El Farol Network Congestion

El Farol Network Congestion preview image

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Uri_dolphin3 Uri Wilensky (Author)


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El Farol is a bar in Santa Fe. The bar is popular, but becomes overcrowded when too many patrons attend. Patrons are happy when less than a certain amount of patrons attend, say 60 for example, but they are unhappy when more than some other amount of patrons attend, say 70. What will happen as time passes and people have pleasant or unpleasant experiences?

Is it always true that the more a bar is popular, the higher its attendance? Does it makes sense to say a bar has its ups and downs, but on the whole it's stable?

This model problematizes a seemingly simple situation of social interaction to reveal that it is not that simple. Working in this model, we encounter and appreciate the inherent coordination challenges that can arise in complex dynamic systems involving agents with intention and specified needs and criteria of satisfaction. Can patrons of a bar somehow self organize to optimize overall satisfaction?


El Farol is a fun place to be, and patrons keep returning. But it can get crowded there. If it is crowded, patrons may not come back as often as they had previously, but if it happens not to be crowded, the patrons will come again sooner.

Patrons of El Farol each have initial inclinations to visit the bar or not. These personal inclinations are expressed in the frequencies of each patron's visits (the variable ATTENDANCE-FREQUENCY. For example, a value of 9 means they go to the bar every 9 days). ATTENDANCE-FREQUENCY is the variable c in the Bell and Sethares paper.

When the model starts running, patrons have different times until their next visit (stored in the variable PHASE. For example, a value of 5 means the patron will go to the bar in 5 days time). PHASE is the variable p in the Bell and Sethares paper. For each patron, the initial values of ATTENDANCE-FREQUENCY and PHASE are chosen randomly, within a designated range determined by the other settings of the model. Each patron's PHASE value decreases as the model runs until it drops below 1, at which time the patron goes to the bar. While in the bar, the patron determines how crowded the bar is and changes the value of ATTENDANCE-FREQUENCY accordingly. If attendance at the bar exceeds the EQUILIBRIUM value, i.e. bar is overcrowded, the patron increases ATTENDANCE-FREQUENCY by the FREQUENCY-UPDATE value. That means that in the future, this patron will wait longer before returning to this bar. If attendance is below the critical value (EQUILIBRIUM - DEAD-ZONE), i.e. bar is not crowded, the patron decreases ATTENDANCE-FREQUENCY by the FREQUENCY-UPDATE value. ATTENDANCE-FREQUENCY remains unchanged if attendance falls within the DEAD-ZONE range. The PHASE is then reset to the new value of ATTENDANCE-FREQUENCY.


POPULATION: the number of patrons that will be created in this experiment
EQUILIBRIUM: the number of patrons beyond which the bar becomes overcrowded
DEAD-ZONE: determines the range below the equilibrium at which the bar is perceived neither as crowded nor as not crowded
FREQUENCY-UPDATE: value to update the ATTENDANCE-FREQUENCY by in response to a positive or negative experience at the bar

SETUP - initiates variables towards a new run
GO ONCE - runs the model for one time tick, so we get the behavior over a single 'day'
GO - runs the model repeatedly, until it is stopped by pressing again

PERFECT-INFORMATION?: if turned on, agents will have access to attendance information whether they are attending or not and will adjust their preferences accordingly

ATTENDANCE HISTORY: shows how many patrons are currently in the bar and the cumulative ratio of total patrons to total days
ATTENDANCE TYPE: shows the current totals of two types of patrons -- casuals and regulars (including those in and out of the bar)

After choosing the variables, click the SETUP button to setup the model. All patrons start on the left side of the world. This means that none of them are attending the bar at this moment. If they choose to attend, they will move to the right side of the world. Patrons are colored sky by default. This means that they are 'casual' patrons (less than every other day). If they attend more than every other day, they will turn red to show that they are now 'regular' patrons.

You can choose between GO ONCE and GO to run the model. Also, for initial runs, you may want to slow down the model, using the speed slider above the View, so as to see the patrons attending and leaving the bar.


Try different settings and examine both plots. Note that the ATTENDANCE HISTORY plot tends to converge on some value. Note how the ATTENDANCE TYPE plot occasionally spikes up or down. This means that there are a lot of casual patrons who are attending the bar often, and once in a while, they all happen to attend on the same day. With PERFECT-INFORMATION? set to Off, the numbers of casuals and regulars tend to converge on some stable values. You will also notice that the average attendance seems to converge toward the (EQUILIBRIUM - DEAD-ZONE) number.

When PERFECT-INFORMATION? is turned On, everyone has access to the same information about attendance, and they all respond uniformly by updating their ATTENDANCE-FREQUENCY values. So the group as a whole usually either all go or they do not go at all. Thus, an increase in information seems to prevent some wiggle room that would make more patrons satisfied.


How does changing the value on the FREQUENCY-UPDATE slider affect the behavior of the system? Try to guess, then run the model under different values for that slider and examine the results.

Play with the relation between values in the POPULATION and EQUILIBRIUM sliders. Try to imagine how these settings would impact your own behavior, and see if the model matches your expectations.


Currently, all patrons have the same tolerance to crowds. Assign random EQUILIBRIUM values to the attending turtles and evaluate how this modification affects the group behavior.

Invent and implement advanced patron strategies for optimizing their experience at the bar. One idea is to have patrons remember historical data such as "it is always crowded every 7th day" or "every time it is crowded 4 days in a row, the next day is always not crowded." What do you expect such an extension might do? Can we, in principle, guarantee more satisfied patrons by making them more savvy? Should we give this power of prediction to all patrons, or should we control who has these strategies (just as we controlled who has perfect information)? Is it fair to favor some patrons over others?

Improve the visual features. Perhaps the bar could be made to look more like an actual bar.

A final idea would be to create a HubNet version of the El Farol simulation.


Look at the code for procedure attendees-skip-across-street.

  to attendees-skip-across-street
    ask patrons with [attending?]
      [ setxy (- xcor) ycor ]

The code asks each patron that has a true value for the 'attending?' (true/false) variable to set their x coordinate. Yet, this procedure is called both when the patron crosses the street to the right so as to enter the bar and again when the patron exits the bar and crosses back to the left. How can it be that the same code both sends a patron to the right and to the left?

The answer lies in the meaning of xcor and how it relates to the minus sign (-) just before it. xcor reports a value representing the right/left position of a turtle. To the right of central vertical line (the y-axis, where the street is in this model), the xcor values are positive, and to the left of the axis the values are negative. When a patron is in the left section of the world, subtracting the xcor flips the xcor to a positive value. For instance, if the patron is at (-5, 3), the patron will be sent to (+5, 3). When this patron has completed attending, this same code sends the patron back from (+5, 3) to (-5, 3).


The Social Science models Party and Segregation each deal with situations in which individuals have specified preferences and act upon these preferences.


Original implementation: Eric Cheng, for the Center for Connected Learning and Computer-Based Modeling.

This model is based on a paper by Ann Bell and William Sethares, "The El Farol Problem and the Internet: Congestion and Coordination Failure".


If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:


Copyright 2003 Uri Wilensky.


This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227.

Comments and Questions

Click to Run Model

breed [ patrons patron ]

;; the 'b', 'a', and 'r' breeds are single turtles that spell 'bar'
breed [ bs b ]
breed [ as a ]
breed [ rs r ]

;; Variables ;;

globals [
  attendance          ;; number of patrons currently attending bar
  sum-attendance      ;; sum of attendance after N days
  average-attendance  ;; sum-attendance / days
  regulars            ;; patrons who attend at least every other day
  casuals             ;; patrons who do not attend every other day

patrons-own [
  attending?          ;; whether or not a patron attended during the previous day
  ;; how often the patron wishes to go to the bar, which is the
  ;; variable c in the Bell and Sethares paper
  ;; the number of days remaining until the patron attends next,
  ;; which is the variable p in the Bell and Sethares paper

;;; Setup Procedures ;;;

to setup

;; creates the colorful background images

to setup-world
  set sum-attendance 0
  set average-attendance 0
  ask patches
    [ set pcolor scale-color green ((random 500) + 5000) 0 9000 ]

;; creates a street that runs vertically in the middle of the world

to create-street
  ask patches with [pxcor >= -1 and pxcor <= 1]
    [set pcolor black]
  ask patches with [pxcor = 0 and pycor mod 2 = 0]
    [set pcolor yellow]

;; draws a black bar with the word "bar" inside

to create-bar
  ask patches with [pycor < 2 and pycor > -2 and pxcor >= 9 and pxcor < 12]
    [set pcolor black]
  create-bs 1
    [set shape "b"
      setxy (max-pxcor - 2) 0]
  create-as 1
    [set shape "a"
      setxy (max-pxcor - 1) 0]
  create-rs 1
    [set shape "r"
      setxy max-pxcor 0]

;; creates patrons and places them in unique patches

to setup-patrons
  if population >= (max-pxcor - 1) * world-height
    [user-message (word "The population is too large for the size of the world."
                        "  Either decrease the population or increase the number of "
                        "patches in the world.")
  create-patrons population
    [ set shape "person"
      set color sky
      set size 1
      set attending? false
      set attendance 0
      set attendance-frequency (1 + random 20)
      set phase (1 + random attendance-frequency) ]

;; locate unoccupied patches for patrons

to find-patch
  setxy ((random min-pxcor ) - 1)
  while [any? other turtles-here]
      [find-patch]    ;; keeps running until each patron is alone on patch

;;; Runtime Procedures ;;;

to go

;; counts down phase. if, following this count down, the phase has been completed,
;; the patron will attend now

to phase-step
  ask patrons
    [if (phase > 1) [set phase (phase - 1)]
      if phase <= 1  [set attending? true]]

;; checks whether or not the bar is overcrowded

to check-attendance
  display  ;; so we see them moving
  ;; Patrons who are in the bar always have perfect information about attendance
  ;; If the perfect-information? is On, then also patrons who are outside have
  ;; this information
  ifelse perfect-information?
    [ask patrons [update-attendance-frequency] ]
    [ask patrons with [attending?] [update-attendance-frequency] ]

;; finds the number of patrons who are attending and determines if they are casuals or regulars

to calculate-attendance-by-type
  set attendance count patrons with [attending?]
  set regulars count patrons with [attendance-frequency < 3]
  ask patrons with [attendance-frequency < 3]
    [set color red]
  set casuals (population - regulars)
  ask patrons with [attendance-frequency >= 3]
    [set color sky]

;; determines the cumulative ratio between total attendance and days since the onset of the
;; current run of the model

to calculate-average-attendance
  set sum-attendance (sum-attendance + attendance)
  set average-attendance (sum-attendance / ticks)

;; skips attending customers to the other side of the world across from the vertical axis

to attendees-skip-across-street
  ask patrons with [attending?]
    [setxy (0 - xcor) ycor]

;; patrons update the frequency of their individual attendance schedule (the phase or cycle).
;; if the bar was crowded, they'll come back less frequently than before, and vice versa
;; returning less frequently means increasing the phase, and vice versa
;; 'frequency-update' is the interface slider value for increasing/decreasing the phase

to update-attendance-frequency ;; patron procedure
  if attendance < (Equilibrium - dead-zone)
    [if (attendance-frequency > 1)
      [set attendance-frequency (attendance-frequency - frequency-update)]]
  if attendance > Equilibrium
    [set attendance-frequency (attendance-frequency + frequency-update)]

;; updates by setting phase to be attendance-frequency

to phase-update
  ;; now that the day is over, attending patrons return across the street
  ;; these patrons now begin counting down all over again from their current personal
  ;; value of 'attendance-frequency'
  ask patrons with [attending?]
    [set attending? false
      set phase attendance-frequency]

; Copyright 2003 Uri Wilensky.
; See Info tab for full copyright and license.

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Uri Wilensky over 12 years ago El Farol Network Congestion Download this version

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