{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "int: N_CLOUD_REGIONS;  % number of cloud regions\n",
      "% set of 1..N_CLOUD_REGIONS: C_REGIONS;\n",
      "\n",
      "int: N_ATTRIBUTES; %  number of capability related attributes\n",
      "% set of 1..N_ATTRIBUTES: ATTRIBS;\n",
      "array[1..N_ATTRIBUTES] of float: w_attributes; % weights of each attribute\n",
      "\n",
      "int: N_UTILIZATION_METRICS; % number of dynamic capacity metrics of interest\n",
      "% set of 1..N_UTILIZATION_METRICS: U_METRICS;\n",
      "array[1..N_UTILIZATION_METRICS] of float: w_metrics; % weights of each capacity metric\n",
      "\n",
      "int: cust_type;  % customer type, 0 = regular, 1 = silver, 2 = gold\n",
      "int: N_VMS; % number of VMs in VNF\n",
      "int: N_CAPACITY_METRICS; % number of metrics for cloud region capacity check\n",
      "\n",
      "float: C_ALLOC_THRESHOLD; % allocation threshold for cloud\n",
      "float: CUST_ALLOC_THRESHOLD; % allocation threshold for customer in cloud\n",
      "float: AVG_CPU_UTILIZATION_THRESHOLD;\n",
      "float: PEAK_CPU_UTILIZATION_THRESHOLD;\n",
      "\n",
      "enum CUST_TYPES = { STANDARD, SILVER, GOLD };\n",
      "enum ATTRIBUTES = { CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };\n",
      "enum METRICS = { AVG_CPU_UTILIZATION, PEAK_CPU_UTILIZATION };\n",
      "enum CLOUD_REGION_CAPACITY = {CPU_CLOUD, MEMORY_CLOUD};\n",
      "enum VNFS_TYPES = { VDNS, VFW };\n",
      "int: N_VNFS;\n",
      "\n",
      "% set of 1..N_CAPACITY_METRICS: CAP_METRICS;\n",
      "\n",
      "% whether a cloud region has the corresponding capability -- data will be customer specific\n",
      "% array[1..N_CLOUD_REGIONS, 1..N_CLOUD_REGIONS] of float: c_dist;\n",
      "array[1..N_CLOUD_REGIONS, 1..N_ATTRIBUTES] of int: capabilities;\n",
      "array[1..N_CLOUD_REGIONS, 1..N_UTILIZATION_METRICS] of float: cpu_utilization;  % how much capacity is already dynamically utilized     (fraction)\n",
      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: c_alloc_capacity; % how much percent is already allocated in the cloud\n",
      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: c_total_capacity;  % total cloud capacity\n",
      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: c_alloc_capacity_norm;\n",
      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: cust_alloc_capacity; % how much percent is already allocated in the cloud for the customer\n",
      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: cust_total_capacity; % total cloud capacity for customer\n",
      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: cust_alloc_capacity_norm;\n",
      "\n",
      "% VM requirements for each type of capacity (vm cpu, memory, etc.)\n",
      "% TODO: establish a standard for units (MB RAM, GB disk, N virtual cores, etc.)\n",
      "array[1..N_VMS, 1..N_CAPACITY_METRICS] of int: vm_reqs;\n",
      "array[1..N_CAPACITY_METRICS] of int: vm_reqs_sums = [ sum(k in 1..N_VMS) (vm_reqs[k,j]) | j in 1..N_CAPACITY_METRICS ];\n",
      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: vm_reqs_sums_norm;\n",
      "%forall(i in 1..N_CLOUD_REGIONS, j in 1..N_CAPACITY_METRICS) (\n",
      "%  vm_reqs_sums_norm[i, j] = vm_reqs_sums[j]/c_total_capacity[i, j]\n",
      "%)\n",
      "%array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: vm_reqs_sums_norm = [ ((vm_reqs_sums[j]/c_total_capacity[i,j]) | j in 1..N_CAPACITY_METRICS) | i in 1..N_CLOUD_REGIONS ];\n",
      "\n",
      "array[1..N_VNFS] of var int: s_regions;  % target cloud regions (solution to the problem)\n",
      "\n",
      "% custom constraints\n",
      "constraint forall (s in s_regions) (\n",
      "    cpu_utilization[s, AVG_CPU_UTILIZATION] <= AVG_CPU_UTILIZATION_THRESHOLD /\\    % hard constraint: need some capacity available\n",
      "    cpu_utilization[s, PEAK_CPU_UTILIZATION] <= PEAK_CPU_UTILIZATION_THRESHOLD /\\  % hard constraint: need some capacity available\n",
      "    cust_alloc_capacity[s, CPU_CLOUD] <= (CUST_ALLOC_THRESHOLD*(cust_total_capacity[s, CPU_CLOUD])) - (vm_reqs_sums[CPU_CLOUD]) /\\\n",
      "    cust_alloc_capacity[s, MEMORY_CLOUD] <= (CUST_ALLOC_THRESHOLD*(cust_total_capacity[s, MEMORY_CLOUD])) - (vm_reqs_sums[MEMORY_CLOUD]) /\\\n",
      "    c_alloc_capacity[s, CPU_CLOUD] <= (C_ALLOC_THRESHOLD*(c_total_capacity[s, CPU_CLOUD])) - (vm_reqs_sums[CPU_CLOUD]) /\\\n",
      "    c_alloc_capacity[s, MEMORY_CLOUD] <= (C_ALLOC_THRESHOLD*(c_total_capacity[s, MEMORY_CLOUD])) - (vm_reqs_sums[MEMORY_CLOUD])\n",
      ");\n",
      "\n",
      "% specific constraints based on the VNF\n",
      "constraint capabilities[s_regions[VDNS], CORE_DC] = 1;  % hard constraint for vDNS: has to be placed in CORE DC\n",
      "\n",
      "% custom soft constraint for gold customers -- give a large weight to direct connection\n",
      "var float: additional_obj = sum(s in s_regions) (bool2int(cust_type = GOLD) * capabilities[s, MIN_GUARANTEE] * 1000);\n",
      "\n",
      "% TODO: global constraints (such as data validation)\n",
      "\n",
      "% Objective for utilization\n",
      "var float: obj_c_capacity = sum(k in 1..N_CAPACITY_METRICS, s in s_regions) (\n",
      "\t\t  (1 - c_alloc_capacity_norm[s, k] - vm_reqs_sums_norm[s, k]) +\n",
      "                  (1 - cust_alloc_capacity_norm[s, k] - vm_reqs_sums_norm[s, k]));\n",
      "\n",
      "% Objective for utilization\n",
      "var float: obj_utilization = sum(k in 1..N_UTILIZATION_METRICS, s in s_regions) ( w_metrics[k] * (1 - cpu_utilization[s, k]) );\n",
      "\n",
      "% Objective for capabilities\n",
      "var float: obj_capabilities = sum(k in 1..N_ATTRIBUTES, s in s_regions) ( w_attributes[k] * capabilities[s, k] );\n",
      "\n",
      "% Overall objective function\n",
      "var float: obj = obj_c_capacity + obj_utilization + obj_capabilities + additional_obj;\n",
      "\n",
      "solve maximize obj;\n",
      "\n",
      "output [ \"Solution: \\nCloud Region for vDNS = \", show(s_regions[VDNS]) ] \n",
      "++ [ if N_VNFS = 2 then \"\\nCloud Region for vFW = \" ++ show(s_regions[VFW]) ++ \"\\n\" else \"\\n\" endif ]\n",
      "++ [ \"Objective function value: \", show(obj), \"\\n\", \"Customer type: \", show(cust_type), \"\\n\"];\n"
     ]
    }
   ],
   "source": [
    "!cat placement.mzn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "% enum CUST_TYPES = { STANDARD, SILVER, GOLD };\n",
      "% enum ATTRIBUTES = { CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };\n",
      "% enum METRICS = { AVG_CPU_UTILIZATION, PEAK_CPU_UTILIZATION };\n",
      "% enum CLOUD_REGION_CAPACITY = {CPU_CLOUD, MEMORY_CLOUD};\n",
      "\n",
      "N_CLOUD_REGIONS = 3;  % e-dc-1, core-dc-1, core-dc-2\n",
      "N_ATTRIBUTES = 4;\n",
      "N_UTILIZATION_METRICS = 2;\n",
      "N_CAPACITY_METRICS = 2;\n",
      "N_VMS = 3;\n",
      "C_ALLOC_THRESHOLD = 0.65;\n",
      "CUST_ALLOC_THRESHOLD = 0.95;\n",
      "AVG_CPU_UTILIZATION_THRESHOLD = 0.7;\n",
      "PEAK_CPU_UTILIZATION_THRESHOLD = 0.95;\n",
      "\n",
      "cust_type = GOLD;\n",
      "N_VNFS = 1;\n",
      "\n",
      "w_metrics = [0.9, 0.1];\n",
      "w_attributes = [0.1, 0.9, 0.05, 0.05]; \n",
      "\n",
      "capabilities = [| 0, 1, 1, 1\n",
      "                | 1, 0, 1, 1\n",
      "                | 1, 1, 0, 1 |];\n",
      "\n",
      "cpu_utilization = [| 0.05, 0.9\n",
      "                   | 0.1, 0.5\n",
      "                   | 0.6, 0.8 |];\n",
      "\n",
      "c_alloc_capacity = [| 600, 1200\n",
      "                    | 1200, 2400\n",
      "                    | 2400, 4800 |];\n",
      "\n",
      "c_total_capacity = [| 1000, 2000\n",
      "                    | 2000, 4000\n",
      "                    | 4000, 8000 |];\n",
      "\n",
      "c_alloc_capacity_norm = [| 0.6, 0.6\n",
      "                         | 0.6, 0.6\n",
      "                         | 0.6, 0.6 |];\n",
      "\n",
      "cust_alloc_capacity = [| 60, 120\n",
      "                       | 120, 240\n",
      "                       | 240, 480 |];\n",
      "\n",
      "cust_total_capacity = [| 100, 200\n",
      "                       | 200, 400\n",
      "                       | 400, 800 |];\n",
      "\n",
      "cust_alloc_capacity_norm = [| 0.6, 0.6\n",
      "                            | 0.6, 0.6\n",
      "                            | 0.6, 0.6 |];\n",
      "\n",
      "vm_reqs = [| 1, 4\n",
      "           | 2, 8\n",
      "           | 4, 16 |];\n",
      "\n",
      "%vm_reqs_sums = [ 14, 56 ];\n",
      "\n",
      "vm_reqs_sums_norm = [| 0.007, 0.014\n",
      "                     | 0.0035, 0.007\n",
      "                     | 0.00175, 0.0035 |];\n"
     ]
    }
   ],
   "source": [
    "!cat gold.dzn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23c23\n",
      "<                 | 1, 0, 1, 1\n",
      "---\n",
      ">                 | 1, 0, 0, 1\n"
     ]
    }
   ],
   "source": [
    "!diff gold.dzn gold-no-min-guarantee.dzn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23c23\n",
      "<                 | 1, 0, 1, 1\n",
      "---\n",
      ">                 | 1, 0, 0, 1\n"
     ]
    }
   ],
   "source": [
    "!diff gold.dzn gold-no-min-guarantee.dzn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "% enum CUST_TYPES = { STANDARD, SILVER, GOLD };\n",
      "% enum ATTRIBUTES = { CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };\n",
      "% enum METRICS = { AVG_CPU_UTILIZATION, PEAK_CPU_UTILIZATION };\n",
      "% enum CLOUD_REGION_CAPACITY = {CPU_CLOUD, MEMORY_CLOUD};\n",
      "\n",
      "N_CLOUD_REGIONS = 3;  % e-dc-1, core-dc-1, core-dc-2\n",
      "N_ATTRIBUTES = 4;\n",
      "N_UTILIZATION_METRICS = 2;\n",
      "N_CAPACITY_METRICS = 2;\n",
      "N_VMS = 3;\n",
      "C_ALLOC_THRESHOLD = 0.65;\n",
      "CUST_ALLOC_THRESHOLD = 0.95;\n",
      "AVG_CPU_UTILIZATION_THRESHOLD = 0.7;\n",
      "PEAK_CPU_UTILIZATION_THRESHOLD = 0.95;\n",
      "\n",
      "cust_type = SILVER;\n",
      "N_VNFS = 2;\n",
      "\n",
      "w_metrics = [0.9, 0.1];\n",
      "w_attributes = [0.1, 0.9, 0.05, 0.05]; \n",
      "\n",
      "capabilities = [| 0, 1, 1, 1\n",
      "                | 1, 0, 1, 1\n",
      "                | 1, 1, 0, 1 |];\n",
      "\n",
      "cpu_utilization = [| 0.05, 0.9\n",
      "                   | 0.1, 0.5\n",
      "                   | 0.6, 0.8 |];\n",
      "\n",
      "c_alloc_capacity = [| 600, 1200\n",
      "                    | 1200, 2400\n",
      "                    | 2400, 4800 |];\n",
      "\n",
      "c_total_capacity = [| 1000, 2000\n",
      "                    | 2000, 4000\n",
      "                    | 4000, 8000 |];\n",
      "\n",
      "c_alloc_capacity_norm = [| 0.6, 0.6\n",
      "                         | 0.6, 0.6\n",
      "                         | 0.6, 0.6 |];\n",
      "\n",
      "cust_alloc_capacity = [| 60, 120\n",
      "                       | 120, 240\n",
      "                       | 240, 480 |];\n",
      "\n",
      "cust_total_capacity = [| 100, 200\n",
      "                       | 200, 400\n",
      "                       | 400, 800 |];\n",
      "\n",
      "cust_alloc_capacity_norm = [| 0.6, 0.6\n",
      "                            | 0.6, 0.6\n",
      "                            | 0.6, 0.6 |];\n",
      "\n",
      "vm_reqs = [| 1, 4\n",
      "           | 2, 8\n",
      "           | 4, 16 |];\n",
      "\n",
      "%vm_reqs_sums = [ 14, 56 ];\n",
      "\n",
      "vm_reqs_sums_norm = [| 0.007, 0.014\n",
      "                     | 0.0035, 0.007\n",
      "                     | 0.00175, 0.0035 |];\n"
     ]
    }
   ],
   "source": [
    "!cat silver.dzn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "26c26\n",
      "< cpu_utilization = [| 0.05, 0.9\n",
      "---\n",
      "> cpu_utilization = [| 0.05, 0.96\n"
     ]
    }
   ],
   "source": [
    "!diff silver.dzn silver-high-edge-load.dzn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution: \n",
      "Cloud Region for vDNS = 2\n",
      "Objective function value: 1002.639\n",
      "Customer type: 3\n",
      "----------\n",
      "==========\n"
     ]
    }
   ],
   "source": [
    "!mzn-gecode -a placement.mzn gold.dzn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution: \n",
      "Cloud Region for vDNS = 2\n",
      "Objective function value: 2.589\n",
      "Customer type: 3\n",
      "----------\n",
      "Solution: \n",
      "Cloud Region for vDNS = 3\n",
      "Objective function value: 3.0195\n",
      "Customer type: 3\n",
      "----------\n",
      "==========\n"
     ]
    }
   ],
   "source": [
    "!mzn-gecode -a placement.mzn gold-no-min-guarantee.dzn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution: \n",
      "Cloud Region for vDNS = 2\n",
      "Cloud Region for vFW = 1\n",
      "Objective function value: 6.062\n",
      "Customer type: 2\n",
      "----------\n",
      "Solution: \n",
      "Cloud Region for vDNS = 3\n",
      "Cloud Region for vFW = 1\n",
      "Objective function value: 6.4425\n",
      "Customer type: 2\n",
      "----------\n",
      "==========\n"
     ]
    }
   ],
   "source": [
    "!mzn-gecode -a placement.mzn silver.dzn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution: \n",
      "Cloud Region for vDNS = 2\n",
      "Cloud Region for vFW = 2\n",
      "Objective function value: 5.278\n",
      "Customer type: 2\n",
      "----------\n",
      "Solution: \n",
      "Cloud Region for vDNS = 3\n",
      "Cloud Region for vFW = 2\n",
      "Objective function value: 5.6585\n",
      "Customer type: 2\n",
      "----------\n",
      "Solution: \n",
      "Cloud Region for vDNS = 3\n",
      "Cloud Region for vFW = 3\n",
      "Objective function value: 6.039\n",
      "Customer type: 2\n",
      "----------\n",
      "==========\n"
     ]
    }
   ],
   "source": [
    "!mzn-gecode -a placement.mzn silver-high-edge-load.dzn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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