extensions [table array] globals [ageList remaining-turtles num-events heap-cap heap-size heap events sim-time avg-time-step num-patch-events num-turtle-events] turtles-own [mySpeed myAge isActive] patches-own [myChangeTime] ;; heap stuff to item-swap [n1 n2] let ntemp array:item heap n1 array:set heap n1 array:item heap n2 array:set heap n2 ntemp end to-report parent [n1] report (n1 - 1) / 2 end to-report left-child [n1] report 2 * n1 + 1 end to-report right-child [n1] report 2 * n1 + 2 end to-report get-min [n1] report array:item heap 0 end to heap-insert [n1] ifelse heap-size = heap-cap [ print "Heap overflow: event not inserted" ] [ ;; insert new item at end of array let i heap-size set heap-size heap-size + 1 array:set heap i n1 ;; fix heap property if it is violated while [ (i > 0) and (array:item heap (parent i) > array:item heap i) ] [ item-swap i (parent i) set i (parent i) ] ] end to heapify let i 0 let smallest -1 while [smallest != i] [ let l (left-child i) let r (right-child i) set smallest i if ((l < heap-size) and (array:item heap l < array:item heap i)) [ set smallest l ] if ((r < heap-size) and (array:item heap r < array:item heap smallest)) [ set smallest r ] if smallest != i [ item-swap i smallest set i smallest set smallest -1 ] ] end to-report extract-min ifelse heap-size <= 0 [ report 9999999 ] [ ifelse heap-size = 1 [ set heap-size 0 report array:item heap 0 ] [ let root array:item heap 0 set heap-size (heap-size - 1) array:set heap 0 array:item heap heap-size heapify report root ] ] end to insert-event [nt p] heap-insert nt table:put events nt p end ;; model code to setup ca set sim-time 0 set ageList [] set num-events 0 set num-patch-events 0 set num-turtle-events 0 set events table:make set heap array:from-list n-values 145 [0] set heap-cap 145 set heap-size 0 ask patches [setupPatches] create-turtles numTurtles [turtleSetup] set remaining-turtles numturtles reset-ticks end to setupPatches ifelse random-float 1 < .8 [ set pcolor green ifelse random-float 1 < .77777778 [set myChangeTime (random-float 70)] [set myChangeTime (20 - sqrt (random-float 441)) + 70] while [table:has-key? events myChangeTime] [ set myChangeTime (myChangeTime + 0.000001) ] insert-event myChangeTime self ] [ set pcolor red ifelse random-float 1 < .3333333 [set myChangeTime (random-float 10)] [set myChangeTime (20 - sqrt (random-float 441)) + 10] while [table:has-key? events myChangeTime] [ set myChangeTime (myChangeTime + 0.000001) ] insert-event myChangeTime self ] end to turtleSetup set heading one-of [0 90 180 270] set shape "dflt-north" set xcor random-float 11 set ycor random-float 11 set color yellow set mySpeed .6 set myAge 0 set isActive true end to go if (all? turtles [isActive = false]) [stop] set sim-time extract-min let p table:get events sim-time table:remove events sim-time ask turtles [doTurtleStuff] ask p [doPatchStuff] set num-events num-events + 1 set avg-time-step sim-time / num-events tick end to-report edge-distance if heading < 10 [ report pycor + 0.5 - ycor ] if heading < 100 [ report pxcor + 0.5 - xcor ] if heading < 190 [ report ycor + 0.5 - pycor ] report xcor + 0.5 - pxcor end to doPatchStuff set num-patch-events num-patch-events + 1 ifelse pcolor = green [ set pcolor red set myChangeTime sim-time + random-float 21 + 10 ] [ set pcolor green set myChangeTime sim-time + random-float 21 + 70 ] ;; make sure no two events have the same time while [table:has-key? events myChangeTime] [ set myChangeTime (myChangeTime + 0.000001) ] insert-event myChangeTime self end to doTurtleStuff set num-turtle-events num-turtle-events + 1 ;; update all turtles let delta-time sim-time - myAge if isActive [ ifelse [pcolor] of patch-here = green [ let dist-to-go mySpeed * delta-time while [dist-to-go > 0.00001] [ let travel-dist min list dist-to-go mySpeed ifelse is-patch? patch-ahead travel-dist [ ifelse [pcolor] of patch-ahead travel-dist = red [ let mdist edge-distance fd mdist set dist-to-go 0 set myAge sim-time ] [ fd travel-dist set dist-to-go dist-to-go - travel-dist set myAge myAge + (travel-dist / mySpeed) ] ] [ if isActive [ let mdist edge-distance fd (mdist - 0.0001) set isActive false set color gray set myAge myAge + (mdist / mySpeed) set ageList fput myAge ageList set remaining-turtles (remaining-turtles - 1) set dist-to-go 0 ] ] ] ] ;; if on a red patch, don't move [ set myAge sim-time ] ] end @#$#@#$#@ GRAPHICS-WINDOW 210 10 818 619 -1 -1 50.0 1 10 1 1 1 0 0 0 1 0 11 0 11 0 0 1 ticks 30.0 BUTTON 2 10 68 43 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 68 10 131 43 step go NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 132 10 195 43 NIL go T 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 6 54 178 87 numTurtles numTurtles 0 100 20.0 1 1 NIL HORIZONTAL MONITOR 19 217 160 262 average age of turtles mean agelist 4 1 11 MONITOR 18 106 158 151 Time: sim-time 10 1 11 MONITOR 18 163 159 208 Average Time Step avg-time-step 5 1 11 @#$#@#$#@ ## WHAT IS IT? Macal and North [WSC 2008] ABM Example written as a discrete event simulation (DES). The model consists of a 12 x 12 grid of patches. Each patch is 100 feet by 100 feet square. Approximately 20% of the patches are red and 80% are green. Each red patch changes to green after 10-30 minutes. Each green patch changes to red after 70-90 minutes. There are a variable number of turtles. Each turtle is randomly placed on the grid with facing of north, east, south, or west. Turtle speed is 60 feet per minute. Ticks are one minute apart. On each tick, each patch determines if it is time for it to change color and each turtle moves, if it can. If a patch changes color, then it will calculate its next color change time (10-30 minutes if it is red, 70-90 minutes iof it is green). Each turtle uses the following rules for movement: 1. A turtle will begin moving at its specific heading if, and only if, it starts on a green patch. 2. If a turtle is on a red patch, it will wait until the patch turns gree to start moving. 3. If a turtle is moving through a patch and reaches the edge, it will only enter the next patch if it is green. 4. If a turtle is travelling through a patch when it turns red, it will stop immediately. It will not move again until the patch turns green. 5. When a turtle reaches one of the edges of the grid, it exits the system, and its total time spent in the simulation is recorded. The simulation is run until all turtles have exited, at which time statistics are calculated. This is a DES (event-driven) version. Instead of time-stepping, the simulation keeps a list of times that patches change colors and "jumps" from one patch color change time to the next. This simulation uses the Array extension to keep the times, organized as a binary heap. Each time is associated with one patch; the patch that changes color at that time. The association of patch to time is kept using the Table extension. ## HOW IT WORKS Each cycle, the earliest time is removed from the heap, the patch associated with the time is retreived from event table (and removed from the table), and the patch doPatchStuff is called. As part of the doPatchStuff procedure, each turtle is checked to see if it can move and, if so, it is moved until 1. time reaches the event time 2. turtle reaches the edge of a red patch 3. turtle reaches the edge of the grid. After all of the turtles are checked, the patch color is changed and the next color change time for the patch is calculated. The Table extension does not allow for two keys with the same value. Therefor, before adding a time to the heap array and event table, the table is checked to see if the time already is in the table. If it is, then the time is incremented slightly, until a time not in the table is calculated, and this is the time that is used for the event. There is another implementation, ExampleABM_Event_Driven_2.nlogo, where agents are kept in a list, so that all agents performing an action at the same time are placed in the table. ## HOW TO USE IT The only input is the number of turtles. Notice that doTurtleStuff is not directly called in the go procedure. Rather, it is called by the doPatchStuff procedure. ## THINGS TO NOTICE It is instructive to single step the simulation. In this simulation, there is one tick when a patch changes color. Prior to the patch actually setting its new color, all of the turtles are moved to the time of the patch color change. Then the patch color is set. This process continues until all turtles have reached the edge of the grid. The results from this simulation should be compared with ExampleABM_TimeStepped.nlogo simulation, where the same model is implemented with the traditional time-stepped simulation mechanism. There, one tick is one minute. The average turtle age and the total simulation time are the same for the same number of turtles, but the execution profile is different. In this implementation, about 2.88 doPatchStuff events occur in a simulated minute, where the time-stepped version does all 144 patches every minute. In the time stepped version, most of the patches do not change color during a tick (in fact about 2.88 change color per tick, on average). In the time-stepped simulation, every turtle is checked once per tick. In this version every turtle is checked for every patch color change event, or 2.88 times per minute. This means that for less than 50 turtles, this simulation will have fewer total doTurtleStuff and doPatchStuff calls, and for more than 50 turtles this simulation will have more total doTurtleStuff and doPatchStuff calls. **Model Setup** The simulation could be executed a few thousand times in order to randomize the patch colors. Many simulations execute a warm-up period to reach steady state. In this case, the expected distribution of color change times can be calculated and set. The calculation is described in a paper, _NetLogo Meets DES_, submitted to the Computational Social Science 2018 annual conference. ## THINGS TO TRY ## EXTENDING THE MODEL Try implementing the list of event times using a sorted list or a sorted array instead of a heap. ## NETLOGO FEATURES This model uses the Array and Table extensions to implement an event queue. ## RELATED MODELS See also ExampleABM_EventDriven_2.nlogo and ExampleABM_TimeStepped.nlogo for different implementations of this model. ExampleABM_TimeStepped is a classical agent-based time stepped simulation. ExampleABM_EventDriven_2.nlogo schedules both patch color changes and turtle moves and is nearly 50 times more efficient. ## CREDITS AND REFERENCES See https://www.geeksforgeeks.org/binary-heap/ for information on heaps. This model has been coded by Emmet Beeker, ebeeker@mitre.org. Feel free to contact me with comments or questions. July 10, 2018 @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 150 240 Polygon -7500403 true true 150 165 89 198 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