docs/usage.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Usage Documentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import Dependencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('../source/ServerlessAppPerfCostMdlOpt')\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import itertools\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "from ServerlessAppWorkflow import ServerlessAppWorkflow\n",
    "from AppGenerator import AppGenerator\n",
    "from PerfOpt import PerfOpt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the workflow of a serverless application"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "AppWorkflow_G = nx.DiGraph()\n",
    "\n",
    "# Define functions and structural vertices in the App\n",
    "# AppWorkflow_G.add_node($Vertex_Name, pos=$Vertex_Position)\n",
    "AppWorkflow_G.add_node('Start', pos=(0, 1))\n",
    "AppWorkflow_G.add_node(1, pos=(1, 1))\n",
    "AppWorkflow_G.add_node(2, pos=(2, 2))\n",
    "AppWorkflow_G.add_node(3, pos=(2, 0))\n",
    "AppWorkflow_G.add_node(9, pos=(2.5, -0.5))\n",
    "AppWorkflow_G.add_node(15, pos=(4, -0.5))\n",
    "AppWorkflow_G.add_node(16, pos=(5, -0.5))\n",
    "AppWorkflow_G.add_node(10, pos=(2.5, 0.5))\n",
    "AppWorkflow_G.add_node(4, pos=(4, 2.5))\n",
    "AppWorkflow_G.add_node(5, pos=(3, 1.5))\n",
    "AppWorkflow_G.add_node(11, pos=(3.5, 2))\n",
    "AppWorkflow_G.add_node(12, pos=(3.5, 1))\n",
    "AppWorkflow_G.add_node(13, pos=(4.5, 1))\n",
    "AppWorkflow_G.add_node(14, pos=(5.5, 1))\n",
    "AppWorkflow_G.add_node(6, pos=(6, 0))\n",
    "AppWorkflow_G.add_node(7, pos=(7, 1))\n",
    "AppWorkflow_G.add_node(8, pos=(8, 1))\n",
    "AppWorkflow_G.add_node('End', pos=(9, 1))\n",
    "\n",
    "# Define edges and the transition probability\n",
    "# AppWorkflow_G.add_weighted_edges_from([$start from, $end at, $transition probability])\n",
    "AppWorkflow_G.add_weighted_edges_from([(1, 2, 1),(1, 3, 1),(2, 4, 0.6),(2, 5, 0.4),(4, 7, 1),(5, 11, 1),(5, 12, 1),(11, 7, 1),(12, 13, 1),(13, 14, 1),(14, 13, 0.3),(14, 7, 0.7),(3, 9, 0.8),(3, 10, 0.2),(9, 15, 1),(15, 16, 0.95),(15, 15, 0.05),(16, 6, 1),(10, 6, 1), (6, 7, 0.9), (6, 3, 0.1), (7, 8, 0.8),(7, 7, 0.2)])\n",
    "AppWorkflow_G.add_weighted_edges_from([('Start', 1, 1), (8, 'End', 1)])\n",
    "\n",
    "# Show the workflow graph\n",
    "pos_AppWorkflow_G = nx.get_node_attributes(AppWorkflow_G, 'pos')\n",
    "nx.draw(AppWorkflow_G, pos_AppWorkflow_G, with_labels=True)\n",
    "labels_AppWorkflow_G = nx.get_edge_attributes(AppWorkflow_G, 'weight')\n",
    "nx.draw_networkx_edge_labels(AppWorkflow_G, pos_AppWorkflow_G, edge_labels=labels_AppWorkflow_G)\n",
    "pos_higher_offset_AppWorkflow_G = {}\n",
    "for k, v in pos_AppWorkflow_G.items():\n",
    "    pos_higher_offset_AppWorkflow_G[k] = (v[0], v[1] + 0.15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Use the performance model to get the average end-to-end response time of a serverless application"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the performance (response time in ms) of functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "AppWorkflow_G.nodes[1]['rt'] = 768.23935\n",
    "AppWorkflow_G.nodes[2]['rt'] = 204.44438666666665\n",
    "AppWorkflow_G.nodes[3]['rt'] = 525.3339015713016\n",
    "AppWorkflow_G.nodes[4]['rt'] = 848.5232830820771\n",
    "AppWorkflow_G.nodes[5]['rt'] = 205.84332234130255\n",
    "AppWorkflow_G.nodes[6]['rt'] = 507.06963577139476\n",
    "AppWorkflow_G.nodes[7]['rt'] = 347.58557048748355\n",
    "AppWorkflow_G.nodes[8]['rt'] = 235.33234666666667\n",
    "AppWorkflow_G.nodes[9]['rt'] = 164.18543685756242\n",
    "AppWorkflow_G.nodes[10]['rt'] = 364.45012288786484\n",
    "AppWorkflow_G.nodes[11]['rt'] = 1049.8307584501235\n",
    "AppWorkflow_G.nodes[12]['rt'] = 787.509307502061\n",
    "AppWorkflow_G.nodes[13]['rt'] = 377.8240525114155\n",
    "AppWorkflow_G.nodes[14]['rt'] = 232.72174657534248\n",
    "AppWorkflow_G.nodes[15]['rt'] = 287.0198944033791\n",
    "AppWorkflow_G.nodes[16]['rt'] = 193.61988628026415"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Inputs:\n",
    "    * App workflow graph\n",
    "    * Performance of functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average End-to-end Response Time in ms: 3591.2615397450927 (use the delay model of AWS Step Functions as the transition delay)\n",
      "Average End-to-end Response Time in ms: 3354.881636236321 (the transition delay is 0 everywhere)\n"
     ]
    }
   ],
   "source": [
    "App = ServerlessAppWorkflow(G=AppWorkflow_G.copy(), delayType='SFN') # delayType='SFN': Use the delay model of AWS Step Functions as the transition delay\n",
    "App.get_simple_dag()\n",
    "AppERT = App.get_avg_rt()\n",
    "print(\"Average End-to-end Response Time in ms: {} (use the delay model of AWS Step Functions as the transition delay)\".format(AppERT))\n",
    "\n",
    "App = ServerlessAppWorkflow(G=AppWorkflow_G.copy(), delayType='None') # delayType='None': The transition delay is considered as 0.\n",
    "App.get_simple_dag()\n",
    "AppERT = App.get_avg_rt()\n",
    "print(\"Average End-to-end Response Time in ms: {} (the transition delay is 0 everywhere)\".format(AppERT)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average End-to-end Response Time in ms: 3464.7099570383257 (use the delay from the input)\n"
     ]
    }
   ],
   "source": [
    "# Define Delay\n",
    "AppWorkflow_G.nodes['Start']['delay'] = 0\n",
    "AppWorkflow_G.nodes[1]['delay'] = 0\n",
    "AppWorkflow_G.nodes[2]['delay'] = 0\n",
    "AppWorkflow_G.nodes[3]['delay'] = 0\n",
    "AppWorkflow_G.nodes[4]['delay'] = 0\n",
    "AppWorkflow_G.nodes[5]['delay'] = 0\n",
    "AppWorkflow_G.nodes[6]['delay'] = 0\n",
    "AppWorkflow_G.nodes[7]['delay'] = 0\n",
    "AppWorkflow_G.nodes[8]['delay'] = 0\n",
    "AppWorkflow_G.nodes[9]['delay'] = 0\n",
    "AppWorkflow_G.nodes[10]['delay'] = 0\n",
    "AppWorkflow_G.nodes[11]['delay'] = 0\n",
    "AppWorkflow_G.nodes[12]['delay'] = 0\n",
    "AppWorkflow_G.nodes[13]['delay'] = 0\n",
    "AppWorkflow_G.nodes[14]['delay'] = 0\n",
    "AppWorkflow_G.nodes[15]['delay'] = 0\n",
    "AppWorkflow_G.nodes[16]['delay'] = 0\n",
    "AppWorkflow_G.nodes['End']['delay'] = 0\n",
    "AppWorkflow_G.edges[('Start', 1)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(1, 2)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(1, 3)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(2, 4)]['delay'] = 14\n",
    "AppWorkflow_G.edges[(2, 5)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(3, 9)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(3, 10)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(9, 15)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(15, 16)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(15, 15)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(16, 6)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(10, 6)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(4, 7)]['delay'] = 18\n",
    "AppWorkflow_G.edges[(5, 11)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(5, 12)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(11, 7)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(12, 13)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(13, 14)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(14, 13)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(14, 7)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(6, 7)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(6, 3)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(7, 8)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(7, 7)]['delay'] = 10\n",
    "AppWorkflow_G.edges[(8, 'End')]['delay'] = 10\n",
    "App = ServerlessAppWorkflow(G=AppWorkflow_G.copy(), delayType='Defined') # delayType='Defined': Use the delay from the input.\n",
    "App.get_simple_dag()\n",
    "AppERT = App.get_avg_rt()\n",
    "print(\"Average End-to-end Response Time in ms: {} (use the delay from the input)\".format(AppERT)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Use the cost model to get the average cost of a serverless application"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the performance (response time in ms) of functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "AppWorkflow_G.nodes[1]['rt'] = 768.23935\n",
    "AppWorkflow_G.nodes[2]['rt'] = 204.44438666666665\n",
    "AppWorkflow_G.nodes[3]['rt'] = 525.3339015713016\n",
    "AppWorkflow_G.nodes[4]['rt'] = 848.5232830820771\n",
    "AppWorkflow_G.nodes[5]['rt'] = 205.84332234130255\n",
    "AppWorkflow_G.nodes[6]['rt'] = 507.06963577139476\n",
    "AppWorkflow_G.nodes[7]['rt'] = 347.58557048748355\n",
    "AppWorkflow_G.nodes[8]['rt'] = 235.33234666666667\n",
    "AppWorkflow_G.nodes[9]['rt'] = 164.18543685756242\n",
    "AppWorkflow_G.nodes[10]['rt'] = 364.45012288786484\n",
    "AppWorkflow_G.nodes[11]['rt'] = 1049.8307584501235\n",
    "AppWorkflow_G.nodes[12]['rt'] = 787.509307502061\n",
    "AppWorkflow_G.nodes[13]['rt'] = 377.8240525114155\n",
    "AppWorkflow_G.nodes[14]['rt'] = 232.72174657534248\n",
    "AppWorkflow_G.nodes[15]['rt'] = 287.0198944033791\n",
    "AppWorkflow_G.nodes[16]['rt'] = 193.61988628026415"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the memory configuration (allocated memory size in MB) of functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "AppWorkflow_G.nodes[1]['mem'] = 1536\n",
    "AppWorkflow_G.nodes[2]['mem'] = 1792\n",
    "AppWorkflow_G.nodes[3]['mem'] = 576\n",
    "AppWorkflow_G.nodes[4]['mem'] = 2240\n",
    "AppWorkflow_G.nodes[5]['mem'] = 896\n",
    "AppWorkflow_G.nodes[6]['mem'] = 1728\n",
    "AppWorkflow_G.nodes[7]['mem'] = 128\n",
    "AppWorkflow_G.nodes[8]['mem'] = 128\n",
    "AppWorkflow_G.nodes[9]['mem'] = 256\n",
    "AppWorkflow_G.nodes[10]['mem'] = 320\n",
    "AppWorkflow_G.nodes[11]['mem'] = 1920\n",
    "AppWorkflow_G.nodes[12]['mem'] = 1984\n",
    "AppWorkflow_G.nodes[13]['mem'] = 1088\n",
    "AppWorkflow_G.nodes[14]['mem'] = 640\n",
    "AppWorkflow_G.nodes[15]['mem'] = 896\n",
    "AppWorkflow_G.nodes[16]['mem'] = 1088"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cost modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Inputs:\n",
    "    * App workflow graph\n",
    "    * Performance of functions\n",
    "    * Memory configuration of functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NE:\n",
      "{'Start': 0, 1: 1, 2: 1, 3: 1.1111111111111112, 9: 0.888888888888889, 15: 0.935672514619883, 16: 0.888888888888889, 10: 0.22222222222222224, 4: 0.6, 5: 0.4, 11: 0.4, 12: 0.4, 13: 0.5714285714285715, 14: 0.5714285714285715, 6: 1.1111111111111112, 7: 1.25, 8: 1, 'End': 0}\n",
      "Average Cost per 1 Million Executions Reported by Model: 117.71743024227234\n"
     ]
    }
   ],
   "source": [
    "App = ServerlessAppWorkflow(G=AppWorkflow_G.copy(), delayType='SFN')\n",
    "App.update_NE()\n",
    "print('NE:')\n",
    "print(App.ne)\n",
    "AppCost = App.get_avg_cost()\n",
    "print(\"Average Cost per 1 Million Executions Reported by Model: {}\".format(AppCost))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inputs for the optimization algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the workflow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "App6_G = nx.DiGraph()\n",
    "\n",
    "# Define functions and structural vertices in the App\n",
    "# AppWorkflow_G.add_node($Vertex_Name, pos=$Vertex_Position)\n",
    "App6_G.add_node('Start', pos=(0, 1))\n",
    "App6_G.add_node(1, pos=(1, 1))\n",
    "App6_G.add_node(2, pos=(2, 0))\n",
    "App6_G.add_node(3, pos=(2, 3))\n",
    "App6_G.add_node(4, pos=(3, 1))\n",
    "App6_G.add_node(5, pos=(2, 2))\n",
    "App6_G.add_node(6, pos=(4, 1))\n",
    "App6_G.add_node('End', pos=(5, 1))\n",
    "\n",
    "# Define edges and the transition probability\n",
    "# AppWorkflow_G.add_weighted_edges_from([$start from, $end at, $transition probability])\n",
    "App6_G.add_weighted_edges_from([(1, 2, 1), (1, 5, 0.2), (1, 3, 0.8), (3, 4, 1), (5, 4, 1), (2, 4, 1), (4, 1, 0.1),\n",
    "                          (4, 4, 0.2), (4, 6, 0.7)])\n",
    "App6_G.add_weighted_edges_from([('Start', 1, 1), (6, 'End', 1)])\n",
    "\n",
    "# Show the workflow graph\n",
    "pos_App6_G = nx.get_node_attributes(App6_G, 'pos')\n",
    "nx.draw(App6_G, pos_App6_G, with_labels=True)\n",
    "labels_App6_G = nx.get_edge_attributes(App6_G, 'weight')\n",
    "nx.draw_networkx_edge_labels(App6_G, pos_App6_G, edge_labels=labels_App6_G)\n",
    "pos_higher_offset_App6_G = {}\n",
    "for k, v in pos_App6_G.items():\n",
    "    pos_higher_offset_App6_G[k] = (v[0], v[1] + 0.15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc-hr-collapsed": true
   },
   "source": [
    "### Define the performance profile of functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Method 1: Define by passing PF directly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "f1_pf = {128: 5500.4866999999995, 192: 3674.8530999999994, 256: 2725.8923, 320: 2148.4905000000003, 384: 1771.1575, 448: 1502.8815, 512: 1301.2842, 576: 1144.3912, 640: 1013.1754000000001, 704: 926.5277999999998, 768: 835.1147, 832: 780.8069000000003, 896: 746.0372, 960: 723.9654999999999, 1024: 742.8131000000001, 1088: 715.9623999999999, 1152: 733.8956000000002, 1216: 767.1371000000003, 1280: 707.7513, 1344: 776.39, 1408: 722.9680000000001, 1472: 676.1344000000001, 1536: 707.1422, 1600: 704.9714, 1664: 761.7915000000003, 1728: 698.8906999999999, 1792: 676.2910999999999, 1856: 767.4296, 1920: 787.3432, 1984: 789.8888000000001, 2048: 688.5601999999999, 2112: 789.7145000000002, 2176: 739.7988000000001, 2240: 701.5542999999999, 2304: 743.8631, 2368: 741.6306999999999, 2432: 740.4686999999998, 2496: 785.0328999999999, 2560: 692.6570999999999, 2624: 700.0512999999999, 2688: 764.4642000000001, 2752: 722.9775000000002, 2816: 700.8738000000001, 2880: 732.8464, 2944: 695.5066, 3008: 753.4839}\n",
    "f2_pf = {128: 2898.2188999999994, 192: 1922.4316000000001, 256: 1425.9775999999995, 320: 1150.7265, 384: 953.4348000000001, 448: 811.3380999999999, 512: 700.4040000000002, 576: 629.4998, 640: 556.3427, 704: 510.6892, 768: 464.2314999999999, 832: 423.41310000000004, 896: 399.03869999999995, 960: 369.6110999999999, 1024: 344.49680000000006, 1088: 322.5969, 1152: 304.1409, 1216: 294.3993, 1280: 271.0062, 1344: 267.3689, 1408: 251.153, 1472: 242.73329999999999, 1536: 235.78379999999999, 1600: 223.15850000000003, 1664: 222.29129999999998, 1728: 215.491, 1792: 202.71560000000002, 1856: 204.17969999999997, 1920: 202.31969999999998, 1984: 203.7646, 2048: 201.59859999999998, 2112: 200.0368, 2176: 203.28369999999998, 2240: 200.2895, 2304: 204.58439999999996, 2368: 200.57219999999998, 2432: 201.2618, 2496: 200.9125, 2560: 200.55780000000001, 2624: 203.90529999999995, 2688: 200.66140000000004, 2752: 203.4133, 2816: 203.4614, 2880: 204.29409999999996, 2944: 201.55410000000003, 3008: 200.59420000000003}\n",
    "f3_pf = {128: 2409.1354, 192: 1605.9911, 256: 1202.6657, 320: 939.6917, 384: 790.8393000000001, 448: 696.9177000000001, 512: 591.0748, 576: 518.7573, 640: 482.61339999999996, 704: 420.4162, 768: 383.089, 832: 358.2605, 896: 336.92420000000004, 960: 328.37669999999997, 1024: 292.5811, 1088: 267.7776, 1152: 261.7981, 1216: 248.14419999999996, 1280: 232.6674, 1344: 221.45959999999997, 1408: 211.8561, 1472: 202.5364, 1536: 195.3067, 1600: 191.68619999999996, 1664: 180.68119999999996, 1728: 179.79210000000003, 1792: 170.52989999999997, 1856: 170.1544, 1920: 170.1789, 1984: 168.60920000000002, 2048: 167.9793, 2112: 172.21650000000002, 2176: 165.96130000000002, 2240: 173.9336, 2304: 175.0984, 2368: 165.9825, 2432: 170.70719999999994, 2496: 169.6841, 2560: 169.5686, 2624: 170.42140000000003, 2688: 172.299, 2752: 170.31539999999998, 2816: 170.0025, 2880: 171.7793, 2944: 168.07539999999997, 3008: 169.77300000000002}\n",
    "f4_pf = {128: 6180.600600000001, 192: 4237.538600000001, 256: 3289.4039000000002, 320: 2739.3443000000007, 384: 2489.5899999999997, 448: 2122.9276, 512: 1933.9807, 576: 1765.8597, 640: 1561.9238, 704: 1522.5382999999995, 768: 1362.6908, 832: 1285.8076, 896: 1247.5121, 960: 1241.3156000000001, 1024: 1172.5088000000003, 1088: 1149.2724, 1152: 1046.2866, 1216: 1025.6652000000001, 1280: 973.8288999999997, 1344: 1013.2251000000001, 1408: 960.9827, 1472: 968.9765999999998, 1536: 956.8087999999999, 1600: 897.5600999999998, 1664: 887.0984999999997, 1728: 862.6254999999999, 1792: 852.2578, 1856: 858.3172999999999, 1920: 859.1973000000002, 1984: 877.1611, 2048: 831.638, 2112: 874.2311, 2176: 823.7024, 2240: 791.3352, 2304: 792.9698999999999, 2368: 784.8208999999999, 2432: 806.5761999999999, 2496: 784.4135000000001, 2560: 779.6768, 2624: 805.4515000000001, 2688: 773.9589, 2752: 774.5977, 2816: 922.8518811881189, 2880: 781.5426, 2944: 779.7493000000001, 3008: 795.1290000000001}\n",
    "f5_pf = {128: 1505.1143, 192: 1015.8741, 256: 754.0495999999999, 320: 600.4303, 384: 495.4806000000001, 448: 427.27439999999996, 512: 370.50690000000003, 576: 331.88309999999996, 640: 295.02630000000005, 704: 259.8384, 768: 241.16710000000003, 832: 222.33810000000003, 896: 205.59129999999996, 960: 194.7629, 1024: 181.9845, 1088: 170.3668, 1152: 163.28100000000003, 1216: 153.24939999999998, 1280: 147.034, 1344: 140.9829, 1408: 134.4757, 1472: 128.98669999999998, 1536: 124.48219999999998, 1600: 117.32459999999999, 1664: 115.7402, 1728: 114.93970000000002, 1792: 108.37849999999999, 1856: 108.16319999999997, 1920: 109.36800000000001, 1984: 108.4496, 2048: 108.77069999999999, 2112: 108.6171, 2176: 105.60330000000002, 2240: 108.2027, 2304: 106.6473, 2368: 106.5465, 2432: 109.14479999999998, 2496: 108.62479999999996, 2560: 107.43009999999998, 2624: 107.8927, 2688: 107.98369999999998, 2752: 108.69229999999999, 2816: 105.01710000000001, 2880: 107.6745, 2944: 108.55629999999995, 3008: 108.42310000000002}\n",
    "f6_pf = {128: 6853.313699999999, 192: 4572.3956, 256: 3423.9434, 320: 2735.9797, 384: 2250.8023, 448: 1905.4582, 512: 1678.1624, 576: 1491.6738, 640: 1336.0081, 704: 1219.7976, 768: 1119.3484, 832: 1030.5255, 896: 949.5354000000001, 960: 883.6967999999999, 1024: 833.8498, 1088: 782.1752, 1152: 738.7052, 1216: 702.24, 1280: 666.9503, 1344: 634.9852000000001, 1408: 605.5608000000001, 1472: 578.5933, 1536: 553.5780000000001, 1600: 531.9501, 1664: 528.2779, 1728: 509.11250000000007, 1792: 478.73449999999997, 1856: 482.9731999999999, 1920: 482.23870000000005, 1984: 480.01300000000003, 2048: 467.88990000000007, 2112: 474.2638999999999, 2176: 474.24989999999997, 2240: 464.3179, 2304: 472.7857, 2368: 480.3647, 2432: 470.5216, 2496: 471.72280000000006, 2560: 475.35470000000004, 2624: 471.7776, 2688: 473.9024, 2752: 473.36300000000006, 2816: 479.9838, 2880: 478.5181, 2944: 479.01469999999995, 3008: 475.2245}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "App6_G.nodes[1]['perf_profile'] = f1_pf\n",
    "App6_G.nodes[2]['perf_profile'] = f2_pf\n",
    "App6_G.nodes[3]['perf_profile'] = f3_pf\n",
    "App6_G.nodes[4]['perf_profile'] = f4_pf\n",
    "App6_G.nodes[5]['perf_profile'] = f5_pf\n",
    "App6_G.nodes[6]['perf_profile'] = f6_pf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc-hr-collapsed": true
   },
   "source": [
    "#### Method 2: Define by querying logs from the FaaS platform (AWS in this work)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "import boto3\n",
    "from datetime import datetime, timezone\n",
    "import time\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "logclient = boto3.client('logs')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Functions for parsing Logs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lambda_report_log_to_dict(log):\n",
    "    res={}\n",
    "    lis=[item.split(': ') for item in log.split('\\t')]\n",
    "    res['RequestId']=lis[0][1]\n",
    "    res['Duration']=float(lis[1][1].split(' ')[0])\n",
    "    res['Billed Duration']=int(lis[2][1].split(' ')[0])\n",
    "    res['Memory Size']=int(lis[3][1].split(' ')[0])\n",
    "    res['Max Memory Used']=int(lis[4][1].split(' ')[0])\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "startTime=int(datetime.timestamp(datetime(year=2020,month=1,day=14,hour=22,minute=44,second=0,tzinfo=timezone.utc))) # Log filter start time\n",
    "endTime=int(datetime.timestamp(datetime(year=2020,month=1,day=15,hour=14,minute=30,second=0,tzinfo=timezone.utc))) # Log filter end time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Query Logs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "query_f1 = logclient.start_query(\n",
    "    logGroupName='/aws/lambda/{}'.format('ServerlessAppPerfOpt_f1'), # Function name\n",
    "    queryString=\"fields @timestamp, @message| filter @message like 'REPORT'| sort @timestamp desc\",\n",
    "    startTime=startTime,\n",
    "    endTime=endTime,\n",
    "    limit=10000\n",
    ")\n",
    "time.sleep(1)\n",
    "query_f2 = logclient.start_query(\n",
    "    logGroupName='/aws/lambda/{}'.format('ServerlessAppPerfOpt_f2'), # Function name\n",
    "    queryString=\"fields @timestamp, @message| filter @message like 'REPORT'| sort @timestamp desc\",\n",
    "    startTime=startTime,\n",
    "    endTime=endTime,\n",
    "    limit=10000\n",
    ")\n",
    "time.sleep(1)\n",
    "query_f3 = logclient.start_query(\n",
    "    logGroupName='/aws/lambda/{}'.format('ServerlessAppPerfOpt_f3'), # Function name\n",
    "    queryString=\"fields @timestamp, @message| filter @message like 'REPORT'| sort @timestamp desc\",\n",
    "    startTime=startTime,\n",
    "    endTime=endTime,\n",
    "    limit=10000\n",
    ")\n",
    "time.sleep(1)\n",
    "query_f4 = logclient.start_query(\n",
    "    logGroupName='/aws/lambda/{}'.format('ServerlessAppPerfOpt_f4'), # Function name\n",
    "    queryString=\"fields @timestamp, @message| filter @message like 'REPORT'| sort @timestamp desc\",\n",
    "    startTime=startTime,\n",
    "    endTime=endTime,\n",
    "    limit=10000\n",
    ")\n",
    "time.sleep(1)\n",
    "query_f5 = logclient.start_query(\n",
    "    logGroupName='/aws/lambda/{}'.format('ServerlessAppPerfOpt_f5'), # Function name\n",
    "    queryString=\"fields @timestamp, @message| filter @message like 'REPORT'| sort @timestamp desc\",\n",
    "    startTime=int(datetime.timestamp(datetime(year=2020,month=1,day=16,hour=21,minute=27,second=0,tzinfo=timezone.utc))),\n",
    "    endTime=int(datetime.timestamp(datetime(year=2020,month=1,day=17,hour=11,minute=50,second=0,tzinfo=timezone.utc))),\n",
    "    limit=10000\n",
    ")\n",
    "time.sleep(1)\n",
    "query_f6 = logclient.start_query(\n",
    "    logGroupName='/aws/lambda/{}'.format('ServerlessAppPerfOpt_f6'), # Function name\n",
    "    queryString=\"fields @timestamp, @message| filter @message like 'REPORT'| sort @timestamp desc\",\n",
    "    startTime=int(datetime.timestamp(datetime(year=2020,month=1,day=16,hour=21,minute=27,second=0,tzinfo=timezone.utc))),\n",
    "    endTime=int(datetime.timestamp(datetime(year=2020,month=1,day=17,hour=11,minute=50,second=0,tzinfo=timezone.utc))),\n",
    "    limit=10000\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "query_results_f1 = logclient.get_query_results(\n",
    "    queryId=query_f1['queryId']\n",
    ")\n",
    "time.sleep(1)\n",
    "query_results_f2 = logclient.get_query_results(\n",
    "    queryId=query_f2['queryId']\n",
    ")\n",
    "time.sleep(1)\n",
    "query_results_f3 = logclient.get_query_results(\n",
    "    queryId=query_f3['queryId']\n",
    ")\n",
    "time.sleep(1)\n",
    "query_results_f4 = logclient.get_query_results(\n",
    "    queryId=query_f4['queryId']\n",
    ")\n",
    "time.sleep(1)\n",
    "query_results_f5 = logclient.get_query_results(\n",
    "    queryId=query_f5['queryId']\n",
    ")\n",
    "time.sleep(1)\n",
    "query_results_f6 = logclient.get_query_results(\n",
    "    queryId=query_f6['queryId']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "for item in f1_log_list:\n",
    "    item['Function']='f1'\n",
    "for item in f2_log_list:\n",
    "    item['Function']='f2'\n",
    "for item in f3_log_list:\n",
    "    item['Function']='f3'\n",
    "for item in f4_log_list:\n",
    "    item['Function']='f4'\n",
    "for item in f5_log_list:\n",
    "    item['Function']='f5'\n",
    "for item in f6_log_list:\n",
    "    item['Function']='f6'\n",
    "App_Lambda_Logs=pd.DataFrame(f1_log_list).append(pd.DataFrame(f2_log_list)).append(pd.DataFrame(f3_log_list)).append(pd.DataFrame(f4_log_list)).append(pd.DataFrame(f5_log_list)).append(pd.DataFrame(f6_log_list))\n",
    "App_Lambda_Logs.index=range(App_Lambda_Logs.shape[0])\n",
    "App_Lambda_Logs=App_Lambda_Logs[['Function', 'Memory Size', 'Max Memory Used', 'Duration', 'Billed Duration', 'RequestId']]\n",
    "App_Lambda_Logs.to_csv('App_Lambda_Logs.csv',index=False)\n",
    "App_Lambda_Logs = pd.read_csv('App_Lambda_Logs.csv', error_bad_lines=False, warn_bad_lines=False,low_memory=False)\n",
    "App_Lambda_Logs.columns = ['Function', 'Memory_Size', 'Max_Memory_Used', 'Duration', 'Billed_Duration', 'RequestId']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "f1_log_list=[lambda_report_log_to_dict(item [1]['value']) for item in query_results_f1['results']]\n",
    "f2_log_list=[lambda_report_log_to_dict(item [1]['value']) for item in query_results_f2['results']]\n",
    "f3_log_list=[lambda_report_log_to_dict(item [1]['value']) for item in query_results_f3['results']]\n",
    "f4_log_list=[lambda_report_log_to_dict(item [1]['value']) for item in query_results_f4['results']]\n",
    "f5_log_list=[lambda_report_log_to_dict(item [1]['value']) for item in query_results_f5['results']]\n",
    "f6_log_list=[lambda_report_log_to_dict(item [1]['value']) for item in query_results_f6['results']]\n",
    "# MOpt for all functions\n",
    "available_mem_list=[128, 192, 256, 320, 384, 448, 512, 576, 640, 704, 768, 832, 896, 960, 1024, 1088, 1152, 1216, 1280, 1344, 1408, 1472, 1536, 1600, 1664, 1728, 1792, 1856, 1920, 1984, 2048, 2112, 2176, 2240, 2304, 2368, 2432, 2496, 2560, 2624, 2688, 2752, 2816, 2880, 2944, 3008]\n",
    "f1_pf = [App_Lambda_Logs.query(\"Function == {} and Memory_Size == {}\".format(\"'f1'\",mem))['Duration'].mean() for mem in available_mem_list]\n",
    "f2_pf = [App_Lambda_Logs.query(\"Function == {} and Memory_Size == {}\".format(\"'f2'\",mem))['Duration'].mean() for mem in available_mem_list]\n",
    "f3_pf = [App_Lambda_Logs.query(\"Function == {} and Memory_Size == {}\".format(\"'f3'\",mem))['Duration'].mean() for mem in available_mem_list]\n",
    "f4_pf = [App_Lambda_Logs.query(\"Function == {} and Memory_Size == {}\".format(\"'f4'\",mem))['Duration'].mean() for mem in available_mem_list]\n",
    "f5_pf = [App_Lambda_Logs.query(\"Function == {} and Memory_Size == {}\".format(\"'f5'\",mem))['Duration'].mean() for mem in available_mem_list]\n",
    "f6_pf = [App_Lambda_Logs.query(\"Function == {} and Memory_Size == {}\".format(\"'f6'\",mem))['Duration'].mean() for mem in available_mem_list]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "App6_G.nodes[1]['perf_profile'] = f1_pf\n",
    "App6_G.nodes[2]['perf_profile'] = f2_pf\n",
    "App6_G.nodes[3]['perf_profile'] = f3_pf\n",
    "App6_G.nodes[4]['perf_profile'] = f4_pf\n",
    "App6_G.nodes[5]['perf_profile'] = f5_pf\n",
    "App6_G.nodes[6]['perf_profile'] = f6_pf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Performance profile curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Duration in ms')"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(8,8))\n",
    "ax=plt.subplot(111)\n",
    "ax.grid()\n",
    "ax.set_xlim(128,3008)\n",
    "ax.plot(available_mem_list, f1_duration, marker='o', label='f1') \n",
    "ax.plot(available_mem_list, f2_duration, marker='o', label='f2') \n",
    "ax.plot(available_mem_list, f3_duration, marker='o', label='f3') \n",
    "ax.plot(available_mem_list, f4_duration, marker='o', label='f4') \n",
    "ax.plot(available_mem_list, f5_duration, marker='o', label='f5') \n",
    "ax.plot(available_mem_list, f6_duration, marker='o', label='f6') \n",
    "ax.legend()\n",
    "ax.set_xlabel('Memory in MB')\n",
    "ax.set_ylabel('Duration in ms')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Use the PRCP algorithm to solve the Best Performance under the Budget Constraint (BPBC) problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Without BCR\n",
      "Optimized Memory Configuration: {1: 1088, 2: 1216, 3: 1024, 4: 2688, 5: 960, 6: 2240}\n",
      "Average end-to-end response time: 2876.492557142856\n",
      "Average Cost: 97.68528571428573\n",
      "PRCP_BPBC Optimization Completed.\n",
      "----------------\n",
      "BCR RT/M greedy strategy, BCR threshold is 0.2\n",
      "Optimized Memory Configuration: {1: 1472, 2: 1216, 3: 1024, 4: 2688, 5: 960, 6: 2048}\n",
      "Average end-to-end response time: 2834.5468428571426\n",
      "Average Cost: 99.09628571428571\n",
      "PRCP_BPBC Optimization Completed.\n",
      "----------------\n",
      "BCR ERT/C greedy strategy, BCR threshold is 0.2\n",
      "Optimized Memory Configuration: {1: 1088, 2: 768, 3: 1600, 4: 2688, 5: 1024, 6: 2240}\n",
      "Average end-to-end response time: 3070.586499999999\n",
      "Average Cost: 98.2782\n",
      "PRCP_BPBC Optimization Completed.\n",
      "----------------\n",
      "BCR MAX greedy strategy, BCR threshold is 0.2\n",
      "Optimized Memory Configuration: {1: 1472, 2: 768, 3: 1600, 4: 2688, 5: 1024, 6: 2048}\n",
      "Average end-to-end response time: 3028.6407857142854\n",
      "Average Cost: 99.6892\n",
      "PRCP_BPBC Optimization Completed.\n",
      "----------------\n"
     ]
    }
   ],
   "source": [
    "App = ServerlessAppWorkflow(G=App6_G.copy(), delayType='SFN')\n",
    "optimizer = PerfOpt(App, generate_perf_profile=False)\n",
    "# Budget constraint is 100 US dollars\n",
    "print('Without BCR')\n",
    "res1 = optimizer.PRCPG_BPBC(100, BCR=False) # Without BCR\n",
    "print('----------------')\n",
    "print('BCR RT/M greedy strategy, BCR threshold is 0.2')\n",
    "res2 = optimizer.PRCPG_BPBC(100, BCR=True, BCRtype='RT/M', BCRthreshold=0.2) # BCR RT/M greedy strategy, BCR threshold is 0.2\n",
    "print('----------------')\n",
    "print('BCR ERT/C greedy strategy, BCR threshold is 0.2')\n",
    "res3 = optimizer.PRCPG_BPBC(100, BCR=True, BCRtype='ERT/C', BCRthreshold=0.2) # BCR ERT/C greedy strategy, BCR threshold is 0.2\n",
    "print('----------------')\n",
    "print('BCR MAX greedy strategy, BCR threshold is 0.2')\n",
    "res4 = optimizer.PRCPG_BPBC(100, BCR=True, BCRtype='MAX') # BCR MAX greedy strategy, BCR threshold is 0.2\n",
    "print('----------------')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Use the PRCP algorithm to solve the Best Cost under the Performance Constraint (BCPC) problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Without BCR\n",
      "Optimized Memory Configuration: {1: 832, 2: 896, 3: 768, 4: 320, 5: 384, 6: 960}\n",
      "Average end-to-end response time: 6319.304634285715\n",
      "Average Cost: 60.41328571428571\n",
      "PRCPG_BCPC Optimization Completed.\n",
      "----------------\n",
      "BCR M/RT greedy strategy, BCR threshold is 0.2\n",
      "Optimized Memory Configuration: {1: 832, 2: 896, 3: 768, 4: 320, 5: 960, 6: 960}\n",
      "Average end-to-end response time: 6297.260771428572\n",
      "Average Cost: 60.41351428571428\n",
      "PRCPG_BCPC Optimization Completed.\n",
      "----------------\n",
      "BCR C/ERT greedy strategy, BCR threshold is 0.2\n",
      "Optimized Memory Configuration: {1: 832, 2: 896, 3: 768, 4: 320, 5: 960, 6: 960}\n",
      "Average end-to-end response time: 6297.260771428572\n",
      "Average Cost: 60.41351428571428\n",
      "PRCPG_BCPC Optimization Completed.\n",
      "----------------\n",
      "BCR MAX greedy strategy, BCR threshold is 0.2\n",
      "Optimized Memory Configuration: {1: 832, 2: 896, 3: 768, 4: 320, 5: 384, 6: 960}\n",
      "Average end-to-end response time: 6319.304634285715\n",
      "Average Cost: 60.41328571428571\n",
      "PRCPG_BCPC Optimization Completed.\n",
      "----------------\n"
     ]
    }
   ],
   "source": [
    "App = ServerlessAppWorkflow(G=App6_G.copy(), delayType='SFN')\n",
    "optimizer = PerfOpt(App, generate_perf_profile=False)\n",
    "# Performance constraint is 6400 ms\n",
    "print('Without BCR')\n",
    "res5 = optimizer.PRCPG_BCPC(6400, BCR=False) # Without BCR\n",
    "print('----------------')\n",
    "print('BCR M/RT greedy strategy, BCR threshold is 0.2')\n",
    "res6 = optimizer.PRCPG_BCPC(6400, BCR=True, BCRtype='M/RT', BCRthreshold=0.2) # BCR M/RT greedy strategy, BCR threshold is 0.2\n",
    "print('----------------')\n",
    "print('BCR C/ERT greedy strategy, BCR threshold is 0.2')\n",
    "res7 = optimizer.PRCPG_BCPC(6400, BCR=True, BCRtype='C/ERT', BCRthreshold=0.2) # BCR C/ERT greedy strategy, BCR threshold is 0.2\n",
    "print('----------------')\n",
    "print('BCR MAX greedy strategy, BCR threshold is 0.2')\n",
    "res8 = optimizer.PRCPG_BCPC(6400, BCR=True, BCRtype='MAX') # BCR MAX greedy strategy, BCR threshold is 0.2\n",
    "print('----------------')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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