NetLogo User Community Models

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## WHAT IS IT?

The model represents in a ruductionist way the organization of the complex urban system of the city of Thessaloniki, Greece and tries to explore the impacts of diverse response and recovery strategies of different levels of smartness, on the resilience after a given disturbance.

The property of resilience is evaluated with three different approaches in this model, namely based on:
the system’s performance levels and
the entropy of system’s performance
the utility of the urban system

The model calculates:
- the performance levels (considering the system's connectivity = number and arrangement of links)
- three different performance-based resilience metrics, i.e.: by Bruneau, by Zobel, and by Henry & Ramirez - Marquez
- the entropy of the possible connections (number of links) of each node of each subsystem (yellow and cyan) presented separately and as a total for the entire system
- the mutual entropy of the nodes possible connections, by estimating the values of marginal and joint entropies, suitable for more complex conditions of disturbance.
- the entropy-based resilence metric
- the utility levels (considering the citizens' needs)
- the utility-based resilience metric

## HOW IT WORKS

In each subsystem of this model, one of the links dies (disruptive event) and the agents/ nodes start to check which one is missing a link. This check occurs in a consecutive order: it starts with the fisrt node and after the completion and if the missing link is not detected, it moves to the second node of the subsystem. The time required for each check is recorded as an incremental delay in the recovery time (recovery_tick), affecting the resilience of the entire system. In this version of the model, the two subsystems start the procedures of check simultaneously, so that they can recover in parallel.

When some links are lost, there is more disorder in the system (potential for more information), which is reflected in the increase of Shannon’s entropy. The different definitions of entropy are developed as follows:

entropy4: p= each node’s remaining connections (number of links) / each subsystem’s maximum initial connections observed in a single node. The different capacities of the two subsystems are effectively reflected as well as the mutual loss of connection between nodes. However, this approach does not provide a convincing formula for the entropy of the entire system. The applied addition of the entropies of the subsystems is only valid if the disturbances are statistically independent (Bais & Farmer, 2007).
entropy41: Based on the approaches of Information Theory (Cover & Thomas, 2017; Lloyd, 2022) the entropy of each subsystem is estimated as the marginal entropy / information with p = each node’s (remaining) connections/ subsystem’s maximum initial node’s connections + each node’s lost connections / subsystem’s maximum initial node’s connections. Then, the joint probability is defined to capture the events of multiple lost connections in a single node by counting the nodes with more than 2 lost connections simultaneously / subsystem’s maximum initial node’s connections. Finally, according to the formula of mutual entropy I(X;Y)=I(X) + I(Y) – I(XY) (Cover & Thomas, 2017) the entire system’s mutual entropy is calculated.
entropy42: combining the approach of entropy4 with the joint probability for the dependent disturbances, the entire system’s mutual entropy is calculated for every type of disturbance.
popneeds: utility amount earned from the operation of each node of the respective subsystems, depending on the relevant population density and the fanctionality of the examined node.

## HOW TO USE IT

The user is expected to start the model’s set up and then run the model either for one step at a time by pressing the button “go once”, or until the end by pressing the “go” button. The simulations stop automatically after 100 ticks.
The user can select and simulate different response and recovery strategies, which represnet various levels of smartness, by combining through the respective choosers the initial response process, the recovery process, and the prioritazion process.

## THINGS TO NOTICE

The user can only observe from run to run that the different measures of resilience describe the same event, but they yield different values. This fact is related with the respective definitions and therefore, the mathematical expressions of entropy. The user can also observe the effectivness of the different response and recovery strategies that represent various levels of smartness and their impacts.