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transactionPool.html
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transactionPool.html
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<div class="title">
Dynamical Analysis of the EIP-1559 Ethereum Fee Market
</div>
<div class="sub-title">
</div>
</div>
<div id="toc-author-block">
<div id="authors"></div>
<div id="toc"></div>
</div>
<div class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs ">
<details><summary>Input 1 (click to open)</summary>
<div class="jp-Cell-inputWrapper">
<div class="jp-InputArea jp-Cell-inputArea">
<div></div>
<div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
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<div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">config</span> InlineBackend.figure_format = 'svg'
<span class="kn">import</span> <span class="nn">os</span><span class="o">,</span> <span class="nn">sys</span>
<span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">realpath</span><span class="p">(</span><span class="n">os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">pardir</span><span class="p">))</span>
<span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Sequence</span><span class="p">,</span> <span class="n">Dict</span><span class="p">,</span> <span class="n">Tuple</span>
<span class="kn">from</span> <span class="nn">abm1559.utils</span> <span class="kn">import</span> <span class="p">(</span>
<span class="n">constants</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">gamma</span> <span class="o">=</span> <span class="mi">76000</span> <span class="c1"># obtained from stats analysis of sample txs</span>
<span class="n">constants</span><span class="p">[</span><span class="s2">"SIMPLE_TRANSACTION_GAS"</span><span class="p">]</span> <span class="o">=</span> <span class="n">gamma</span>
<span class="kn">from</span> <span class="nn">abm1559.txpool</span> <span class="kn">import</span> <span class="n">TxPool</span>
<span class="kn">from</span> <span class="nn">abm1559.users</span> <span class="kn">import</span> <span class="p">(</span>
<span class="n">User1559</span><span class="p">,</span>
<span class="n">User</span>
<span class="p">)</span>
<span class="kn">from</span> <span class="nn">abm1559.config</span> <span class="kn">import</span> <span class="n">rng</span>
<span class="kn">from</span> <span class="nn">abm1559.txs</span> <span class="kn">import</span> <span class="n">Tx1559</span>
<span class="kn">from</span> <span class="nn">abm1559.userpool</span> <span class="kn">import</span> <span class="n">UserPool</span>
<span class="kn">from</span> <span class="nn">abm1559.chain</span> <span class="kn">import</span> <span class="p">(</span>
<span class="n">Chain</span><span class="p">,</span>
<span class="n">Block1559</span><span class="p">,</span>
<span class="p">)</span>
<span class="kn">from</span> <span class="nn">abm1559.simulator</span> <span class="kn">import</span> <span class="p">(</span>
<span class="n">spawn_poisson_heterogeneous_demand</span><span class="p">,</span>
<span class="n">update_basefee</span><span class="p">,</span>
<span class="n">generate_gbm</span><span class="p">,</span>
<span class="n">apply_block_time_variance</span><span class="p">,</span>
<span class="n">generate_poisson_process</span><span class="p">,</span>
<span class="n">generate_abm</span><span class="p">,</span>
<span class="n">generate_jump_process</span><span class="p">,</span>
<span class="p">)</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
<span class="n">pd</span><span class="o">.</span><span class="n">set_option</span><span class="p">(</span><span class="s1">'display.max_rows'</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">time</span>
<span class="kn">from</span> <span class="nn">tqdm.notebook</span> <span class="kn">import</span> <span class="n">tqdm</span>
<span class="kn">from</span> <span class="nn">itertools</span> <span class="kn">import</span> <span class="n">product</span>
</pre></div>
</div>
</div>
</div>
</div>
</details>
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<details><summary>Input 2 (click to open)</summary>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">MAX_TX_POOL</span> <span class="o">=</span> <span class="mi">4096</span>
<span class="n">MIN_PREMIUM</span> <span class="o">=</span> <span class="mf">1e9</span>
<span class="k">class</span> <span class="nc">TxPool1559</span><span class="p">(</span><span class="n">TxPool</span><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">max_txs</span><span class="o">=</span><span class="n">MAX_TX_POOL</span><span class="p">,</span> <span class="n">min_premium</span><span class="o">=</span><span class="n">MIN_PREMIUM</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">max_txs</span> <span class="o">=</span> <span class="n">max_txs</span>
<span class="bp">self</span><span class="o">.</span><span class="n">min_premium</span> <span class="o">=</span> <span class="n">MIN_PREMIUM</span>
<span class="k">def</span> <span class="nf">add_txs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">txs</span><span class="p">:</span> <span class="n">Sequence</span><span class="p">[</span><span class="n">Tx1559</span><span class="p">],</span> <span class="n">env</span><span class="p">:</span> <span class="nb">dict</span><span class="p">)</span> <span class="o">-></span> <span class="n">Sequence</span><span class="p">[</span><span class="n">Tx1559</span><span class="p">]:</span>
<span class="k">for</span> <span class="n">tx</span> <span class="ow">in</span> <span class="n">txs</span><span class="p">:</span>
<span class="bp">self</span><span class="o">.</span><span class="n">txs</span><span class="p">[</span><span class="n">tx</span><span class="o">.</span><span class="n">tx_hash</span><span class="p">]</span> <span class="o">=</span> <span class="n">tx</span>
<span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">pool_length</span><span class="p">()</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">max_txs</span><span class="p">:</span>
<span class="n">sorted_txs</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">txs</span><span class="o">.</span><span class="n">values</span><span class="p">(),</span> <span class="n">key</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">tx</span><span class="p">:</span> <span class="o">-</span><span class="n">tx</span><span class="o">.</span><span class="n">tip</span><span class="p">(</span><span class="n">env</span><span class="p">))</span>
<span class="bp">self</span><span class="o">.</span><span class="n">empty_pool</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">add_txs</span><span class="p">(</span><span class="n">sorted_txs</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="bp">self</span><span class="o">.</span><span class="n">max_txs</span><span class="p">],</span> <span class="n">env</span><span class="p">)</span>
<span class="k">return</span> <span class="n">sorted_txs</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">max_txs</span><span class="p">:]</span>
<span class="k">return</span> <span class="p">[]</span>
<span class="k">def</span> <span class="nf">select_transactions</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">env</span><span class="p">,</span> <span class="n">user_pool</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">rng</span><span class="o">=</span><span class="n">rng</span><span class="p">)</span> <span class="o">-></span> <span class="n">Sequence</span><span class="p">[</span><span class="n">Tx1559</span><span class="p">]:</span>
<span class="c1"># Miner side</span>
<span class="n">max_tx_in_block</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">constants</span><span class="p">[</span><span class="s2">"MAX_GAS_EIP1559"</span><span class="p">]</span> <span class="o">/</span> <span class="n">constants</span><span class="p">[</span><span class="s2">"SIMPLE_TRANSACTION_GAS"</span><span class="p">])</span>
<span class="n">valid_txs</span> <span class="o">=</span> <span class="p">[</span><span class="n">tx</span> <span class="k">for</span> <span class="n">tx</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">txs</span><span class="o">.</span><span class="n">values</span><span class="p">()</span> <span class="k">if</span> <span class="n">tx</span><span class="o">.</span><span class="n">is_valid</span><span class="p">(</span><span class="n">env</span><span class="p">)</span> <span class="ow">and</span> <span class="n">tx</span><span class="o">.</span><span class="n">tip</span><span class="p">(</span><span class="n">env</span><span class="p">)</span> <span class="o">>=</span> <span class="bp">self</span><span class="o">.</span><span class="n">min_premium</span><span class="p">]</span>
<span class="n">rng</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">valid_txs</span><span class="p">)</span>
<span class="n">sorted_valid_demand</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span>
<span class="n">valid_txs</span><span class="p">,</span>
<span class="n">key</span> <span class="o">=</span> <span class="k">lambda</span> <span class="n">tx</span><span class="p">:</span> <span class="o">-</span><span class="n">tx</span><span class="o">.</span><span class="n">tip</span><span class="p">(</span><span class="n">env</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">selected_txs</span> <span class="o">=</span> <span class="n">sorted_valid_demand</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">max_tx_in_block</span><span class="p">]</span>
<span class="k">return</span> <span class="n">selected_txs</span>
<span class="k">class</span> <span class="nc">TxPoolTrendPicker</span><span class="p">(</span><span class="n">TxPool1559</span><span class="p">):</span>
<span class="c1"># window = 1 <=> Fixed band policy</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">band_width</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">window</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">band_width</span> <span class="o">=</span> <span class="n">band_width</span>
<span class="bp">self</span><span class="o">.</span><span class="n">window</span> <span class="o">=</span> <span class="n">window</span>
<span class="k">def</span> <span class="nf">should_evict</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tx</span><span class="p">:</span> <span class="n">Tx1559</span><span class="p">,</span> <span class="n">basefee</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">delta</span><span class="p">:</span> <span class="nb">float</span><span class="p">)</span> <span class="o">-></span> <span class="nb">bool</span><span class="p">:</span>
<span class="c1"># band_width = 1 <=> never evict</span>
<span class="k">return</span> <span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">delta</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">band_width</span><span class="p">)</span> <span class="o">*</span> <span class="n">basefee</span> <span class="o">></span> <span class="n">tx</span><span class="o">.</span><span class="n">max_fee</span>
<span class="k">def</span> <span class="nf">apply_eviction_policy</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">txs</span><span class="p">:</span> <span class="n">Sequence</span><span class="p">[</span><span class="n">Tx1559</span><span class="p">],</span> <span class="n">env</span><span class="p">:</span> <span class="nb">dict</span><span class="p">)</span> <span class="o">-></span> <span class="n">Tuple</span><span class="p">[</span><span class="n">Sequence</span><span class="p">[</span><span class="n">Tx1559</span><span class="p">],</span> <span class="n">Sequence</span><span class="p">[</span><span class="n">Tx1559</span><span class="p">]]:</span>
<span class="n">current_basefee</span> <span class="o">=</span> <span class="n">env</span><span class="p">[</span><span class="s2">"basefees"</span><span class="p">][</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
<span class="n">moving_average</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">env</span><span class="p">[</span><span class="s2">"basefees"</span><span class="p">])</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">env</span><span class="p">[</span><span class="s2">"basefees"</span><span class="p">])</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">env</span><span class="p">[</span><span class="s2">"basefees"</span><span class="p">])</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">window</span> <span class="k">else</span> <span class="nb">sum</span><span class="p">([</span><span class="n">env</span><span class="p">[</span><span class="s2">"basefees"</span><span class="p">][</span><span class="o">-</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">window</span><span class="o">+</span><span class="mi">1</span><span class="p">)])</span> <span class="o">//</span> <span class="bp">self</span><span class="o">.</span><span class="n">window</span>
<span class="n">delta</span> <span class="o">=</span> <span class="p">(</span><span class="n">current_basefee</span> <span class="o">-</span> <span class="n">moving_average</span><span class="p">)</span> <span class="o">/</span> <span class="n">current_basefee</span>
<span class="n">evicted_txs</span> <span class="o">=</span> <span class="p">[</span><span class="n">tx</span> <span class="k">for</span> <span class="n">tx</span> <span class="ow">in</span> <span class="n">txs</span> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">should_evict</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">current_basefee</span><span class="p">,</span> <span class="n">delta</span><span class="p">)]</span>
<span class="n">accepted_txs</span> <span class="o">=</span> <span class="p">[</span><span class="n">tx</span> <span class="k">for</span> <span class="n">tx</span> <span class="ow">in</span> <span class="n">txs</span> <span class="k">if</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">should_evict</span><span class="p">(</span><span class="n">tx</span><span class="p">,</span> <span class="n">current_basefee</span><span class="p">,</span> <span class="n">delta</span><span class="p">)]</span>
<span class="k">return</span> <span class="p">(</span><span class="n">evicted_txs</span><span class="p">,</span> <span class="n">accepted_txs</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">purge_pool_after_basefee_update</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">env</span><span class="p">:</span> <span class="nb">dict</span><span class="p">)</span> <span class="o">-></span> <span class="n">Sequence</span><span class="p">[</span><span class="n">Tx1559</span><span class="p">]:</span>
<span class="n">evicted_txs</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">apply_eviction_policy</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">txs</span><span class="o">.</span><span class="n">values</span><span class="p">(),</span> <span class="n">env</span><span class="p">)</span>
<span class="bp">self</span><span class="o">.</span><span class="n">remove_txs</span><span class="p">([</span><span class="n">tx</span><span class="o">.</span><span class="n">tx_hash</span> <span class="k">for</span> <span class="n">tx</span> <span class="ow">in</span> <span class="n">evicted_txs</span><span class="p">])</span>
<span class="k">return</span> <span class="n">evicted_txs</span>
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<details><summary>Input 3 (click to open)</summary>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">StrategicUser</span><span class="p">(</span><span class="n">User1559</span><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">wakeup_block</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">wakeup_block</span><span class="p">,</span> <span class="n">cost_per_unit</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="c1"># self.value = (1 + self.rng.pareto(2) * 20) * 1e9</span>
<span class="bp">self</span><span class="o">.</span><span class="n">value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rng</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1e9</span>
<span class="k">def</span> <span class="nf">decide_parameters</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">env</span><span class="p">):</span>
<span class="c1"># If previous block was close to full, consider being strategic</span>
<span class="k">if</span> <span class="n">env</span><span class="p">[</span><span class="s2">"wallet_mode"</span><span class="p">]</span> <span class="o">==</span> <span class="s2">"posted"</span><span class="p">:</span>
<span class="n">gas_premium</span> <span class="o">=</span> <span class="n">MIN_PREMIUM</span>
<span class="n">max_fee</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="n">env</span><span class="p">[</span><span class="s2">"basefee"</span><span class="p">]</span> <span class="o">*</span> <span class="mi">3</span><span class="p">,</span> <span class="n">MIN_PREMIUM</span> <span class="o">*</span> <span class="mi">3</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">max_fee</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="n">env</span><span class="p">[</span><span class="s2">"basefee"</span><span class="p">]</span> <span class="o">*</span> <span class="mi">3</span><span class="p">,</span> <span class="n">MIN_PREMIUM</span> <span class="o">*</span> <span class="mi">3</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">value</span><span class="p">)</span>
<span class="n">gas_premium</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">max_fee</span><span class="p">,</span> <span class="n">env</span><span class="p">[</span><span class="s2">"previous_avg_tip"</span><span class="p">]</span> <span class="o">+</span> <span class="n">MIN_PREMIUM</span><span class="p">)</span>
<span class="k">return</span> <span class="p">{</span>
<span class="s2">"max_fee"</span><span class="p">:</span> <span class="n">max_fee</span><span class="p">,</span> <span class="c1"># in wei</span>
<span class="s2">"gas_premium"</span><span class="p">:</span> <span class="n">gas_premium</span><span class="p">,</span> <span class="c1"># in wei</span>
<span class="s2">"start_block"</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">wakeup_block</span><span class="p">,</span>
<span class="p">}</span>
<span class="k">def</span> <span class="nf">create_transaction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">env</span><span class="p">):</span>
<span class="n">tx_params</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">decide_parameters</span><span class="p">(</span><span class="n">env</span><span class="p">)</span>
<span class="n">tx</span> <span class="o">=</span> <span class="n">Tx1559</span><span class="p">(</span>
<span class="n">sender</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">pub_key</span><span class="p">,</span>
<span class="n">tx_params</span> <span class="o">=</span> <span class="n">tx_params</span><span class="p">,</span>
<span class="p">)</span>
<span class="k">return</span> <span class="n">tx</span>
<span class="k">def</span> <span class="nf">export</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="k">return</span> <span class="p">{</span>
<span class="o">**</span><span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">export</span><span class="p">(),</span>
<span class="s2">"user_type"</span><span class="p">:</span> <span class="s2">"strategic_user"</span><span class="p">,</span>
<span class="p">}</span>
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<h2 id="Demand-generation">Demand generation<a class="anchor-link" href="#Demand-generation">¶</a></h2>
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<details><summary>Input 7 (click to open)</summary>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">generate_gbm_demand</span><span class="p">(</span><span class="n">S0</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">duration</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">blocks</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">volatility</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">mean_ia_time</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">rng</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">Generator</span><span class="p">)</span> <span class="o">-></span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
<span class="n">mu</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">volatility</span><span class="o">**</span><span class="mi">2</span>
<span class="n">gbm</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">generate_gbm</span><span class="p">(</span><span class="n">S0</span><span class="p">,</span> <span class="n">duration</span><span class="p">,</span> <span class="n">paths</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">mu</span><span class="o">=</span><span class="n">mu</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">volatility</span><span class="p">,</span> <span class="n">rng</span><span class="o">=</span><span class="n">rng</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="k">return</span> <span class="n">apply_block_time_variance</span><span class="p">(</span><span class="n">gbm</span><span class="p">,</span> <span class="n">blocks</span><span class="p">,</span> <span class="n">mean_ia_time</span><span class="o">=</span><span class="n">mean_ia_time</span><span class="p">,</span> <span class="n">rng</span><span class="o">=</span><span class="n">rng</span><span class="p">)</span>
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<details><summary>Input 8 (click to open)</summary>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">generate_decaying_abm_demand</span><span class="p">(</span><span class="n">S0</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">duration</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">blocks</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">volatility</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">mean_ia_time</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">rng</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">Generator</span><span class="p">)</span> <span class="o">-></span> <span class="n">Sequence</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
<span class="n">pp</span> <span class="o">=</span> <span class="n">poisson_process</span><span class="p">(</span><span class="mf">0.001</span><span class="p">,</span> <span class="n">duration</span><span class="p">,</span> <span class="n">rng</span><span class="p">)</span>
<span class="n">jp</span> <span class="o">=</span> <span class="n">jump_process</span><span class="p">(</span><span class="n">pp</span><span class="p">,</span> <span class="n">duration</span><span class="p">,</span> <span class="n">S0</span><span class="p">,</span> <span class="n">rng</span><span class="p">,</span> <span class="n">discount</span> <span class="o">=</span> <span class="mf">0.01</span><span class="p">)</span>
<span class="n">abm</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">generate_abm</span><span class="p">(</span><span class="n">S0</span><span class="p">,</span> <span class="n">duration</span><span class="p">,</span> <span class="n">paths</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">mu</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">volatility</span><span class="p">,</span> <span class="n">rng</span><span class="o">=</span><span class="n">rng</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">())</span>
<span class="k">return</span> <span class="n">apply_block_time_variance</span><span class="p">(</span><span class="n">abm</span> <span class="o">+</span> <span class="n">jp</span><span class="p">,</span> <span class="n">blocks</span><span class="p">,</span> <span class="n">mean_ia_time</span><span class="o">=</span><span class="n">mean_ia_time</span><span class="p">,</span> <span class="n">rng</span><span class="o">=</span><span class="n">rng</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">simulate</span><span class="p">(</span><span class="n">demand_scenario</span><span class="p">,</span> <span class="n">demand_id</span><span class="p">,</span> <span class="n">shares_scenario</span><span class="p">,</span> <span class="n">txpool</span><span class="p">,</span> <span class="n">extra_metrics</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">rng</span> <span class="o">=</span> <span class="n">rng</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="c1"># Instantiate a couple of things</span>
<span class="n">chain</span> <span class="o">=</span> <span class="n">Chain</span><span class="p">()</span>
<span class="n">metrics</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">user_pool</span> <span class="o">=</span> <span class="n">UserPool</span><span class="p">()</span>
<span class="n">max_basefee_window</span> <span class="o">=</span> <span class="mi">30</span>
<span class="n">start_time</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span>
<span class="n">block_target</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">constants</span><span class="p">[</span><span class="s2">"MAX_GAS_EIP1559"</span><span class="p">]</span> <span class="o">/</span> <span class="n">constants</span><span class="p">[</span><span class="s2">"SIMPLE_TRANSACTION_GAS"</span><span class="p">]</span> <span class="o">/</span> <span class="mf">2.0</span><span class="p">)</span>
<span class="c1"># `env` is the "environment" of the simulation</span>
<span class="n">env</span> <span class="o">=</span> <span class="p">{</span>
<span class="s2">"basefee"</span><span class="p">:</span> <span class="n">constants</span><span class="p">[</span><span class="s2">"INITIAL_BASEFEE"</span><span class="p">],</span>
<span class="s2">"current_block"</span><span class="p">:</span> <span class="kc">None</span><span class="p">,</span>
<span class="s2">"basefees"</span><span class="p">:</span> <span class="p">[</span><span class="n">constants</span><span class="p">[</span><span class="s2">"INITIAL_BASEFEE"</span><span class="p">]],</span>
<span class="s2">"previous_gas_used"</span><span class="p">:</span> <span class="mi">50</span><span class="p">,</span> <span class="c1"># in percent</span>
<span class="s2">"previous_avg_tip"</span><span class="p">:</span> <span class="mf">1e9</span><span class="p">,</span>
<span class="s2">"wallet_mode"</span><span class="p">:</span> <span class="s2">"posted"</span><span class="p">,</span>
<span class="p">}</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">tqdm</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">demand_scenario</span><span class="p">)),</span> <span class="n">disable</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="n">desc</span><span class="o">=</span><span class="s2">"simulation loop"</span><span class="p">,</span> <span class="n">leave</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="k">if</span> <span class="n">demand_scenario</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="o">></span> <span class="mi">5</span> <span class="o">*</span> <span class="n">MAX_TX_POOL</span><span class="p">:</span>
<span class="k">break</span>
<span class="c1"># Sets current block</span>
<span class="n">env</span><span class="p">[</span><span class="s2">"current_block"</span><span class="p">]</span> <span class="o">=</span> <span class="n">t</span>
<span class="c1"># Reset the random number generator with new seed to generate users with same values across runs</span>
<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">((</span><span class="mi">2</span> <span class="o">**</span> <span class="n">t</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">3</span> <span class="o">**</span> <span class="n">demand_id</span><span class="p">))</span>
<span class="c1">### SIMULATION ###</span>
<span class="c1"># The transaction pool applies its eviction policy after basefee update</span>
<span class="n">basefee_update_evicted_txs</span> <span class="o">=</span> <span class="n">txpool</span><span class="o">.</span><span class="n">purge_pool_after_basefee_update</span><span class="p">(</span><span class="n">env</span><span class="p">)</span>
<span class="c1"># We return some demand which on expectation yields `demand_scenario[t]` new users per round</span>
<span class="n">users</span> <span class="o">=</span> <span class="n">spawn_poisson_heterogeneous_demand</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">demand_scenario</span><span class="p">[</span><span class="n">t</span><span class="p">],</span> <span class="n">shares_scenario</span><span class="p">[</span><span class="n">t</span><span class="p">],</span> <span class="n">rng</span><span class="o">=</span><span class="n">rng</span><span class="p">)</span>
<span class="c1"># Add new users to the pool</span>
<span class="c1"># We query each new user with the current basefee value</span>
<span class="c1"># Users either return a transaction or None if they prefer to balk</span>
<span class="n">decided_txs</span> <span class="o">=</span> <span class="n">user_pool</span><span class="o">.</span><span class="n">decide_transactions</span><span class="p">(</span><span class="n">users</span><span class="p">,</span> <span class="n">env</span><span class="p">)</span>
<span class="c1"># Divide incoming transactions between accepted and rejected ones</span>
<span class="n">incoming_evicted_txs</span><span class="p">,</span> <span class="n">accepted_txs</span> <span class="o">=</span> <span class="n">txpool</span><span class="o">.</span><span class="n">apply_eviction_policy</span><span class="p">(</span><span class="n">decided_txs</span><span class="p">,</span> <span class="n">env</span><span class="p">)</span>
<span class="c1"># New transactions are added to the transaction pool</span>
<span class="c1"># `evicted_txs` holds the transactions removed from the pool for lack of space</span>
<span class="n">pool_limit_evicted_txs</span> <span class="o">=</span> <span class="n">txpool</span><span class="o">.</span><span class="n">add_txs</span><span class="p">(</span><span class="n">accepted_txs</span><span class="p">,</span> <span class="n">env</span><span class="p">)</span>
<span class="c1"># The best valid transactions are taken out of the pool for inclusion</span>
<span class="n">selected_txs</span> <span class="o">=</span> <span class="n">txpool</span><span class="o">.</span><span class="n">select_transactions</span><span class="p">(</span><span class="n">env</span><span class="p">,</span> <span class="n">rng</span> <span class="o">=</span> <span class="n">rng</span><span class="p">)</span>
<span class="n">txpool</span><span class="o">.</span><span class="n">remove_txs</span><span class="p">([</span><span class="n">tx</span><span class="o">.</span><span class="n">tx_hash</span> <span class="k">for</span> <span class="n">tx</span> <span class="ow">in</span> <span class="n">selected_txs</span><span class="p">])</span>
<span class="c1"># We create a block with these transactions</span>
<span class="n">block</span> <span class="o">=</span> <span class="n">Block1559</span><span class="p">(</span>
<span class="n">txs</span> <span class="o">=</span> <span class="n">selected_txs</span><span class="p">,</span> <span class="n">parent_hash</span> <span class="o">=</span> <span class="n">chain</span><span class="o">.</span><span class="n">current_head</span><span class="p">,</span>
<span class="n">height</span> <span class="o">=</span> <span class="n">t</span><span class="p">,</span> <span class="n">basefee</span> <span class="o">=</span> <span class="n">env</span><span class="p">[</span><span class="s2">"basefee"</span><span class="p">]</span>
<span class="p">)</span>
<span class="c1"># Record the gas used and avg tip in the block</span>
<span class="n">env</span><span class="p">[</span><span class="s2">"previous_gas_used"</span><span class="p">]</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">block</span><span class="o">.</span><span class="n">gas_used</span><span class="p">()</span> <span class="o">/</span> <span class="n">constants</span><span class="p">[</span><span class="s2">"MAX_GAS_EIP1559"</span><span class="p">]</span> <span class="o">*</span> <span class="mi">100</span><span class="p">)</span>
<span class="n">env</span><span class="p">[</span><span class="s2">"previous_avg_tip"</span><span class="p">]</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">block</span><span class="o">.</span><span class="n">average_tip</span><span class="p">()</span> <span class="o">*</span> <span class="mf">1e9</span><span class="p">)</span>
<span class="n">env</span><span class="p">[</span><span class="s2">"wallet_mode"</span><span class="p">]</span> <span class="o">=</span> <span class="s2">"posted"</span> <span class="k">if</span> <span class="n">env</span><span class="p">[</span><span class="s2">"previous_gas_used"</span><span class="p">]</span> <span class="o"><=</span> <span class="mi">90</span> <span class="k">else</span> <span class="s2">"expert"</span>
<span class="c1"># The block is added to the chain</span>
<span class="n">chain</span><span class="o">.</span><span class="n">add_block</span><span class="p">(</span><span class="n">block</span><span class="p">)</span>
<span class="c1">### METRICS ###</span>
<span class="n">user_efficiency</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="n">user_pool</span><span class="o">.</span><span class="n">get_user</span><span class="p">(</span><span class="n">tx</span><span class="o">.</span><span class="n">sender</span><span class="p">)</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">tx</span> <span class="ow">in</span> <span class="n">selected_txs</span><span class="p">])</span>
<span class="n">row_metrics</span> <span class="o">=</span> <span class="p">{</span>
<span class="s2">"block"</span><span class="p">:</span> <span class="n">t</span><span class="p">,</span>
<span class="s2">"basefee_update_evictions"</span><span class="p">:</span> <span class="nb">len</span><span class="p">(</span><span class="n">basefee_update_evicted_txs</span><span class="p">),</span>
<span class="s2">"users"</span><span class="p">:</span> <span class="nb">len</span><span class="p">(</span><span class="n">users</span><span class="p">),</span>
<span class="s2">"decided_txs"</span><span class="p">:</span> <span class="nb">len</span><span class="p">(</span><span class="n">decided_txs</span><span class="p">),</span>
<span class="s2">"incoming_evictions"</span><span class="p">:</span> <span class="nb">len</span><span class="p">(</span><span class="n">incoming_evicted_txs</span><span class="p">),</span>
<span class="s2">"pool_limit_evictions"</span><span class="p">:</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool_limit_evicted_txs</span><span class="p">),</span>
<span class="s2">"included_txs"</span><span class="p">:</span> <span class="nb">len</span><span class="p">(</span><span class="n">selected_txs</span><span class="p">),</span>
<span class="s2">"basefee"</span><span class="p">:</span> <span class="n">env</span><span class="p">[</span><span class="s2">"basefee"</span><span class="p">]</span> <span class="o">/</span> <span class="mf">1e9</span><span class="p">,</span> <span class="c1"># to Gwei</span>
<span class="s2">"gas_used"</span><span class="p">:</span> <span class="n">env</span><span class="p">[</span><span class="s2">"previous_gas_used"</span><span class="p">],</span>
<span class="s2">"avg_tip"</span><span class="p">:</span> <span class="n">env</span><span class="p">[</span><span class="s2">"previous_avg_tip"</span><span class="p">]</span> <span class="o">/</span> <span class="mf">1e9</span><span class="p">,</span>
<span class="s2">"pool_length"</span><span class="p">:</span> <span class="n">txpool</span><span class="o">.</span><span class="n">pool_length</span><span class="p">(),</span>
<span class="s2">"user_efficiency"</span><span class="p">:</span> <span class="n">user_efficiency</span><span class="p">,</span>
<span class="p">}</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">extra_metrics</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">row_metrics</span> <span class="o">=</span> <span class="p">{</span>
<span class="o">**</span><span class="n">row_metrics</span><span class="p">,</span>
<span class="o">**</span><span class="n">extra_metrics</span><span class="p">(</span><span class="n">env</span><span class="p">,</span> <span class="n">users</span><span class="p">,</span> <span class="n">user_pool</span><span class="p">,</span> <span class="n">txpool</span><span class="p">),</span>
<span class="p">}</span>
<span class="n">metrics</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row_metrics</span><span class="p">)</span>
<span class="c1"># Finally, basefee is updated and a new round starts</span>
<span class="n">env</span><span class="p">[</span><span class="s2">"basefee"</span><span class="p">]</span> <span class="o">=</span> <span class="n">update_basefee</span><span class="p">(</span><span class="n">block</span><span class="p">,</span> <span class="n">env</span><span class="p">[</span><span class="s2">"basefee"</span><span class="p">])</span>
<span class="n">env</span><span class="p">[</span><span class="s2">"basefees"</span><span class="p">]</span> <span class="o">=</span> <span class="n">env</span><span class="p">[</span><span class="s2">"basefees"</span><span class="p">][</span><span class="o">-</span><span class="p">(</span><span class="n">max_basefee_window</span><span class="o">-</span><span class="mi">1</span><span class="p">):]</span> <span class="o">+</span> <span class="p">[</span><span class="n">env</span><span class="p">[</span><span class="s2">"basefee"</span><span class="p">]]</span>
<span class="k">return</span> <span class="p">(</span><span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">metrics</span><span class="p">),</span> <span class="n">user_pool</span><span class="p">,</span> <span class="n">chain</span><span class="p">)</span>
<span class="n">volatilities</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]</span>
<span class="c1"># volatilities = [1.0]</span>
<span class="n">demand_paths</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span>
<span class="n">band_widths</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="o">/</span><span class="mi">3</span><span class="p">,</span> <span class="mf">2.0</span><span class="o">/</span><span class="mi">3</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]</span>
<span class="c1"># band_widths = [0.0]</span>
<span class="n">blocks</span> <span class="o">=</span> <span class="mi">600</span>
<span class="n">metrics</span> <span class="o">=</span> <span class="p">{}</span>
<span class="n">dfs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">run</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">gamma</span> <span class="o">=</span> <span class="mi">76000</span>
<span class="n">mean_ia_time</span> <span class="o">=</span> <span class="mi">13</span>
<span class="n">max_k</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">blocks</span> <span class="o">*</span> <span class="n">mean_ia_time</span><span class="p">)</span>
<span class="n">max_txs_in_block</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">constants</span><span class="p">[</span><span class="s2">"MAX_GAS_EIP1559"</span><span class="p">]</span> <span class="o">/</span> <span class="n">gamma</span><span class="p">)</span>
<span class="n">S0s</span> <span class="o">=</span> <span class="p">[</span><span class="nb">int</span><span class="p">(</span><span class="n">k</span> <span class="o">*</span> <span class="n">max_txs_in_block</span> <span class="o">/</span> <span class="n">mean_ia_time</span><span class="p">)</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">,</span> <span class="mi">2</span><span class="p">]]</span>
<span class="k">for</span> <span class="n">params</span> <span class="ow">in</span> <span class="n">tqdm</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">product</span><span class="p">(</span>
<span class="n">demand_paths</span><span class="p">,</span> <span class="n">volatilities</span><span class="p">,</span> <span class="n">band_widths</span><span class="p">,</span> <span class="n">S0s</span>
<span class="p">)),</span> <span class="n">desc</span><span class="o">=</span><span class="s2">"session loop"</span><span class="p">,</span> <span class="n">leave</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="p">(</span><span class="n">demand_path</span><span class="p">,</span> <span class="n">volatility</span><span class="p">,</span> <span class="n">band_width</span><span class="p">,</span> <span class="n">S0</span><span class="p">)</span> <span class="o">=</span> <span class="n">params</span>
<span class="c1"># Generate demand</span>
<span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="n">demand_path</span><span class="p">)</span>
<span class="n">demand_scenario</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">generate_decaying_abm_demand</span><span class="p">(</span><span class="n">S0</span><span class="p">,</span> <span class="n">max_k</span><span class="p">,</span> <span class="n">blocks</span><span class="p">,</span> <span class="n">volatility</span><span class="p">,</span> <span class="n">mean_ia_time</span><span class="p">,</span> <span class="n">rng</span><span class="p">),</span> <span class="mi">0</span><span class="p">)</span>
<span class="c1"># Shares of new users per time step</span>
<span class="n">shares_scenario</span> <span class="o">=</span> <span class="p">[{</span>
<span class="n">StrategicUser</span><span class="p">:</span> <span class="mf">1.00</span><span class="p">,</span>
<span class="p">}</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">blocks</span><span class="p">)]</span>
<span class="c1"># Transaction pool</span>
<span class="n">txpool</span> <span class="o">=</span> <span class="n">TxPoolTrendPicker</span><span class="p">(</span><span class="n">band_width</span> <span class="o">=</span> <span class="n">band_width</span><span class="p">)</span>
<span class="c1"># Simulate</span>
<span class="p">(</span><span class="n">df</span><span class="p">,</span> <span class="n">user_pool</span><span class="p">,</span> <span class="n">chain</span><span class="p">)</span> <span class="o">=</span> <span class="n">simulate</span><span class="p">(</span><span class="n">demand_scenario</span><span class="p">,</span> <span class="n">demand_path</span><span class="p">,</span> <span class="n">shares_scenario</span><span class="p">,</span> <span class="n">txpool</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">df</span><span class="p">[</span><span class="s2">"run"</span><span class="p">]</span> <span class="o">=</span> <span class="n">run</span>
<span class="n">df</span><span class="p">[</span><span class="s2">"volatility"</span><span class="p">]</span> <span class="o">=</span> <span class="n">volatility</span>
<span class="n">df</span><span class="p">[</span><span class="s2">"band_width"</span><span class="p">]</span> <span class="o">=</span> <span class="n">band_width</span>
<span class="n">df</span><span class="p">[</span><span class="s2">"demand_path"</span><span class="p">]</span> <span class="o">=</span> <span class="n">demand_path</span>
<span class="n">df</span><span class="p">[</span><span class="s2">"S0"</span><span class="p">]</span> <span class="o">=</span> <span class="n">S0</span>
<span class="n">run</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="n">dfs</span> <span class="o">+=</span> <span class="p">[</span><span class="n">df</span><span class="p">]</span>
</pre></div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">concat</span><span class="p">(</span><span class="n">dfs</span><span class="p">)</span>
<span class="n">df</span><span class="o">.</span><span class="n">to_csv</span><span class="p">(</span><span class="s2">"../data/sim_runs.csv"</span><span class="p">,</span> <span class="n">index</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">index_label</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
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