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‎examples/.ipynb_checkpoints/Ross_Simulation_7.7_A_repair_problem-checkpoint.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# A Repair Problem\n",
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"Ross, Simulation 5th edition, Section 7.7, p. 124-126"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Description"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"A system needs $n$ working machines to be operational. To guard against machine breakdown, additional machines are kept available as spares. Whenever a machine breaks down it is immediately replaced by a spare and is itself sent to the repair facility, which consists of a single repairperson who repairs failed machines one at a time. Once a failed machine has been repaired it becomes available as a spare to be used when the need arises. All repair times are independent random variables having the common distribution function $G$. Each time a machine is put into use the amount of time it functions before breaking down is a random variable, independent of the past, having distribution function $F$.\n",
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"\n",
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"The system is said to “crash” when a machine fails and no spares are available. Assuming that there are initially $n + s$ functional machines of which $n$ are put in use and $s$ are kept as spares, we are interested in simulating this system so as to approximate $E[T]$, where $T$ is the time at which the system crashes."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Install packages"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"Pkg.update()\n",
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"Pkg.add(\"Distributions\")\n",
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"Pkg.add(\"SimJulia\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Use Distributions.jl and SimJulia.jl"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"using Distributions\n",
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"using ResumableFunctions\n",
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"using SimJulia"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Define constants"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"const RUNS = 5\n",
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"const N = 10\n",
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"const S = 3\n",
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"const SEED = 150\n",
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"const LAMBDA = 100\n",
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"const MU = 1;"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Define the behaviour of a machine"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"ename": "LoadError",
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"evalue": "\u001b[91mMethodError: no method matching start(::Void)\u001b[0m\nClosest candidates are:\n start(\u001b[91m::SimpleVector\u001b[39m) at essentials.jl:258\n start(\u001b[91m::Base.MethodList\u001b[39m) at reflection.jl:560\n start(\u001b[91m::ExponentialBackOff\u001b[39m) at error.jl:107\n ...\u001b[39m",
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"output_type": "error",
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"traceback": [
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"\u001b[91mMethodError: no method matching start(::Void)\u001b[0m\nClosest candidates are:\n start(\u001b[91m::SimpleVector\u001b[39m) at essentials.jl:258\n start(\u001b[91m::Base.MethodList\u001b[39m) at reflection.jl:560\n start(\u001b[91m::ExponentialBackOff\u001b[39m) at error.jl:107\n ...\u001b[39m",
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""
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]
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}
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],
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"source": [
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"@resumable function machine(sim::Simulation, repair_facility::Resource, spares::Store{Coroutine})\n",
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" dist_work = Exponential(LAMBDA)\n",
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" dist_repair = Exponential(MU)\n",
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" while true\n",
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" try \n",
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" @yield Timeout(sim, Inf)\n",
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" catch\n",
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" end\n",
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" #println(\"At time $(now(sim)): $(active_process(sim)) starts working.\")\n",
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" @yield Timeout(sim, rand(dist_work))\n",
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" #println(\"At time $(now(sim)): $(active_process(sim)) stops working.\")\n",
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" get_spare = Get(spares)\n",
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" @yield get_spare | Timeout(sim, 0.0)\n",
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" if state(get_spare) != SimJulia.idle\n",
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" interrupt(value(get_spare))\n",
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" else\n",
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" throw(SimJulia.StopSimulation(\"No more spares!\"))\n",
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" end\n",
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" @yield Request(repair_facility)\n",
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" #println(\"At time $(now(sim)): $(active_process(sim)) repair starts.\")\n",
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" @yield Timeout(sim, rand(dist_repair))\n",
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" @yield Release(repair_facility)\n",
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" #println(\"At time $(now(sim)): $(active_process(sim)) is repaired.\")\n",
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" @yield Put(spares, active_process(sim))\n",
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" end\n",
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"end\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Startup procedure"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"start_sim (generic function with 1 method)"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"@resumable function start_sim(sim::Simulation, repair_facility::Resource, spares::Store{Coroutine})\n",
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" procs = Coroutine[]\n",
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" for i=1:N\n",
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" push!(procs, @coroutine machine(sim, repair_facility, spares))\n",
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" end\n",
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" @yield Timeout(sim, 0.0)\n",
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" for proc in procs\n",
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" interrupt(proc)\n",
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" end\n",
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" for i=1:S\n",
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" @yield Put(spares, @coroutine machine(sim, repair_facility, spares))\n",
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" end\n",
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"end"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## One simulation run"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"sim_repair (generic function with 1 method)"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"function sim_repair()\n",
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" sim = Simulation()\n",
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" repair_facility = Resource(sim)\n",
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" spares = Store(Coroutine, sim)\n",
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" @coroutine start_sim(sim, repair_facility, spares)\n",
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" msg = run(sim)\n",
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" stop_time = now(sim)\n",
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" println(\"At time $stop_time: $msg\")\n",
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" stop_time\n",
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"end"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Multiple simulations"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"ename": "LoadError",
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"evalue": "\u001b[91mUndefVarError: machine not defined\u001b[39m",
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"output_type": "error",
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"traceback": [
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"\u001b[91mUndefVarError: machine not defined\u001b[39m",
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"",
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"Stacktrace:",
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" [1] \u001b[1mmacro expansion\u001b[22m\u001b[22m at \u001b[1m/home/juser/.julia/v0.6/ResumableFunctions/src/transforms.jl:16\u001b[22m\u001b[22m [inlined]",
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" [2] \u001b[1mmacro expansion\u001b[22m\u001b[22m at \u001b[1m./In[4]:14\u001b[22m\u001b[22m [inlined]",
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" [3] \u001b[1mmacro expansion\u001b[22m\u001b[22m at \u001b[1m/home/juser/.julia/v0.6/ResumableFunctions/src/macro.jl:66\u001b[22m\u001b[22m [inlined]",
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" [4] \u001b[1m(::##660)\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Void\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/home/juser/.julia/v0.6/ResumableFunctions/src/macrotoolutils.jl:99\u001b[22m\u001b[22m",
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" [5] \u001b[1mexecute\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::SimJulia.Timeout, ::SimJulia.Coroutine\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/home/juser/.julia/v0.6/SimJulia/src/coroutines.jl:27\u001b[22m\u001b[22m",
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" [6] \u001b[1m(::SimJulia.##3#4{SimJulia.#execute,SimJulia.Timeout,Tuple{SimJulia.Coroutine}})\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/home/juser/.julia/v0.6/SimJulia/src/base.jl:43\u001b[22m\u001b[22m",
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" [7] \u001b[1mstep\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::SimJulia.Simulation\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/home/juser/.julia/v0.6/SimJulia/src/simulations.jl:39\u001b[22m\u001b[22m",
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" [8] \u001b[1mrun\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::SimJulia.Simulation, ::SimJulia.Timeout\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m/home/juser/.julia/v0.6/SimJulia/src/base.jl:87\u001b[22m\u001b[22m",
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" [9] \u001b[1msim_repair\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./In[5]:6\u001b[22m\u001b[22m",
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" [10] \u001b[1mmacro expansion\u001b[22m\u001b[22m at \u001b[1m./In[6]:4\u001b[22m\u001b[22m [inlined]",
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" [11] \u001b[1manonymous\u001b[22m\u001b[22m at \u001b[1m./<missing>:?\u001b[22m\u001b[22m"
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]
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}
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],
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"source": [
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"srand(SEED)\n",
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"results = Float64[]\n",
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"for i=1:RUNS\n",
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" push!(results, sim_repair())\n",
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"end\n",
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"println(sum(results)/RUNS)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 0.6.0",
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"language": "julia",
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"name": "julia-0.6"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "0.6.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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