{
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   "source": [
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "import os, sys\n",
    "sys.path.insert(1, os.path.realpath(os.path.pardir))\n",
    "\n",
    "from typing import Sequence, Dict, Tuple\n",
    "\n",
    "from abm1559.utils import (\n",
    "    constants,\n",
    ")\n",
    "\n",
    "gamma = 500000\n",
    "constants[\"SIMPLE_TRANSACTION_GAS\"] = gamma\n",
    "\n",
    "from abm1559.txpool import TxPool\n",
    "\n",
    "from abm1559.users import (\n",
    "    User1559,\n",
    "    User\n",
    ")\n",
    "\n",
    "from abm1559.config import rng\n",
    "\n",
    "from abm1559.txs import Tx1559\n",
    "\n",
    "from abm1559.userpool import UserPool\n",
    "\n",
    "from abm1559.chain import (\n",
    "    Chain,\n",
    "    Block1559,\n",
    "    BlockAMMImplied,\n",
    "    eth_qty,\n",
    ")\n",
    "\n",
    "from abm1559.simulator import (\n",
    "    spawn_poisson_demand,\n",
    "    update_basefee,\n",
    "    generate_gbm,\n",
    "    apply_block_time_variance,\n",
    "    generate_poisson_process,\n",
    "    generate_abm,\n",
    "    generate_jump_process,\n",
    ")\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "pd.set_option('display.max_rows', 1000)\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from tqdm.notebook import tqdm\n",
    "from itertools import product"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f00177a-4aa9-4f8a-ab21-19e2842d4432",
   "metadata": {},
   "source": [
    "Model assumptions:\n",
    "\n",
    "- All transactions use 500,000 gas, block limit is 25,000,000 gas (i.e., 50 transactions).\n",
    "- Simulation lasts for 200 steps.\n",
    "- Each step, a random number of users $N_t$ is drawn from a Poisson distribution of size 100.\n",
    "- User value is drawn from uniform distribution between 0 and 20 Gwei per gas unit.\n",
    "- Users bid the miner fee as premium, = 1 Gwei.\n",
    "- Excess gas issued starts from an arbitrary value set to 3,600 Mgas (~0.06 Gwei implied basefee)\n",
    "- Implied basefee in a block providing `gas_used`, given `excess_gas_issued` is\n",
    "\n",
    "$$ b = \\frac{\\text{ethqty}(\\text{excess gas issued} + \\text{gas used}) - \\text{ethqty}(\\text{excess gas issued})}{\\text{gas used}} $$\n",
    "\n",
    "where\n",
    "\n",
    "$$ \\text{ethqty}(g) = \\exp \\Big( \\frac{g}{\\text{target gas used} \\times \\text{adjustment quotient}} \\Big) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6450a82-8a3d-4311-b47f-8891cae21164",
   "metadata": {},
   "source": [
    "## Transaction pool\n",
    "\n",
    "- Evicts transactions whenever there are more than 500 pending in the queue (reminder: we set transaction such that a full block = 50 transactions)\n",
    "- Given the current `excess_gas_issued`, miner computes their revenue should they include 0 transaction, 1 transaction, 2 transactions, ..., 50 transactions. Number of transactions included is set so that max revenue is achieved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "53d30544-0006-4945-bb3b-30b9aa7438c1",
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   "source": [
    "MAX_TX_POOL = 500\n",
    "MIN_PREMIUM = 1e9\n",
    "\n",
    "class TxPoolLimit(TxPool):\n",
    "    \n",
    "    def __init__(self, max_txs=MAX_TX_POOL, min_premium=MIN_PREMIUM, **kwargs):\n",
    "        super().__init__(**kwargs)\n",
    "        self.max_txs = max_txs\n",
    "        self.min_premium = MIN_PREMIUM\n",
    "    \n",
    "    def add_txs(self, txs: Sequence[Tx1559], env: dict) -> Sequence[Tx1559]:\n",
    "        for tx in txs:\n",
    "            self.txs[tx.tx_hash] = tx\n",
    "                    \n",
    "        if self.pool_length() > self.max_txs:\n",
    "            sorted_txs = sorted(self.txs.values(), key = lambda tx: -tx.tip(env))\n",
    "            self.empty_pool()\n",
    "            self.add_txs(sorted_txs[0:self.max_txs], env)\n",
    "            return sorted_txs[self.max_txs:]\n",
    "        \n",
    "        return []\n",
    "\n",
    "class TxPool1559(TxPoolLimit):\n",
    "    \n",
    "    def select_transactions(self, env, user_pool=None, rng=rng) -> Sequence[Tx1559]:\n",
    "        # Miner side\n",
    "        max_tx_in_block = int(constants[\"MAX_GAS_EIP1559\"] / constants[\"SIMPLE_TRANSACTION_GAS\"])\n",
    "\n",
    "        valid_txs = [tx for tx in self.txs.values() if tx.is_valid(env) and tx.tip(env) >= self.min_premium]\n",
    "        rng.shuffle(valid_txs)\n",
    "\n",
    "        sorted_valid_demand = sorted(\n",
    "            valid_txs,\n",
    "            key = lambda tx: -tx.tip(env)\n",
    "        )\n",
    "        selected_txs = sorted_valid_demand[0:max_tx_in_block]\n",
    "\n",
    "        return selected_txs\n",
    "\n",
    "class TxPoolAMMImplied(TxPoolLimit):\n",
    "    \n",
    "    def select_transactions(self, env, user_pool=None, rng=rng) -> Sequence[Tx1559]:\n",
    "        # Miner side\n",
    "        max_tx_in_block = int(constants[\"MAX_GAS_EIP1559\"] / constants[\"SIMPLE_TRANSACTION_GAS\"])\n",
    "        excess_gas_issued = env[\"excess_gas_issued\"]\n",
    "        revenues = [0]\n",
    "        \n",
    "        for i in range(1, max_tx_in_block + 1):        \n",
    "            implied_basefee = eth_qty(excess_gas_issued + i * constants[\"SIMPLE_TRANSACTION_GAS\"]) - eth_qty(excess_gas_issued)\n",
    "            implied_basefee = implied_basefee / (i * constants[\"SIMPLE_TRANSACTION_GAS\"])\n",
    "            valid_txs = [tx for tx in self.txs.values() if tx.is_valid({ \"basefee\": implied_basefee }) and tx.tip({ \"basefee\": implied_basefee }) >= self.min_premium]\n",
    "            sorted_valid_demand = sorted(\n",
    "                valid_txs,\n",
    "                key = lambda tx: -tx.tip({ \"basefee\": implied_basefee })\n",
    "            )\n",
    "            revenues += [sum([tx.tip({ \"basefee\": implied_basefee }) for tx in sorted_valid_demand[0:(i-1)]])]\n",
    "        \n",
    "        max_revenue = max(revenues)\n",
    "        \n",
    "        if max_revenue == 0:\n",
    "            return []\n",
    "        \n",
    "        opt_n_tx = len(revenues) - 1 - revenues[::-1].index(max_revenue)\n",
    "        implied_basefee = eth_qty(excess_gas_issued + opt_n_tx * constants[\"SIMPLE_TRANSACTION_GAS\"]) - eth_qty(excess_gas_issued)\n",
    "        implied_basefee = implied_basefee / (opt_n_tx * constants[\"SIMPLE_TRANSACTION_GAS\"])\n",
    "        valid_txs = [tx for tx in self.txs.values() if tx.is_valid({ \"basefee\": implied_basefee }) and tx.tip({ \"basefee\": implied_basefee }) >= self.min_premium]\n",
    "        sorted_valid_demand = sorted(\n",
    "            valid_txs,\n",
    "            key = lambda tx: -tx.tip({ \"basefee\": implied_basefee })\n",
    "        )\n",
    "        selected_txs = sorted_valid_demand[0:opt_n_tx]\n",
    "\n",
    "        return selected_txs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44752398-41d8-43aa-83fa-5fc79eb70427",
   "metadata": {},
   "source": [
    "## Main simulation loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bc1f68b9-5673-4d46-999f-a273fdf00bfd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_amm_implied(demand_scenario, txpool, UserClass, extra_metrics = None, rng = rng, silent=False):\n",
    "    # Instantiate a couple of things\n",
    "    chain = Chain()\n",
    "    metrics = []\n",
    "    user_pool = UserPool()\n",
    "    \n",
    "    # `env` is the \"environment\" of the simulation\n",
    "    env = {\n",
    "        \"basefee\": 0,\n",
    "        \"current_block\": None,\n",
    "        \"excess_gas_issued\": 3625 * 1e6,\n",
    "    }\n",
    "\n",
    "    for t in tqdm(range(len(demand_scenario)), disable=silent, desc=\"simulation loop\", leave=False):\n",
    "        if demand_scenario[t] > 5 * MAX_TX_POOL:\n",
    "            break\n",
    "        \n",
    "        # Sets current block\n",
    "        env[\"current_block\"] = t\n",
    "        \n",
    "        # Reset the random number generator with new seed to generate users with same values across runs\n",
    "        rng = np.random.default_rng((2 ** t) * (3 ** 1))\n",
    "        \n",
    "        ### SIMULATION ###\n",
    "\n",
    "        # We return some demand which on expectation yields `demand_scenario[t]` new users per round\n",
    "        users = spawn_poisson_demand(t, demand_scenario[t], User1559, rng=rng)\n",
    "        \n",
    "        # Add new users to the pool\n",
    "        # We query each new user with the current basefee value\n",
    "        # Users either return a transaction or None if they prefer to balk\n",
    "        decided_txs = user_pool.decide_transactions(users, env)\n",
    "\n",
    "        # New transactions are added to the transaction pool\n",
    "        # `evicted_txs` holds the transactions removed from the pool for lack of space\n",
    "        pool_limit_evicted_txs = txpool.add_txs(decided_txs, env)\n",
    "\n",
    "        # The best valid transactions are taken out of the pool for inclusion\n",
    "        selected_txs = txpool.select_transactions(env, rng = rng)\n",
    "        \n",
    "        txpool.remove_txs([tx.tx_hash for tx in selected_txs])\n",
    "\n",
    "        # We create a block with these transactions\n",
    "        block = BlockAMMImplied(\n",
    "            txs = selected_txs, parent_hash = chain.current_head,\n",
    "            height = t, excess_gas_issued = env[\"excess_gas_issued\"]\n",
    "        )\n",
    "        \n",
    "        env[\"excess_gas_issued\"] = max(0, env[\"excess_gas_issued\"] + block.gas_used() - constants[\"TARGET_GAS_USED\"])\n",
    "        env[\"basefee\"] = eth_qty(env[\"excess_gas_issued\"])\n",
    "        env[\"basefee\"] = env[\"basefee\"] / constants[\"BASEFEE_MAX_CHANGE_DENOMINATOR\"] / constants[\"TARGET_GAS_USED\"]\n",
    "        \n",
    "        # The block is added to the chain\n",
    "        chain.add_block(block)\n",
    "        \n",
    "        ### METRICS ###                \n",
    "        row_metrics = {\n",
    "            \"block\": t,\n",
    "            \"users\": len(users),\n",
    "            \"decided_txs\": len(decided_txs),\n",
    "            \"pool_limit_evictions\": len(pool_limit_evicted_txs),\n",
    "            \"included_txs\": len(selected_txs),\n",
    "            \"basefee\": env[\"basefee\"] / 1e9, # to Gwei\n",
    "            \"excess_gas_issued\": env[\"excess_gas_issued\"] / 1e6, # in Mgas\n",
    "            \"pool_length\": txpool.pool_length(),\n",
    "            \"gas_used\": block.gas_used(),\n",
    "        }\n",
    "        \n",
    "        if not extra_metrics is None:\n",
    "            row_metrics = {\n",
    "                **row_metrics,\n",
    "                **extra_metrics(env, users, user_pool, txpool),\n",
    "            }\n",
    "        \n",
    "        metrics.append(row_metrics)\n",
    "\n",
    "    return (pd.DataFrame(metrics), user_pool, chain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5048ee6c-1e2f-4f83-b165-c41a8328ea8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "demand_scenario = [100 for i in range(200)]\n",
    "txpool = TxPoolAMMImplied()\n",
    "(df, user_pool, chain) = simulate_amm_implied(demand_scenario, txpool, User1559)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb93e79f-8653-4e26-ad52-7add6aaac5ba",
   "metadata": {},
   "source": [
    "## Plots\n",
    "\n",
    "### Basefee over time"
   ]
  },
  {
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   "execution_count": 5,
   "id": "729f099f-0cff-4b11-b33a-df4fac2e0536",
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   "outputs": [
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     "execution_count": 5,
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   "source": [
    "df[\"basefee\"].plot()"
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  },
  {
   "cell_type": "markdown",
   "id": "d4f3e68d-624c-4316-bf3f-ca3be0c490bb",
   "metadata": {},
   "source": [
    "### Transaction pool over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5c79ab18-8876-4dc8-bb50-ec295ddf7411",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
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     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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  {
   "cell_type": "markdown",
   "id": "bfbd76b9-bad9-401f-ad6b-f69eae65cfa0",
   "metadata": {},
   "source": [
    "### Excess gas issued over time"
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  },
  {
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   "execution_count": 7,
   "id": "fa8fdc8b-27c4-441c-86a5-7a9ac5ba53aa",
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   "source": [
    "df[\"excess_gas_issued\"].plot()"
   ]
  },
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   "cell_type": "markdown",
   "id": "f6867c38-7721-496c-8b98-1c3a2345aa3a",
   "metadata": {},
   "source": [
    "## Oscillations revisited\n",
    "\n",
    "- Users have value between 10 and 11 Gwei per gas unit.\n",
    "- 1000 users show up each step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6a0bf03a-ae67-44f6-b5c1-daad314f56cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "class NarrowUser(User1559):\n",
    "    def __init__(self, wakeup_block, **kwargs):\n",
    "        super().__init__(wakeup_block, cost_per_unit = 0, **kwargs)\n",
    "        self.value = self.rng.uniform(low=10, high=11) * (10 ** 9)"
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  {
   "cell_type": "markdown",
   "id": "dca19a85-9e8b-4d7f-ac1d-5fc650bf5826",
   "metadata": {},
   "source": [
    "### With AMM design"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2ae91d8d-dd25-4755-a3d9-1d52ac2f5ed1",
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "demand_scenario = [1000 for i in range(200)]\n",
    "txpool = TxPoolAMMImplied()\n",
    "(df_amm, _, _) = simulate_amm_implied(demand_scenario, txpool, NarrowUser)"
   ]
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  {
   "cell_type": "markdown",
   "id": "f27573a9-4a86-4b90-a374-1249dcf050ee",
   "metadata": {},
   "source": [
    "#### Basefee over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "515334e6-ac5f-42f8-8ff9-f52fcb6c267f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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     "execution_count": 10,
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     "output_type": "execute_result"
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   "source": [
    "df_amm[\"basefee\"].plot()"
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  {
   "cell_type": "markdown",
   "id": "6f6b8799-faad-400a-ae4a-96a4c27d19d0",
   "metadata": {},
   "source": [
    "#### Gas used per block"
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  },
  {
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   "execution_count": 11,
   "id": "e4e81e9c-c4a3-4429-84e4-2948710c0d1b",
   "metadata": {},
   "outputs": [
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     "execution_count": 11,
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    "df_amm[\"gas_used\"].plot()"
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   "id": "fbcfd2f2-b820-4ceb-b32d-e28a1831d9ac",
   "metadata": {},
   "source": [
    "### With classic 1559"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f7291bd0-5067-4691-8662-30bbe93aaa16",
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   "outputs": [],
   "source": [
    "def simulate_1559(demand_scenario, txpool, UserClass, extra_metrics = None, rng = rng, silent=False):\n",
    "    # Instantiate a couple of things\n",
    "    chain = Chain()\n",
    "    metrics = []\n",
    "    user_pool = UserPool()\n",
    "    \n",
    "    # `env` is the \"environment\" of the simulation\n",
    "    env = {\n",
    "        \"basefee\": 0.06 * 1e9,\n",
    "        \"current_block\": None,\n",
    "    }\n",
    "\n",
    "    for t in tqdm(range(len(demand_scenario)), disable=silent, desc=\"simulation loop\", leave=False):\n",
    "        \n",
    "        # Sets current block\n",
    "        env[\"current_block\"] = t\n",
    "        \n",
    "        # Reset the random number generator with new seed to generate users with same values across runs\n",
    "        rng = np.random.default_rng((2 ** t) * (3 ** 1))\n",
    "        \n",
    "        ### SIMULATION ###\n",
    "\n",
    "        # We return some demand which on expectation yields `demand_scenario[t]` new users per round\n",
    "        users = spawn_poisson_demand(t, demand_scenario[t], User1559, rng=rng)\n",
    "        \n",
    "        # Add new users to the pool\n",
    "        # We query each new user with the current basefee value\n",
    "        # Users either return a transaction or None if they prefer to balk\n",
    "        decided_txs = user_pool.decide_transactions(users, env)\n",
    "\n",
    "        # New transactions are added to the transaction pool\n",
    "        # `evicted_txs` holds the transactions removed from the pool for lack of space\n",
    "        pool_limit_evicted_txs = txpool.add_txs(decided_txs, env)\n",
    "\n",
    "        # The best valid transactions are taken out of the pool for inclusion\n",
    "        selected_txs = txpool.select_transactions(env, rng = rng)\n",
    "        \n",
    "        txpool.remove_txs([tx.tx_hash for tx in selected_txs])\n",
    "\n",
    "        # We create a block with these transactions\n",
    "        block = Block1559(\n",
    "            txs = selected_txs, parent_hash = chain.current_head,\n",
    "            height = t, basefee = env[\"basefee\"]\n",
    "        )\n",
    "        \n",
    "        # The block is added to the chain\n",
    "        chain.add_block(block)\n",
    "        \n",
    "        ### METRICS ###                \n",
    "        row_metrics = {\n",
    "            \"block\": t,\n",
    "            \"users\": len(users),\n",
    "            \"decided_txs\": len(decided_txs),\n",
    "            \"pool_limit_evictions\": len(pool_limit_evicted_txs),\n",
    "            \"included_txs\": len(selected_txs),\n",
    "            \"basefee\": env[\"basefee\"] / 1e9, # to Gwei\n",
    "            \"pool_length\": txpool.pool_length(),\n",
    "            \"gas_used\": block.gas_used(),\n",
    "        }\n",
    "        \n",
    "        if not extra_metrics is None:\n",
    "            row_metrics = {\n",
    "                **row_metrics,\n",
    "                **extra_metrics(env, users, user_pool, txpool),\n",
    "            }\n",
    "        \n",
    "        metrics.append(row_metrics)\n",
    "        \n",
    "        # Finally, basefee is updated and a new round starts\n",
    "        env[\"basefee\"] = update_basefee(block, env[\"basefee\"])\n",
    "\n",
    "    return (pd.DataFrame(metrics), user_pool, chain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3f38dcb6-c649-46ed-8944-0efc03fa5719",
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "demand_scenario = [1000 for i in range(200)]\n",
    "txpool = TxPool1559()\n",
    "(df_1559, _, _) = simulate_1559(demand_scenario, txpool, NarrowUser)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79db5813-71d4-4aa3-a318-add9f208eac6",
   "metadata": {},
   "source": [
    "#### Basefee over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d7335a03-f50f-4028-bbec-288a09183f75",
   "metadata": {},
   "outputs": [
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   "source": [
    "df_1559[\"basefee\"].plot()"
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   "cell_type": "markdown",
   "id": "d11e5ddf-4d4c-48cd-8439-54b6ad9f63a2",
   "metadata": {},
   "source": [
    "#### Gas used per block"
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  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c4cc83ef-e722-4963-b319-a4682a8f138e",
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     "execution_count": 15,
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