truncate exponential delay to practical limits based on probablity

Author: chaitanyaprem

libp2p/protocols/mix/delay_strategy.nim

@@ -38,18 +38,26 @@ method generateForIntermediate*(
   encodedDelayMs
 
 const DefaultMeanDelayMs* = 100
+const DefaultNegligibleProb* = 1e-6
+  ## Probability below which the tail of the exponential distribution is truncated.
+  ## Yields a maximum delay of mean * -ln(negligibleProb) ≈ mean * 13.8.
 
 type ExponentialDelayStrategy* = ref object of DelayStrategy
   ## Recommended strategy: encodes mean delay, samples from exponential distribution.
+  ## The distribution is truncated at -mean*ln(negligibleProb), discarding the
+  ## impractically long tail while preserving the mixing properties.
   meanDelayMs: uint16
+  negligibleProb: float64
 
 proc new*(
     T: typedesc[ExponentialDelayStrategy],
     meanDelayMs: uint16 = DefaultMeanDelayMs,
     rng: ref HmacDrbgContext,
+    negligibleProb: float64 = DefaultNegligibleProb,
 ): T =
   doAssert(rng != nil, "random is not set")
-  T(meanDelayMs: meanDelayMs, rng: rng)
+  doAssert(negligibleProb > 0.0 and negligibleProb < 1.0, "negligibleProb must be in (0, 1)")
+  T(meanDelayMs: meanDelayMs, rng: rng, negligibleProb: negligibleProb)
 
 method generateForEntry*(
     self: ExponentialDelayStrategy
@@ -59,11 +67,12 @@ method generateForEntry*(
 method generateForIntermediate*(
     self: ExponentialDelayStrategy, meanDelayMs: uint16
 ): uint16 {.gcsafe, raises: [].} =
-  ## Samples from exponential distribution: delay = -mean * ln(U)
-  ## Fall back to no delay in case of errors
+  ## Samples from exponential distribution: delay = -mean * ln(U), truncated to
+  ## -mean*ln(negligibleProb) to discard the impractically long tail.
   if meanDelayMs == 0:
     return 0u16
+  let maxDelayMs = -float64(meanDelayMs) * ln(self.negligibleProb)
   let randVal = self.rng[].generate(uint64)
   let u = (float64(randVal) + 1.0) / (float64(high(uint64)) + 1.0)
   let delay = -float64(meanDelayMs) * ln(u)
-  min(delay, float64(high(uint16))).uint16
+  min(delay, maxDelayMs).uint16

tests/libp2p/mix/test_delay_strategy.nim

@@ -3,7 +3,7 @@
 
 {.used.}
 
-import std/[sets]
+import std/[math, sets]
 import ../../../libp2p/protocols/mix/delay_strategy
 import ../../tools/[unittest, crypto]
 
@@ -66,3 +66,24 @@ suite "DelayStrategy":
       delays.incl(delay)
 
     check delays.len > NumSamples div 2
+
+  test "ExponentialDelayStrategy truncates at negligible probability threshold":
+    let
+      meanDelayMs: uint16 = 100
+      negligibleProb = DefaultNegligibleProb
+      strategy = ExponentialDelayStrategy.new(meanDelayMs, rng(), negligibleProb)
+      # maxDelay = -mean * ln(negligibleProb)
+      maxDelayMs = uint16(-float64(meanDelayMs) * ln(negligibleProb))
+
+    for _ in 0 ..< 10000:
+      check strategy.generateForIntermediate(meanDelayMs) <= maxDelayMs
+
+  test "ExponentialDelayStrategy respects custom negligibleProb":
+    let
+      meanDelayMs: uint16 = 100
+      negligibleProb = 0.01 # aggressive truncation: max ≈ mean * 4.6
+      strategy = ExponentialDelayStrategy.new(meanDelayMs, rng(), negligibleProb)
+      maxDelayMs = uint16(-float64(meanDelayMs) * ln(negligibleProb))
+
+    for _ in 0 ..< 10000:
+      check strategy.generateForIntermediate(meanDelayMs) <= maxDelayMs