A smarter ShipMarket in SpaceStation

data/libs/SpaceStation.lua

@@ -204,40 +204,77 @@ local isPlayerShip = function (def) return def.tag == "SHIP" and def.basePrice >
 local groundShips = utils.build_array(utils.filter(function (k,def) return isPlayerShip(def) and def.equipSlotCapacity.atmo_shield > 0 end, pairs(ShipDef)))
 local spaceShips  = utils.build_array(utils.filter(function (k,def) return isPlayerShip(def) end, pairs(ShipDef)))
 
+
+-- Dynamics of ship adverts in ShipMarket --
+--------------------------------------------
+-- N(t) = Number of ads, lambda = decay constant:
+--    d/dt N(t) = prod - lambda * N
+-- and equilibrium:
+--    dN/dt = 0 = prod - lambda * N_equil
+-- and solution (if prod=0), with N_0 initial number:
+--    N(t) = N_0 * exp(-lambda * t)
+-- with tau = half life, i.e. N(tau) = 0.5*N_0 we get:
+--    0.5*N_0 = N_0*exp(-lambda * tau)
+-- else, with production:
+--   N(t) = prod/lambda - N_0*exp(-lambda * t)
+-- We want to have N_0 = N_equil, since ShipMarket should spawn in equilibrium
+
+-- Average number of ship for sale for station
+local function N_equilibrium(station)
+	local pop = station.path:GetSystemBody().parent.population -- E.g. Earth=7, Mars=0.3
+	local pop_bonus = 9 * math.log(pop*0.45 + 1)       -- something that gives resonable result
+	if station.type == "STARPORT_SURFACE" then
+		pop_bonus = pop_bonus * 1.5
+	end
+
+	return 2 + pop_bonus
+end
+
+-- add num random ships for sale to station ShipMarket
+local function addRandomShipAdvert(station, num)
+	for i=1,num do
+		local avail = station.type == "STARPORT_SURFACE" and groundShips or spaceShips
+		local def = avail[Engine.rand:Integer(1,#avail)]
+		local model = Engine.GetModel(def.modelName)
+		local pattern = model.numPatterns ~= 0 and Engine.rand:Integer(1,model.numPatterns) or nil
+		addShipOnSale(station, {
+			def     = def,
+			skin    = ModelSkin.New():SetRandomColors(Engine.rand):SetDecal(def.manufacturer),
+			pattern = pattern,
+			label   = Ship.MakeRandomLabel(),
+		})
+	end
+end
+
+local function createShipMarket (station)
+	shipsOnSale[station] = {}
+
+	local shipAdsToSpawn = Engine.rand:Poisson(N_equilibrium(station))
+	addRandomShipAdvert(station, shipAdsToSpawn)
+end
+
 local function updateShipsOnSale (station)
 	if not shipsOnSale[station] then shipsOnSale[station] = {} end
 	local shipsOnSale = shipsOnSale[station]
 
-	local toAdd, toRemove = 0, 0
-	if #shipsOnSale == 0 then
-		toAdd = Engine.rand:Integer(20)
-	elseif Engine.rand:Integer(1) > 0 then
-		toAdd = 1
-	elseif #shipsOnSale > 0 then
-		toRemove = 1
-	else
-		return
-	end
+	local tau = 7*24                              -- half life of a ship advert in hours
+	local lambda = 0.693147 / tau                 -- removal probability= ln(2) / tau
+	local prod = N_equilibrium(station) * lambda  -- creation probability
 
-	if toAdd > 0 then
-		local avail = station.type == "STARPORT_SURFACE" and groundShips or spaceShips
-		for i=1,toAdd do
-			local def = avail[Engine.rand:Integer(1,#avail)]
-			local model = Engine.GetModel(def.modelName)
-			local pattern = model.numPatterns ~= 0 and Engine.rand:Integer(1,model.numPatterns) or nil
-			addShipOnSale(station, {
-				def     = def,
-				skin    = ModelSkin.New():SetRandomColors(Engine.rand):SetDecal(def.manufacturer),
-				pattern = pattern,
-				label   = Ship.MakeRandomLabel(),
-			})
+	-- remove with decay rate lambda. Call ONCE/hour for each ship advert in station
+	for ref,ad in pairs(shipsOnSale) do
+		if Engine.rand:Number(0,1) < lambda then  -- remove one random ship (sold)
+			removeShipOnSale(station, Engine.rand:Integer(1,#shipsOnSale))
 		end
 	end
 
-	if toRemove > 0 then
-		removeShipOnSale(station, Engine.rand:Integer(1,#shipsOnSale))
+	-- spawn a new ship adverts, call for each station
+	if Engine.rand:Number(0,1) <= prod then
+		addRandomShipAdvert(station, 1)
 	end
 
+	if prod > 1 then print("Warning: ShipMarket not in equilibrium") end
+
 	Event.Queue("onShipMarketUpdate", station, shipsOnSale)
 end
 
@@ -473,6 +510,14 @@ local function updateSystem ()
 		updateAdverts(stations[i])
 	end
 end
+
+local function createSystem()
+	local stations = Space.GetBodies(function (b) return b.superType == "STARPORT" end)
+	for i=1,#stations do
+		createShipMarket(stations[i])
+	end
+end
+
 local function destroySystem ()
 	equipmentStock = {}
 	equipmentPrice = {}
@@ -511,11 +556,13 @@ Event.Register("onGameStart", function ()
 		loaded_data = nil
 	end
 
+	createSystem()
 	updateSystem()
 	Timer:CallEvery(3600, updateSystem)
 end)
 Event.Register("onEnterSystem", function (ship)
 	if ship ~= Game.player then return end
+	createSystem()
 	updateSystem()
 end)