Overview

Purpose

Collaborative workspaces are commonly touted as “the way of the future”. When designed correctly, collaborative workspaces are cost-saving due to lower furniture requirements. They can increase productivity by bringing several minds together to work through issues. The spaces also foster innovation by bringing people together who may not have ever met in an individualized environment (Cisco).

However, these designs do not always consider variations in job descriptions and personality types that necessitate individual work. Without these considerations, the spaces can become incredibly distracting, severely decreasing or even nullifying any benefit that the collaborative workspace had on increased productivity (Cisco). To alter the space repeatedly until it performs optimally can become expensive. Considering individual desires for the space leads to larger patterns that can be used for effective design.

But cubicle farms aren’t any better. A quick search of Google Images of the word “cubicle” brings back hundreds of images likening it to prison cells, and one will even find articles such as one where a woman died sitting in her chair in a cubicle and nobody even noticed for at least a day. Cubicles are great for individualized work, but awful for collaborating with employees, innovating, and improving company morale.

This problem isn’t easily solved by just thinking it over, as individual people have needs that can be difficult to anticipate without surveying or trial and error. Trial and error can quickly get costly. Surveys about how people think that a space would work for them are also complicated, because can one truly predict how an entirely new type of space will feel in day-to-day work?

Happily, modeling offers a solution to the problem. Modeling offers the option to simulate thousands of possible configurations quickly. A strong model can determine the likely drivers of desirable patterns and interpret them to improve the space.

I set out to use modeling to solve the problem. Because I wanted it based in realism, I used a survey to gather data on the factors many recent studies are concerned with – introversion and extroversion. How do these traits affect desired group sizes in collaborative work? With a variety of identities and desired group sizes, will an ideal space emerge from the model through its thousands of iterations that can finally solve the problem?

Entities, state variables, scales

To set up the model, I first considered the individual people – the workers, the agents. Each worker is categorized as an introvert, extrovert, or “somewhere in between” – an ambivert. The percentages of these personality types in the population varies with each run of the model. The percentages are based on studies later quoted in Psychology Today. Over 1000 runs of the model, the model results (based on the first and third quartiles) showed 13-38% of the agents were introverts, 44-70% of the agents were extroverts, and 10-27% of the agents were ambiverts. Having the percentages of each identity vary with every run of the model created a fresh environment and added realism.

The agents also have ideal group sizes. These ideal group sizes come from a survey that I performed of 23 people. They were asked to comment on their ideal group sizes for five types of tasks – creative, technical, focus-oriented, repetitive, and public interaction – as well as to self-identify as either an introvert, extrovert, or “somewhere in between”.

Using the data from the survey, each individual agent was assigned an ideal group size that varied in a set range based on their identity. After 1000 runs of the model, the model results (based on the first and third quartiles) showed that extroverts ideally wanted groups of 6-7, introverts sought groups of 2-3, and ambiverts ideally wanted groups of 4-5. correlated with the survey results (after all, the model was based on them). Additionally, though these numbers seem to suggest that the ideal group sizes were averaged over the runs of the model, this was not the case – individuals always had the options for much smaller or larger group sizes, and statistics of the totals simply end up reaching an average when grouped together.

Because each individual agent could have a different ideal group size, this replicated realism by providing variety. This variety simulates either the level of introversion or extroversion or the different types of tasks a person could perform. For example, from the graphs above from the survey results, many people prefer to work on tasks that require focus alone, and many people working on repetitive projects would prefer to be in a larger group, despite their level of introversion and extroversion. These are very important considerations. It is not enough to simply provide individual cubicle farm spaces for introverts and sweeping collaborative spaces for extroverts. Extroverts also do focus work, and introverts can also greatly benefit from collaboration.

Process overview, scheduling

The model itself around the agents also had its purposes in the overall function. The model itself had the user inputs of the total number of people, total number of tables, and desired percent of happy people. There can be 10-200 people, 2-75 tables, and a desired percentage of happiness from 0-100%.

Temporal and spatial factors aren’t much of a consideration. Spatially, the tables simply appear in a horizontal line with agents stacking up in columns to represent groups. This is from the coding of the “Party” model by Uri Wilensky. The spatial arrangement here is an abstraction, as arrangement of a real space would require significant additional considerations. In regards to time, agents simply move until they reach the desired happiness percentage, and because offices typically don’t arrange their workers by having them play musical chairs, this is also not realistic, but simply to reach a conclusion by virtual trial and error until the desired result is reached.

When the model runs, the number of people input by the user is generated. Each individual is assigned an identity (introvert, extrovert, or ambivert) and a desired group size (based on the ranges determined from the survey). All individuals are randomly placed at tables, and the total number of tables also depends on user input. When the model user starts the model, agents move if they are not happy in their current group, and continue to move until the total desired happiness percentage is reached. Variables are updated at every time step to show the percentage and number of happy agents. These numbers are also divided into happy agents by their identities for further honed spatial planning.

Design concepts

Basic principles

One important concept of this model is the idea of introversion and extroversion. A concept first introduced by the psychiatrist Carl Jung, these personality traits drive the way that a person functions. Extroversion is “the act, state, or habit of being predominantly concerned with obtaining gratification from what is outside the self” and introversion is “the state of or tendency toward being wholly or predominantly concerned with and interested in one’s own mental life” (Merriam-Webster). However, these definitions tend to make it sound as if extroverts are constantly seeking attention and validation while introverts are shy and antisocial.

Perhaps a better way to think about it is with Susan Cain’s definitions. She says “introverts have a preference for a quiet, more minimally stimulating environment” and that “extroverts are energized by social situations and tend to be assertive multi-taskers who think out loud and on their feet”. These definitions are much easier to apply to the work environment, and even to apply the personality types to corresponding work behaviors that they replicate.

Another important concept is the dichotomy of cubicle farms and open space working environments. The former is better suited for individual work, while the latter is best for collaboration. Here we see the introverted and extroverted personalities being directly applied to spatial environments. If each is better suited for one environment, both cannot thrive in the same environment, so the space must have a way to accommodate them both.

However, this also doesn’t mean simply separating the introverts and extroverts into their own spaces. Another result of the survey showed that there are different levels of introversion and extroversion. Some of the more extroverted “introverts” prefer being around more people than the introverted “extroverts”. And it’s not that one personality type annoys the other or needs to be removed from the others’ space. It is more about the size of the group than the people within that group, hence why the model focuses on the total group size instead of who ends up being in the group.

There are also different types of tasks that could be performed in these spaces, and it’s not always predictable how each group prefers to interact in the spaces. For example, based on the survey results, introverts even preferred to be in much larger groups if the task at hand was boring. Additionally, extroverts prefer smaller groups for creative and focus oriented endeavors.

Emergence

The key results emerging from the system are:

• Introverts are much unhappier with the spaces than extroverts or ambiverts.
• If an agent’s ideal group size is less than or equal to the mean group size (number of people divided by number of groups), the agent will not be nearly as happy.
• As group sizes get larger, percent happy drops.

Some results are varying in unpredictable ways. One example is that introverts are much unhappier with the spaces overall than one might originally expect. Despite the ability to make smaller groups while extroverts make larger groups, it is still difficult to make small enough groups to satisfy the introverts because the extroverts also don’t like their groups to be over a certain size.

The other finding was that no identity group can be happy unless their ideal group size is less than or equal to the mean group size of the model. The mean group size is simply the total number of individuals playing “musical tables” divided by the number of tables they have to choose from. This finding is interesting because, though extroverts are fine with larger groups, to make up for the smaller groups of the introverts, they still are not happy with groups of the size required to make up for many introverts.

Similarly, as group sizes get larger, the percent happy drops off until no group can be happy.

Adaptation

Agents do not learn in the model, but their reasoning behind their decisions is arguably a form of adaptation. Some agents in the group may be happy with the group size reached (say there is a group of three where two of the agents have ideal group sizes of three), but another agent isn’t (say the third agent in this group wanted a group of four). The unhappy agent will move. The other agents are not unhappy because they are also happy with group sizes smaller than their ideal. However, at any time, additional agents could move into the group and make it too large for all of the other agents, forcing them to move. In this way, the system is perpetually adapting until all agents happen to fall into groups that make them all happy. This can make the model run longer than expected because agents cannot “predict” or “learn” or even “see” which groups they should go to, and so are randomly choosing over and over.

Objectives

The objective in the model is to reach the desired percentage of happiness, set by the user. Each agent will check at every tick to see if the size of the group they are currently in matches or is less than their ideal group size. Agents are happy if the group fits that criteria, and will stay put. Agents are unhappy if the group is too large, and will move until they are happy. The overall happiness of all of the agents is averaged, and if the average happiness overall is greater than or equal to the desired percentage of happiness, the model stops.

The model can be used to “maximize” the desired happiness percentage by setting it higher than the truly desired amount. For example, if a company wanted to ensure that 75% of its workforce was happy with the new spatial arrangements, but was also curious about making that number even higher, they could set it to any number above 75% (even 100%) to see what percentages the model will eventually reach and the configurations of agents at these higher happiness levels.

Sensing

The agents in this model have a very limited form of sensing. Agents in the model are simply able to “count” how many total agents are in their group. Because the identities of these agents are not important in regards to individual groups (for example, extroverts and introverts can group together), and the spatial setup of the model is simply an abstraction and not one that is being used to directly correlate to an actual design, agents do not need to “sense” the identities of the other agents, of nearby agents, or even which group they are in.

The total number of agents in their group is compared to the agent’s ideal group size property, and this determines the agent’s “happiness” and whether or not the agent should move.

Interaction

Agents in this model have very limited interaction, and it is indirect. As mentioned previously, the agents are able to “sense” other agents in order to count the total number of agents in their group. In this manner, agents do have an impact on each other. Depending on where an agent randomly ends up, they affect the happiness of the other agents in the group that they just landed in.

Stochasticity

A stochastic system has some quality of randomness that can be analyzed and understood, but not predicted precisely. This model is a perfect example of a stochastic system, because every run of the model will have a slightly different outcome. It is also not unheard of for a run of the model with the same inputs as another run of the model to have very different results.

This is partly due to the randomness in the percentages of identities assigned to the agents, and to the ideal group sizes assigned to the agents. However, even if these values were kept constant, the overall percent happy that resulted could vary, because the agents are still free to move around at random in any run of the model, and they will likely end up in different groups.

Here is an example from the sensitivity test, where the values varied significantly over 5 runs of the model.

Collectives

Agents do form a sort of collective in the form of their group. The group does not have properties other than the number of agents in the group, and some basic descriptors about where it is, but only for display purposes on the model – its location serves no purpose in the modeling calculations. The group forms for display purposes and to serve as an intermediate step in the calculations, to tie everything together. The group can count how many agents are in it, and report this number to each agent when the agent checks to see the total number of agents in its group, for the happiness calculation.

Agents are seeking groups to join and even an agent that is by itself in a group is still technically grouped in a group of one. Additionally, groups of zero can exist.

The number of agents in a group and the behavior of said agents could be considered an emergent property while the group itself functions more as a place, a separate kind of entity with its own properties (the number of agents in it, and display properties).

Observation

Quite a bit of data can be collected from the model.

Not only does the model provide the percent per identity, the count of people per identity, the mean ideal group sizes by identity, the mean group size, the people currently happy, the count happy by identity, and the percent happy by identity, and a graph of the happy groups – but so many things can be calculated from these numbers if they are collected in a sensitivity analysis.

Details

Initialization

The initial state of the model generates the number of agents that the user has input, as well as the number of groups (tables) the user has input, assigns the identities to the agents based on the percentage ranges, and assigns each agent an ideal group size. Then, the agents are randomly distributed amongst the groups.

The percent by identity, percent happy, count happy by individuals, and mean group sizes are not counted or calculated before the simulation starts, so they will stay at zero, as shown above, until the user presses “go”.

Each initialization of the model will be different, even if the user keeps the same number of agents and the same number of tables. This is because the agents’ identities are assigned based on a range of percentages, so with each new initialization of the model, a different percentage of agents will end up being the three identities. In addition to that, each individual agent is assigned a different ideal group size. While this isn’t noticeable at the start of the model because the ideal group sizes and happiness don’t have an effect on the model until the simulation starts, the varying group sizes also mean that the model is not the same every time it starts.

Methods of Analysis

Sensitivity Analysis

For the sensitivity analysis, I ran 1000 runs of the model, varying all of the user-input variables in order to find the patterns that emerged from various combinations of them. I then made a giant table and studied it, and made several charts and graphs until I found patterns in the data. A piece of the table is shown below.

Evaluation

I set out to perform the evaluation to verify and validate the model to ensure that it is realistic enough to use for spatial planning.

Results

Sensitivity Analysis

The model is most sensitive to:

• The mean group size (the number of people divided by the number of groups)
• The randomly chosen percentages of introverts and extroverts

As has been mentioned previously, if the mean group size is greater than the ideal group size, agents cannot be happy.

Additionally, because introverts tend to be less happy with the collaborative spaces, the more introverts there are, the likelier it is that their happiness will be less, and because the overall happiness includes them in the average, this can cause the overall happiness to drop.

Evaluation

Verification is used to determine if the model behaves as expected and gives results as expected. After running through several thousand runs with this model, and seeing how it behaves in a variety of situations, it is realistic for its intended usage. Because it is based on a survey of only 23 people and some research that gives ranges of the identities, it does have the potential to be improved by better understanding the identities as well as the ideal group sizes of a larger range of people. However, given the input that I was able to use, it worked very well.

Validation is used to compare the model to realistic data to ensure that the results are in fact realistic and don’t just seem realistic. Unfortunately, this is still a relatively new area of design, and one study could say that workers in a certain configuration were very happy while another study of the same space could come out saying that the workers were distracted compared to their previous workspace and productivity was declining. The truth of the matter is that the reality is much more complicated, and depends heavily on the jobs that the workers have, the work environment itself (nobody is going to be very happy in a dark, cold room with no windows, for example), the management and company feel (places like Google and Pixar with toys and games everywhere might make employees happy, but are they happy because of the toys or because they like their workspace?).

For these reasons, the model cannot be fully validated, as it is not meant to fully simulate reality, but instead serve as a starting point in research and design to ensure that people are thinking of all of the possibilities and not simply looking at the dichotomy of fully collaborative and fully cubicle farm.

Discussion

Feedbacks

Feedbacks in the model exist in the form of agents that randomly end up in a happy group. As has previously been mentioned, if a group of agents is already happy with the number of people in their group, this doesn’t present another agent from randomly being placed there. For example, if one of the agennts in a group of 3 agents has an ideal group size of 3, it would seem that it is now in a stable place and doesn’t have to move. However, if another agent is placed there, the group is now too large for the previously happy agent, and it will all be forced to move. This can happen on a grander scale if several of the agents in a group were happy – many agents may be forced to move on the influence of just one agent.

Because this has a detrimental effect to the goal of reaching the desired overall happiness percentage, it would seem immediately that this is a form of negative feedback. However, this effect also has a positive impact on the model. By “shaking things up”, this prevents a phenomenon that can happen if many agents are “locked in” to a situation. If a few outlier agents are the only ones able to move, but they cannot move to groups that are already satisfied, they may not end up in a group at all, or the configurations of the groups that exist may not be the best configurations.

For example, since agents are happy when the count of agents in their group is equal to or less than their ideal group size, an extrovert with an ideal group size of 7 could also be happy in a group of one or two. Just because this agent is happy doesn’t mean that this is the best configuration of space. If the agent would also be happy in a larger group, it would be beneficial if it was forced to move or if several agents were able to join its group.

Path Dependence

Path dependence isn’t a huge factor in this model, but it does have a small impact. The agents don’t “remember” what happened in previous time steps. The things that happened in those time steps do affect the future of the model, though. For example, if a group of agents was happy, but another agent randomly ended up there and forced all of the previously happy agents to move, the future has been affected by a past event – the previously happy agents are now no longer happy. The agents are still free to move to any other group, and the only path dependence is that agents are no longer in the group that they were previously in and are no longer happy due to the effects of that group. This doesn’t mean that the agent can’t move back to that group at the next time step, but it is unlikely that its previous groupmates will also end up there.

Non-Linearity

The system is definitely nonlinear. It is not a simple calculation to input a total number of people, a total number of groups, and a desired happiness percentage and come out with happiness levels of each identity group within that total number of people and a determination of whether or not that number of people and that number of groups can result in the desired happiness level. This is partly due to some random factors being input (the percentage of identities is one, and the individual ideal group sizes is another).

There is also a factor of randomness in the “success” of the model. Because the agents randomly move until the desired percent happiness is reached, and do not move unless their group size is greater than their ideal group size, it’s likely that several runs with the same inputs won’t end up with the same concluding happiness percentages. With the basic settings, the model automatically ends if the average happiness percentage is higher than or equal to the desired happiness percentage.

Emergence

A pattern of emergence develops in that agents self-organize into differently sized groups despite their identity, despite their ideal group size (as they are randomly going to groups until they are happy, not choosing a group because they know it will make them happy), and some end up in groups that are smaller than their ideal size.

This means that the same model can come out with different results over two runs. This means that in one run, all the tables could be the same size, and in the next, the table sizes could very wildly. This means that in one run, everyone is happy on the first time step, and in another run, agents move forever and are never happy because the ideal group sizes no longer work with the mean group size.

Conclusion

With all that said, how does the model work to improve the design of spaces that both introverts and extroverts can work together in?

The model performs this task for the user by displaying it visually. Here is an example:

Immediately from the results of a successful simulation we see that there are many small groups, a few medium-sized groups, and a couple of much larger groups.

One way to analyze this further is to collect data from several successful trials.

Here I took data from 10 successful trials of 15 tables and 50 people, with a desired percent happiness of 85. Here you can see the run number, and the size of each of the 15 groups as well as some averages.

I counted the frequency of each group size, then found the percent and number of people in all of the runs (on average) that ended up in that size group. From there, adding up the number of people for each evenly-sized table size allowed me to calculate the tables to provide for each group size. At this stage, one could also decide to make individual workspaces based on the groups of one, or a variety of other configurations. Knowing the needed sizes of tables means that the only step left to solving the design problem is to figure out where to put the tables in the space!

The model successfully followed my predictions that there would not be simply several groups of one for the introverts and several much larger groups for the extroverts. It follows the idea that some introverts are more extroverted than they might think, and vice versa. It also follows the idea that introverts and extroverts can and often do work together on projects.

Overall, the model was very successful. I hoped to create something that would allow users to input the information for their own office or workspace, and come up with a model that allows them to play around with different numbers of tables until they reach a design that maximizes happiness for all types of people.

References