From 7b529807b8259e04c90901be0f6fd3c3dd5a64de Mon Sep 17 00:00:00 2001
From: Sergei Tikhomirov <sergey.s.tikhomirov@gmail.com>
Date: Wed, 13 Mar 2024 13:38:55 +0100
Subject: [PATCH 1/2] add updated figure for hops

---
 rln-delay-simulations/message_hops.py  |  11 +-
 rln-delay-simulations/message_hops.svg | 826 +++++++++++--------------
 2 files changed, 356 insertions(+), 481 deletions(-)

diff --git a/rln-delay-simulations/message_hops.py b/rln-delay-simulations/message_hops.py
index b4afb7e..2e74ec0 100644
--- a/rln-delay-simulations/message_hops.py
+++ b/rln-delay-simulations/message_hops.py
@@ -12,9 +12,12 @@
 
 def delay_last_hop(n, d, l):
     # multiply by l for latencies
-    return ceil(log(n)/log(d))
+    numerator = log(((n - 1) * (d - 2) / d) + 1)
+    denominator = log(d - 1)
+    return ceil(numerator / denominator)
 
-ds = np.arange(2,15)
+
+ds = np.arange(3,15)
 ls = np.ones(len(ds))*L
 
 # astype(int) is ok since ceil() returns integers
@@ -39,8 +42,8 @@ def delay_last_hop(n, d, l):
     ax2.set(**dict(ylabel='\nBandwidth amplification'))
 
     # Set the limits of the x-axis and y-axis
-    ax1.set_xlim(2, 14)
-    ax1.set_ylim(2, ax1.get_ylim()[1])  # Ensure that the lower limit is 2
+    ax1.set_xlim(3, 14)
+    ax1.set_ylim(3, ax1.get_ylim()[1])  # Ensure that the lower limit is 2
     
     # Set the limits of the second y-axis to match the first y-axis
     ax2.set_ylim(ax1.get_ylim())
diff --git a/rln-delay-simulations/message_hops.svg b/rln-delay-simulations/message_hops.svg
index 2527a06..e18aa64 100644
--- a/rln-delay-simulations/message_hops.svg
+++ b/rln-delay-simulations/message_hops.svg
@@ -6,7 +6,7 @@
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-    <dc:date>2024-03-05T16:33:36.471747</dc:date>
+    <dc:date>2024-03-13T13:38:23.988327</dc:date>
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From b746f4caadb459900f46745702ca26b5c9e2ce72 Mon Sep 17 00:00:00 2001
From: Sergei Tikhomirov <sergey.s.tikhomirov@gmail.com>
Date: Wed, 13 Mar 2024 13:40:10 +0100
Subject: [PATCH 2/2] delete redundant plot

---
 rln-delay-simulations/plot_message_hops.svg | 2188 -------------------
 1 file changed, 2188 deletions(-)
 delete mode 100644 rln-delay-simulations/plot_message_hops.svg

diff --git a/rln-delay-simulations/plot_message_hops.svg b/rln-delay-simulations/plot_message_hops.svg
deleted file mode 100644
index 924357f..0000000
--- a/rln-delay-simulations/plot_message_hops.svg
+++ /dev/null
@@ -1,2188 +0,0 @@
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