df_part[df_part["button"] == "right"]["time"])
+    times_both = np.array(df_part[df_part["button"] == "both"]["time"])
+
+    sizes_left = times_left * flowrate_left
+    sizes_right = times_right * flowrate_right
+    sizes_both = times_both * flowrate_both
+
+    sizes = np.concatenate([sizes_left, sizes_right, sizes_both])
+
+    S = sizes / flowrate_right
+
+    # Calculate response time
+
+    W, rho = get_response_time_and_utilization(S, arrival_rate)
+
+    print(f"//")
+    print(f"// Best possible response time")
+    print(f"// ")
+    print(f"    E{{S}} = {S.mean():.3f} s")
+    print(f"1/lambda = {1/arrival_rate:.3f} s")
+    print(f"     rho = {rho:.3f}")
+    print(f"       W = {W:.3f} s")
+
+
+def main():
+    print_response_time()
+    print_best_achievable_response_time()
+
+
+if __name__ == "__main__":
+    main()