## 1 Introduction
### Related Works  
Interconnection means an information transfer from one system or subsystem to another; this definition applies to a comprehensive set of systems: biological organisms, electronic devices, or even abstract concepts, such as equations [2].  
The main elements representing the different subsystems of an interconnected system can be identified and schematized in subsystem diagrams. Each subsystem represents the cause-effect relationship between input variables and output variables of each subsystem. Such a system can be represented by a graph whose nodes are the system's subsystems. [PERSON] and [PERSON] [33] gave an effective definition of an interconnected system: it can be viewed as a linear/non-linear system with a Multiple-Input-Multiple-Output (MIMO) transfer function composed of the interconnection of subsystems. Each subsystem is, in turn, characterized by a linear/non-linear MIMO transfer function. Therefore, by introducing the mathematical model of the elements into each subsystem, a quantitative evaluation of the whole system's evolution over time is possible.  
According to [PERSON] and [PERSON] [34], nowadays, the modern industry is heavily based on natural and/or generated resources (e.g., water, electricity, heat, etc.) and their distribution. Moreover, there is wide literature on this argument [35; 36]. Therefore, there is no unique approach to the numeric solution of such systems.  
There are several modelling approaches as reviewed in [29], but also in [37] for Time-driven and Event-driven approaches, [38; 39] for Agent driven approach, and [40] for co-simulation:  
* In the Time-driven approach, time is incremented with discrete time steps as in classical numerical simulation methods.
* In the Event-driven approach, discrete events occur in a sequence regardless of time between events ruling the model evolution; a mixed Time-Event driven approach is sometimes adopted.
* In the Agent-driven approach, different units can operate independently but communicate and cooperate with a defined environment. It can be either a Time-driven, Event-driven, or mixed approach.
* In the Co-simulation approach, a global simulation of interacting systems is carried out by composing its components' (independent) simulations. At each iteration of the global system simulation, each subsystem's inputs and outputs are transferred to the other appliable subsystems.  
An interesting modelling and simulation method of interconnected systems composed of subsystems and suitable interconnections relies on the co-simulation approach and the Individual Subsystem Models (ISMs) paradigm. Conceptually, the ISMs were introduced by [PERSON] [41], where a continuous or a discrete model for each subsystem is built, and interconnections between these models are defined to produce the overall system simulation. Despite this old definition, no general work has been carried out to solve ISM but only some subclasses. A class of a non-linear dynamical models is the Block-Oriented Model (BOM, a subclass of ISM). We can find a separately linear and memoryless non-linear models, each one represented as a single subsystem [42]. These models, also defined as causal models [43], are widely applied in numerical simulation (among many others: [PERSON] and [PERSON] [44], [PERSON] et al. [45], and [PERSON] et al. [46]). Another studied subclass of ISM is that of acausal models [43], consisting in defining instances of each subsystem model where only the relations among the different variables of each model are defined (e.g., thorough linear/non-linear algebraic/differential equations) and the relations among the different models too. Then, the whole model is solved as a whole or through reduction-model algorithms.