Teggy · February 18, 2019 14:20 · Feb 18, 2019 · Feb 18, 2019
diff --git a/NaSchl.sql b/NaSchl.sql
@@ -11,10 +11,10 @@
 -- - velocity: v
 
 -- Model update (time t → t+1):
--- ➊ move:       xₜ   ← xₜ + vₜ
--- ➋ accelerate: v    ← min(vₜ + 1, v_max)
--- ➌ brake:      v    ← min(v, front.xₜ - xₜ - 1)  # front.xₜ: position of car immediately in front of us
--- ➍ linger:     vₜ₊₁ ← if random() < linger then v ← max(0, v - 1) else v
+-- (1) move:       xₜ   ← xₜ + vₜ
+-- (2) accelerate: v    ← min(vₜ + 1, v_max)
+-- (3) brake:      v    ← min(v, front.xₜ - xₜ - 1)  # front.xₜ: position of car immediately in front of us
+-- (4) linger:     vₜ₊₁ ← if random() < linger then v ← max(0, v - 1) else v
 
 -- To produce pure JSON output (psql ... -q | jq .)
 \set quiet on
@@ -46,7 +46,7 @@ INSERT INTO road(car, x, v)
          floor((1 / :density) * c) AS x,
          0 AS v
   FROM   generate_series(0, floor(:road_length * :density) - 1) AS c;
---                          ───────────────────────────
+--                          └────────────────────────────┘
 --                              # of cars on the road
 
 WITH RECURSIVE nasch(iter, c, x, v) AS (
@@ -58,14 +58,14 @@ WITH RECURSIVE nasch(iter, c, x, v) AS (
   (WITH nasch AS (TABLE nasch)
      SELECT n.iter + 1 AS iter,
             n.c,
-            (n.x + n.v) % :road_length AS x,                                                       --   ➊ move
-            GREATEST(0,                                                                            --                          ⎫
-                     LEAST(LEAST(n.v + 1, :v_max),                                                 -- } ➋ accelerate ⎱ ➌ brake ⎬  ➍ linger
-                           ((front.x + front.v) + :road_length - (n.x + n.v)) % :road_length - 1)  --                ⎰         ⎪
-                       - CASE WHEN random() < :linger THEN 1 ELSE 0 END) AS v                      --                          ⎭
+            (n.x + n.v) % :road_length AS x,                                                       --   (1) move
+            GREATEST(0,                                                                            --                               ⎤
+                     LEAST(LEAST(n.v + 1, :v_max),                                                 -- ] (2) accelerate ⎤ (3) brake  ⎟  (4) linger
+                           ((front.x + front.v) + :road_length - (n.x + n.v)) % :road_length - 1)  --                  ⎦            ⎟
+                       - CASE WHEN random() < :linger THEN 1 ELSE 0 END) AS v                      --                               ⎦
      FROM   nasch AS n, nasch AS front
      WHERE  front.c = (n.c + 1)   % floor(:road_length * :density)
-     AND    n.iter < :iterations -- ───────────────────────────
+     AND    n.iter < :iterations -- └────────────────────────────┘
                                  -- # of cars on the road (wrap-around)
   )
 )

diff --git a/NaSchl.sql b/NaSchl.sql
@@ -0,0 +1,85 @@
+-- Traffic flow simulation based on a simple cellular automaton
+--
+-- Based on a 1992 model by Kai Nagel and Michael Schreckenberg (NaSch),
+-- also see:
+-- http://www.christophschuette.com/blog/?p=50
+-- http://www.thp.uni-koeln.de/~as/Mypage/traffic.html
+
+-- Car model:
+-- - ID:       c
+-- - position: x
+-- - velocity: v
+
+-- Model update (time t → t+1):
+-- ➊ move:       xₜ   ← xₜ + vₜ
+-- ➋ accelerate: v    ← min(vₜ + 1, v_max)
+-- ➌ brake:      v    ← min(v, front.xₜ - xₜ - 1)  # front.xₜ: position of car immediately in front of us
+-- ➍ linger:     vₜ₊₁ ← if random() < linger then v ← max(0, v - 1) else v
+
+-- To produce pure JSON output (psql ... -q | jq .)
+\set quiet on
+\pset border 0
+\pset footer off
+\pset tuples_only on
+\timing off
+
+-- # of iterations to simulate
+\set iterations  100
+
+-- NaSch model parameters
+\set road_length 200  -- length of road (in cells), ⚠ circular road, wraps around
+\set density     0.2  -- density of cars on road (0 < density ⩽ 1)
+\set linger      0.15 -- probability of spontaneous/unforced braking
+\set v_max       5    -- maximum velocity
+
+-- (Initial) road representation
+DROP TABLE IF EXISTS road;
+CREATE TABLE road (
+  car int, -- car ID
+  x   int, -- position on road
+  v   int  -- velocity
+);
+
+-- Populate road (initially: cars equi-distant, velocity 0)
+INSERT INTO road(car, x, v)
+  SELECT c AS car,
+         floor((1 / :density) * c) AS x,
+         0 AS v
+  FROM   generate_series(0, floor(:road_length * :density) - 1) AS c;
+--                          ───────────────────────────
+--                              # of cars on the road
+
+WITH RECURSIVE nasch(iter, c, x, v) AS (
+  SELECT 0 AS iter, r.*
+  FROM   road AS r
+
+    UNION ALL
+
+  (WITH nasch AS (TABLE nasch)
+     SELECT n.iter + 1 AS iter,
+            n.c,
+            (n.x + n.v) % :road_length AS x,                                                       --   ➊ move
+            GREATEST(0,                                                                            --                          ⎫
+                     LEAST(LEAST(n.v + 1, :v_max),                                                 -- } ➋ accelerate ⎱ ➌ brake ⎬  ➍ linger
+                           ((front.x + front.v) + :road_length - (n.x + n.v)) % :road_length - 1)  --                ⎰         ⎪
+                       - CASE WHEN random() < :linger THEN 1 ELSE 0 END) AS v                      --                          ⎭
+     FROM   nasch AS n, nasch AS front
+     WHERE  front.c = (n.c + 1)   % floor(:road_length * :density)
+     AND    n.iter < :iterations -- ───────────────────────────
+                                 -- # of cars on the road (wrap-around)
+  )
+)
+-- ➊ JSON output (needed for JavaScript-based traffic-sim.html)
+SELECT array_to_json(array_agg(row_to_json(n.*) ORDER BY n.iter, n.c)) AS traffic
+FROM   nasch AS n;
+
+
+-- -- ➋ Average speed per iteration
+-- SELECT n.iter, AVG(n.v)
+-- FROM   nasch AS n
+-- GROUP BY n.iter
+-- ORDER BY n.iter;
+
+-- -- ➌ Complete output for debugging
+-- TABLE nasch
+-- ORDER BY iter, c;