Olivier Cardin
email: olivier.cardin@ls2n.fr

Classification of cyber-physical production systems applications: proposition of an analysis framework

Keywords: Cyber-physical production systems, classification, cognition, framework, human factor, Manufacturing control

Cyber-physical systems have encountered a huge success in the past decade in several scientific communities, and specifically in production topics. The main attraction of the concept relies in the fact that it encompasses many scientific topics that were distinct before. The downside is the lack of readability of the current developments about cyber-physical production systems (CPPS). Indeed, the large scientific area of CPPS makes it difficult to identify clearly and rapidly, in the various applications that were made of CPPS, what are the choices, best practices and methodology that are suggested and that could be used for a new application. This work intends to introduce an analysis framework able to classify those developments. An extensive study of literature enabled to extract the major criteria that are to be used in the framework, namely: Development Extent; Research Axis; Instrumenting; Communication standards; Intelligence deposit; Cognition level; Human factor. Several recent examples of CPPS developments in literature are used to illustrate the use of the framework and brief conclusions are drawn from the comparative analysis of those examples.

Introduction

First definition that can be found about cyber-physical systems (CPS) dates from 2006 [START_REF] Lee | Cyber-Physical Systems -Are Computing Foundations Adequate?[END_REF], during a workshop with the American National Science Foundation1 (NSF). The extension of cybernetic systems towards CPS is therefore explicitly dealt with in literature since 2006-2007 and is constantly growing in popularity. Fig. 1 shows a short analysis of the evolution of the number of journal article mentioning explicitly the term "cyber-physical" in the 5 major scientific publishers. This term was chosen as it encompasses various aspects and applications of the CPS. In the past decades, many research articles were dealing about notions and concepts that have been at the origin of current CPS. These works are not listed here as they do not mention the cyber-physical keyword even though the scientific content is compatible. The objective of this figure is to exhibit the trend of acceptance of the notion in literature, whatever the field of research and the publisher. Over the last six years, i.e. since the total number of publications reached 1000, a 40% increase in average per year can be noticed, which demonstrates the high level of acceptance of the notion.

Looking at the publisher proportions, it can be noticed that IEEE was very present in the early years, whereas the publication rate is more shared nowadays. This is an effect of the dissemination of the notion to a large number of new fields of application that were not present in the first years.

Fig. 1. CPS notion dissemination in literature

All along their development, more synthetic definitions were suggested, such as those of [START_REF] Rajkumar | Cyber-physical systems: The next computing revolution[END_REF] or [START_REF] Baheti | Cyber-physical systems[END_REF]. For example, CPS are defined by [START_REF] Schuh | Collaboration Moves Productivity to the Next Level[END_REF] as cooperating systems, having a decentralized control, resulting from the fusion between the real world and the virtual world, having autonomous behaviors and dependent on the context in which they are, being able to constitute in systems of systems with other CPS and leading a deep collaboration with the human. For this, embedded software in CPS uses sensors and actuators, connect to each other and to human operators by communicating via interfaces, and have storage and data processing capabilities from the sensors or the network [START_REF] Strang | Assembly Process driven Component Data Model in Cyber-Physical Production Systems[END_REF]. The recent one, suggested by [START_REF] Monostori | Cyber-physical Production Systems: Roots, Expectations and R&D Challenges[END_REF], allows a clear synthesis of the various aspects of this large concept, coupling in addition the notion of services with CPS : "Cyber-Physical Systems (CPS) are systems of collaborating computational entities which are in intensive connection with the surrounding physical world and its on-going processes, providing and using, at the same time, data-accessing and data-processing services available on the internet". To do so, embedded software in CPS uses sensors and actuators, connect with each other and with humans communicating via standard interfaces, and have abilities of storage and processing of data coming from sensors or from the network [START_REF] Strang | Assembly Process driven Component Data Model in Cyber-Physical Production Systems[END_REF]. This interconnection of systems, as stated by [START_REF] Gengarle | Characteristics, Capabilities, Potential Applications of Cyber-Physical Systems: a Preliminary analysis[END_REF], derives from the fact that a CPS encompasses together control, computation but also communication devices [START_REF] Klimeš | Using Formal Concept Analysis for Control in Cyber-physical Systems[END_REF]. What can be spotted in the evolution of the definition is the notion of system of systems that was not considered in the early definition of 2006 [START_REF] Lee | Cyber-Physical Systems -Are Computing Foundations Adequate?[END_REF].

The notion of CPS is very wide and encompasses an extremely large class of systems. As a matter of fact, numerous fields of research are relevant of this keyword. This is probably a huge opportunity as it gives the possibility to create a consistent ecosystem in numerous fields of applications: from autonomous vehicles [START_REF] Fink | Robust control for mobility and wireless communication in cyber-physical systems with application to robot teams[END_REF] to health devices [START_REF] Santos | A personal connected health system for the Internet of Things based on the Constrained Application Protocol[END_REF], from electrical grid management [START_REF] Al-Hammouri | A comprehensive co-simulation platform for cyber-physical systems[END_REF] to HVAC building control [START_REF] Wang | An Integrated Scheme for Cyber-physical Building Energy Management System[END_REF].

The industrial domain is of course interested in this field, and the development of major evolutions such as Industrie4.0 in Germany [START_REF] Zezulka | Industry 4.0 -An Introduction in the phenomenon[END_REF] is based on CPS. The application of CPS in the field of production management was formalized in the past few years [START_REF] Monostori | Cyber-physical Production Systems: Roots, Expectations and R&D Challenges[END_REF], under the term of Cyber-Physical Production Systems (CPPS). According to [START_REF] Rudtsch | Pattern-based Business Model Development for Cyber-Physical Production Systems[END_REF], the main benefits that can be expected from the generalization of CPPS are: (i) Optimization of production processes; (ii) Optimized product customization; (iii) Resource-efficient production; (iv) Human-centered production processes.

Many fundamental research questions emerge from the development of the concept of CPPS. Among these, the modelling and forecasting of their emergent behavior, the optimization of the control laws at each level of the system and the establishment of a convenient environment for developing autonomy, cooperation, optimization and responsiveness can be cited [START_REF] Monostori | Cyber-physical Production Systems: Roots, Expectations and R&D Challenges[END_REF][START_REF] Klöber-Koch | Knowledge-Based Decision Making in a Cyber-Physical Production Scenario[END_REF]. In parallel, a credible answer to this last element was given thanks to the development of Holonic Manufacturing Systems [START_REF] Barbosa | Dynamic self-organization in holonic multi-agent manufacturing systems: The ADACOR evolution[END_REF][START_REF] Van Brussel | Reference architecture for holonic manufacturing systems: PROSA[END_REF][START_REF] Chirn | A holonic component-based approach to reconfigurable manufacturing control architecture[END_REF][START_REF] Pach | ORCA-FMS: a dynamic architecture for the optimized and reactive control of flexible manufacturing scheduling[END_REF][START_REF] Leitão | ADACOR: A holonic architecture for agile and adaptive manufacturing control[END_REF], but still needs to be developed in order to fit the requirements of industrial implementation at a large scale. On the other hand, a special interest is being given nowadays to cloud technologies, which are becoming a more and more credible actor of future industrial systems [START_REF] Colombo | Towards the Next Generation of Industrial Cyber-Physical Systems[END_REF][START_REF] Gamboa Quintanilla | Implementation framework for cloud-based holonic control of cyber-physical production systems[END_REF][START_REF] Liu | Cyber-physical manufacturing cloud: Architecture, virtualization, communication, and testbed[END_REF]. Projects such as IMC-AESOP [START_REF] Colombo | IMC-AESOP outcomes: Paving the way to collaborative manufacturing systems[END_REF] for example studied the benefits that can be expected from the coupling between cloud and CPPS, and technologies such as Service-oriented Architectures (SoA) are given a certain credit in order to foster interoperability, agility and self-* abilities of systems [START_REF] Morgan | The Cyber Physical Implementation of Cloud Manufactuirng Monitoring Systems[END_REF]. The human-machine interaction [START_REF] Liu | Augmented Reality-assisted Intelligent Window for Cyber-Physical Machine Tools[END_REF][START_REF] Stern | Development of a Model for the Integration of Human Factors in Cyber-physical Production Systems[END_REF], the social aspect [START_REF] Jiang | Towards a cyber-physical-social-connected and service-oriented manufacturing paradigm: Social Manufacturing[END_REF] and the cyber-security issues [START_REF] Brooks | Chapter 26 -Cyber-Physical Security of Automotive Information Technology[END_REF][START_REF] Lu | Cyberphysical security for industrial control systems based on wireless sensor networks[END_REF][START_REF] Zhang | Security threats and measures for the cyber-physical systems[END_REF] applied to industry and manufacturing are also major questions that are under study and directly connected to CPPS.

Considering this extremely large field of research and the large perimeter of the definition of CPPS, there is a risk of scattering of research efforts inside this wide notion. The main challenge of the next few years is to provide proofs of concepts, industrial applications and laboratory developments able to prove the advantages given by the CPPS paradigm in terms of flexibility and performance. This article intends to introduce an analysis framework aiming at classifying the various developments and applications of literature. This framework is intended for future researchers or engineers willing to establish rapidly an overview of the main trends of literature developments.

First, an analysis of the research context from the international roadmaps perspective is presented. Then, the framework will be presented and the items defining the axes of the framework are described. Finally, the application of the framework to various examples of developments found in literature in order to illustrate the use of the framework is introduced, and a preliminary analysis of the state of the art based on the use of the framework is proposed in the agility domain.

2

Cyber-physical production systems research context

Definition and fundamentals

CPPS classical definition [START_REF] Monostori | Cyber-physical Production Systems: Roots, Expectations and R&D Challenges[END_REF] is widely accepted in the last few years as it exhibits well the notion of the necessary cooperation between CPS in a CPPS. However, the notion of knowledge management and decision making, which constitute still nowadays a large field of research, are missing. Notions such as digital twins used for dynamic simulation and forecasting are not present for example. Furthermore, notions of learning and auto-adaptation are not clearly mentioned. Finally, the adaptability of the system to new technologies, new organizations or major reconfigurations are not expressed. As a matter fact, clearly defining the goals, objectives and benefits obtained by a paradigm shift towards CPPS is difficult to establish.

In this article, the following definition, adapted from [START_REF] Monostori | Cyber-physical Production Systems: Roots, Expectations and R&D Challenges[END_REF], is suggested in order to encompass these missing notions: "Cyber-Physical Production Systems are systems of systems of autonomous and cooperative elements connecting with each other in situation dependent ways, on and across all levels of production, from processes through machines up to production and logistics networks, enhancing decision-making processes in real-time, response to unforeseen conditions and evolution along time".

As this definition shows, if the notion of CPPS is new and brings many different fields of research together towards high-level objectives, the fundamentals of the notion considered one by one are not really new. Several flagship notions in the past decades were already addressing the same objectives with globally the same ideas of solutions, among which Intelligent Manufacturing Systems [START_REF] Hatvani | Intelligent Manufacturing Systems-A Tentative Forecast[END_REF], Biological Manufacturing Systems [START_REF] Ueda | A Concept for Bionic Manufacturing Systems Based on DNA-type Information[END_REF], Reconfigurable Manufacturing Systems [START_REF] Chalfoun | Specification of a Reconfigurable and Agile Manufacturing System (RAMS)[END_REF], Digital Factory [START_REF] Viharos | Realizing the Digital Factory: Monitoring of Complex Production Systems[END_REF], Holonic Manufacturing Systems [START_REF] Valckenaers | Designing Holonic manufacturing systems[END_REF], Industrial Agents [START_REF] Leitao | Multi-agent System Approach for the Strategic Planning in Ramp-Up Production of Small Lots[END_REF], etc. However, the major benefit of embracing CPPS is that it is able in the next few years to be accepted by the largest audience and gather all the publications in a single trend, that shall make the readability of the scientific community more clear and thus more visible.

If CPS characterization in Computation, Control and Communication [START_REF] Klimeš | Using Formal Concept Analysis for Control in Cyber-physical Systems[END_REF] is currently widely disseminated, CPPS were also characterized many times in various ways by the different authors of literature. An interesting synthesis of these various characterizations is however defined in [START_REF] Monostori | Cyber-physical systems in manufacturing[END_REF], which states that CPPS are globally characterized by three main characteristics: Intelligence, Connectedness and Responsiveness. Fig. 2, adapted from [START_REF] Klimeš | Using Formal Concept Analysis for Control in Cyber-physical Systems[END_REF], positions the main characteristics of CPS and integrates the fundamentals of CPPS. It exhibits how all these characteristics finally fit well together and shows the clear relation between these notions, each in their field. In the following, the basic characteristics of the CPS will therefore be extended to CPPS for clarity purposes.

Fig. 2. Basic capabilities of a CPS and the analogy to CPPS

Research context overview

In order to establish the context in which the researches in CPPS field are developed, the idea here was to concentrate on the international research roadmaps in order to exhibit the main trends in the field. A study of these roadmaps in literature [START_REF] Cardin | Future Industrial Systems: Best Practices of the Intelligent Manufacturing and Services Systems (IMS2) French Research Group[END_REF], classifies these international roadmaps towards the main axes they put forward. Several conclusions can be drawn from this comparative study. First, it may be noted that although different terminologies are used, these different roadmaps provide a fairly coherent and identical view of both the objectives and the means of achieving these objectives. Moreover, innovation objectives can be classified into three major development axes, relatively stable regardless of the roadmap studied over the last decade.

The first axis is the development of advanced technologies for production. The idea of offering high technology in manufacturing processes is assumed to have in the near future an important impact on next-generation production systems. Current trends focus on nanoscale structures, additive manufacturing (e.g. the PHOCAM-Photopolymerbased Customized Additive Manufacturing Technologies project) or intelligent materials (e.g. project AMITERM [START_REF] Parton | In situ polymerization of thermoplastic composites based on cyclic oligomers[END_REF]). All these processes have the particularity of being more and more connected, which implies notions of cyber-security that are present transversally in many projects.

The second axis deals with sustainable production. In order to reduce the impact of production on the environment, an initial idea is to increase the energy efficiency of processes, as in projects such as Co2PE! (Cooperative effort on Process Emissions in manufacturing) [START_REF] Kellens | Methodology for systematic analysis and improvement of manufacturing unit process life cycle inventory (UPLCI) CO2PE! initiative (cooperative effort on process emissions in manufacturing). Part 2: case studies[END_REF][START_REF] Kellens | Methodology for systematic analysis and improvement of manufacturing unit process life-cycle inventory (UPLCI)-CO2PE! initiative (cooperative effort on process emissions in manufacturing). Part 1: Methodology description[END_REF], DAPhNE (Development of Adaptive ProductioN systems for Ecoefficient firing processes), EEM (Energy Efficient Manufacturing) or Factory Ecomation (Factory ECO-Friendly and energy efficient technologies and adaptive automation solutions). A second idea is to develop closed-loop (PLM) lifecycle concepts in the context of a dynamic supply chain (e.g. PROMISE [START_REF] Jun | Research issues on closed-loop PLM[END_REF]). The objective is to be able to identify, retrieve and reuse useful components of obsolete or dysfunctional equipment in order to reduce the environmental impact of the design and production of new equipment (e.g. SuPLIGHT project: Sustainable and Efficient Production of Lightweight Solutions). The place of humans in the new workshops is also studied, because it is necessary to design the future environments in which human operators and new technologies can evolve in total cooperation. The aim is to create human-centered production systems, as is clearly illustrated by the SO-PC-PRO (Subject-Orientation for People-Centered Production) project, to study the respective layouts of each element , with, for example, MAN-MADE (Manufacturing through ergonoMic and safe Anthropocentric aDaptive workplaces for context aware factories in Europe), and the whole virtual operator training phase, with VISTRA (Virtual Simulation and Training of Assembly and Service Processes in Digital Factories ).

Finally, the third axis of development aims at the agility of systems, i.e. collaborative, mobile, intelligent and adaptive systems. They are supposed to be able to change, reconfigure and evolve rapidly over time, depending on market demand. A lot of work is dedicated to the interoperability of these systems, in an open production context (e.g.

Computation Communication Control

Information systems

CPS CPPS

Intelligence

Connectedness Responsiveness

ACMN -Automation Competency Model Network or LinkedDesign -Linked Knowledge in Manufacturing, Engineering and Design for Next Generation Production), or to mass customization, from the workshops to the supply chain as for example in MIGOODS (Manufacturing Intelligence for Consumer Goods: Fit4U, SShoes, A-Footprint). Finally, the need for reconfigurable and flexible systems is expressed through concepts such as distributed intelligence, industrial agents or intelligent products. Projects such as ARUM [START_REF] Leitao | Multi-agent System Approach for the Strategic Planning in Ramp-Up Production of Small Lots[END_REF][START_REF] Stellingwerff | An Agent-Based Architecture to Model and Manipulate Context Knowledge[END_REF], PABADIS [START_REF] Lüder | Distributed intelligence for plant automation based on multiagent systems: the PABADIS approach[END_REF], GRACE [START_REF] Matthias | Implementation of a Methodology for Consideration of Product Quality within Discrete Manufacturing[END_REF] or ERRIC [START_REF] Giuseppe | A Low-Cost Control Architecture for User-Oriented Service Applications of Cassino Parallel Manipulator[END_REF] have shown great advances in the introduction of distributed / holonic / multi-agent technologies and paradigms in manufacturing control.

Framework items description

The core of the framework is to design a set of characteristics that are of interest for classifying the applications and implementations of CPPS in literature. To do so, one possibility was to analyze the main characteristics and objectives of global CPPS and deduce the criteria of the framework. Exploring this possibility resulted in various criteria that were not directly related to the developments of the CPPS, but rather on the methodology and objectives.

In this work, the different points of view of a CPPS application were analyzed, and some corresponding criteria were expressed. To do so, the three main basic capabilities of a CPS expressed by [START_REF] Klimeš | Using Formal Concept Analysis for Control in Cyber-physical Systems[END_REF] were adapted, namely Communication, Computation and Control (see Fig. 2) in addition to a global point of view on the application, as CPPS clearly inherit from CPS and therefore can be expressed through the same scope of basic capabilities:

• ▪ Criteria 7: human-machine interface. Fig. 3 represents a graphical view of the framework and shows how it inherits from the decomposition adapted from [START_REF] Klimeš | Using Formal Concept Analysis for Control in Cyber-physical Systems[END_REF] and presented before.

Fig. 3. Graphical expression of the framework

The following subsections detail these criteria.

Development extent

The first item to specify the CPPS developments is designed to indicate the extent to which the development was made. To this end, four different levels were specified:

• Lab XP: this level deals with Laboratory eXPeriments where technologies are developed and evaluated. This extent can be found currently for co-manipulation of robots, connectivity of CNC or development of new communication standards for PLCs, where the notion of collaboration is only evaluated at a quasisingle level; • POC: the Proof Of Concept level is dedicated for laboratory setups including the notion of collaboration between CPPS and a behavior close to the one that could be found in an industrial context. This level is currently representative of the large-scale demonstrators that can be found in [START_REF] Cardin | Proactive production activity control by online simulation[END_REF][START_REF] Dubromelle | RFID synchronisation for ambient services in a holonic and isoarchic control model[END_REF][START_REF] Sallez | Semi-heterarchical control of FMS: From theory to application[END_REF][START_REF] Pujo | Wireless Holons Network for Intralogistics Service[END_REF][START_REF] Gamboa Quintanilla | Evolution of a Flexible Manufacturing System: From Communicating to Autonomous Product[END_REF] for example; • Industry: the objective of these applications is to reach the industrial application level, where actual developments are made on a running production system. At this level, coherent performance evaluation can be made and feasibility purposes can be identified; • Learning factory: one of the biggest challenge that will face industry when CPPS-based manufacturing systems will be extensively available will be to have engineers and technicians trained to work in full cooperation with those kind of systems. This is why, as soon as possible, Learning Factories need to be developed in order to foresee the arrival of CPPS technologies on the market.

Research axis

Considering the analysis that was developed in section 2, this item is meant to indicate what is the aspect of CPPS evolution the development emphasizes the most. As suggested and analyzed in [START_REF] Cardin | Future Industrial Systems: Best Practices of the Intelligent Manufacturing and Services Systems (IMS2) French Research Group[END_REF], the considered level for this item for the time being are:

• Agility;

• Technology; • Sustainability. However, this list is meant to evolve in the next few years with the resolution of some of the issues and the creation of new research items. For example, it is clear that the current development are specifically focused on providing additional functionalities to CPPS comparing to traditional manufacturing systems. However, in the next few years, economic questions about cost (implementation and exploitation) and productivity of these systems will probably occur.

Communication standards

The mutation in the high-level control architecture of production systems brings about potentially significant changes in the technology of the production systems themselves. The control of production machines is currently at a very low semantic level, often of the order of bit or word, via communication protocols inherited from industrial local networks developed in the last 40 years.

From our perspective, the constraints requiring the use of such protocols are not justified throughout the workshop. Indeed, their first quality is the determinism of their behavior, which imposes constraints on the volume of data exchanged so as not to saturate the network. However, while some functions require this determinism and a certain notion of real-time within the control, other coordination functions do not have this need: this aspect is often referred to as real-real-time (near real-time) in the literature. While some cloud-based work proposes PLC-free control architectures, we propose rather a technological breakdown according to the objectives and constraints of each part of the system. Figure 4 provides an example of an instantiation of the SoHMS model deployed in the cloud presented in [START_REF] Gamboa Quintanilla | A modeling framework for manufacturing services in Service-oriented Holonic Manufacturing Systems[END_REF]. It is very clear that robots always need a controller, just as it seems unreasonable to completely remove controllers as close as possible to sensors and actuators in the case of high-speed production systems. Moreover, it is possible to consider that some systems, controlled by separate systems (two systems, each with an API, for example) need a lowlevel communication medium as described above. The level of atomic aggregation of the CPPS is generally considered as the element of the system which cannot be dissociated without altering its communication performance with the other CPPS. In the case presented earlier, the proposed CPPS would encompass both systems as if they were one. Thus, the communication between CPPS would be only in soft real-time, which makes it possible to envisage communications at higher semantic level, in particular by using Service-oriented Architectures [START_REF] Alho | Service-oriented approach to fault tolerance in CPSs[END_REF].

Figure 4 Example of instantiating the SoHMS architecture in a cloud context [START_REF] Gamboa Quintanilla | Implementation framework for cloud-based holonic control of cyber-physical production systems[END_REF] The major development axis still to be studied at the technological level corresponds to the SIL layer presented in Figure 4. Through this architecture, the transition between the services resulting from the cloud and the communication protocol accepted by the low-level entities must be realized. The aim is to propose an open protocol allowing to minimize or even eliminate this transition by increasing the semantic level accepted by the entities at their superior interface. It is therefore necessary to develop PLCs, robot controllers or service-oriented CNC machines, not only in their communication, but also in the parameterization of the programs executed on these elements. Indeed, at the programming level, new elements have to be proposed in order to simplify the modularity of the programs and their reusability. At the communication level, attempts at solutions have already been proposed, proprietary such as OPC-UA [START_REF] Domingues | Building automation systems: Concepts and technology review[END_REF] or not such as MSB (Manufacturing Service Bus) [START_REF] Morariu | Manufacturing Service Bus Integration Model for Highly Flexible and Scalable Manufacturing Systems[END_REF], but their integration with the concept of services remains to be studied and developed.

The current item aims at indicating which communication protocols are used:

• If available in the lower level, close to the machines; • If available in the higher level, close to the cloud or enterprise information systems;

• If necessary, the protocols matching the communication between the lower and the higher levels.

Intelligence deposit

The notion of CPPS encompasses a wide variety of control architectures, having the common feature to avoid the rigid hierarchy that can be currently encountered very frequently. In those so-called heterarchic architectures [START_REF] Sallez | Product-based and resource-based heterarchical approaches for dynamic FMS scheduling[END_REF], the notion of intelligence is widely distributed within the whole system, even if a centralized coordination is still present. This presence can dynamically evolve throughout the life of the system, considering the disturbances occurring during the production [START_REF] Jimenez | Pollux: a dynamic hybrid control architecture for flexible job shop systems[END_REF].

Nevertheless, this classification item is meant to represent the location where the intelligence of the system is distributed. The most common levels this item can have are:

• Machines: the most common decentralization of intelligence currently found in literature deals with the enhancement of machines' abilities in terms of decision making. The machines are for example able to negotiate and establish their own planning in order to decide whether they accept the contract to be established by an order [START_REF] Gamboa Quintanilla | A Petri net-based methodology to increase flexibility in service-oriented holonic manufacturing systems[END_REF]; • Products: many works in the last decade were focused on the activity of the product all along the production phase [START_REF] Sallez | Proposition of an Analysis Framework to Describe the "Activeness" of a Product during Its Life Cycle[END_REF][START_REF] Sallez | The Lifecycle of Active and Intelligent Products: The Augmentation Concept[END_REF][START_REF] Sallez | A stigmergic approach for dynamic routing of active products in FMS[END_REF]. Meanwhile, several parallel directions lead to the concept of "Intelligent Product" [START_REF] Herrera | A viable system model for product-driven systems[END_REF][START_REF] Huet | A new reengineering methodology for the product-driven system applied to the medication-use process[END_REF][START_REF] Pannequin | Another interpretation of stigmergy for product-driven systems architecture[END_REF][START_REF] Trentesaux | Intelligent products: a spinal column to handle information exchanges in supply chains[END_REF][START_REF] Trentesaux | Product-Driven Control: A State of the Art and Future Trends[END_REF], where the product was the trigger and a true actor of the all the decisions that were dynamically taken during the production thanks to storing and processing capabilities that are physically implemented on the product himself. This concept is now globally replaced by a more cooperative one, where the product can still be a carrier of information or of some distributed intelligence, but is rarely alone in the system. • Transport: In many applications, part of the intelligence is distributed among the resources enabling the products to be conveyed from one machine to another, may it be using AGVs [START_REF] Demesure | Navigation Scheme with Priority-Based Scheduling of Mobile Agents: Application to AGV-Based Flexible Manufacturing System[END_REF] or conveyors [START_REF] Gamboa Quintanilla | Evolution of a Flexible Manufacturing System: From Communicating to Autonomous Product[END_REF][START_REF] Berger | Personal Rapid Transit in an opencontrol framework[END_REF] for example; • Digital twin: For some applications, the intelligence is not physically implemented in the machines, products or any other assets of the system, but is directly connected to a digital twin of these entities [START_REF] -J. Uhlemann | The Digital Twin: Realizing the Cyber-Physical Production System for Industry 4.0[END_REF]. This aspect of intelligence is especially relevant when the products cannot be physically equipped with network adaptor, data carriers or data process units or if the legacy systems that are actually used are not yet able to implement those elements.

Cognition level

Such abilities are often referred as self-adaptation, self-organization or more generally self-* abilities [START_REF] Leitao | Self-Adaptation for Robustness and Cooperation in Holonic Multi-Agent Systems[END_REF]. The objective of this criterion is to evaluate the degree of maturity of the development regarding cognition. A classification of CPS in five categories (5C) according to the level of integration it offers was presented in [START_REF] Lee | A Cyber-Physical Systems architecture for Industry 4.0-based manufacturing systems[END_REF] and can be extended to CPPS. This classification was chosen for the pertinent graduation it offers, and is getting more and more attention from the community [START_REF] Ahmadi | A Review of CPS 5 Components Architecture for Manufacturing Based on Standards[END_REF]. It can be described in the following way:

• C1. At Connection level, CPPS operate on a Plug&Play network and use data provided by sensors on the network;

• C2. At Conversion level, CPPS process data and aggregate them in a higher semantic level;

• C3. At Cyber level, CPPS can apprehend other CPPS and their environment and can interact with them in order to enrich their own data processing; • C4. At Cognition level, CPPS are able to process data in order to diagnose their own state, based on simulations and a differential analysis of sensors data; • C5. At Configuration level, CPPS shall adapt on their own facing disturbances, reconfigure or adjust their parameters in an autonomous way in order to get back to a nominal behavior as soon as possible.

This classification was initially introduced in order to provide a step by step CPPS deployment tutorial, from sensing functionalities to functions creating more added value. The total integration of these 5 levels in a CPPS is currently extremely rare and might not be pertinent in any situations. We suggest in this article to extend the use of this functional decomposition and use it in order to evaluate the level of autonomy and intelligence embedded in a given CPPS. This constitutes the cognition-oriented criterion of the framework that we suggest to define (C1 to C5).

Pervasive Instrumenting

One of the core notions of CPS, and therefore of CPPS, is the notion of connectivity to its environment. Indeed, those systems are meant to be able, at a high degree of changeability, to sense the evolution of their direct environment and make their own behavior evolve in consequence, by themselves or via a negotiation with the other elements of the CPPS. This is one of the main notions that make the design of CPPS different and difficult to apprehend.

Even if this is not quite yet fully implemented in CPPS, it is necessary to anticipate the next step of CPPS development, which will be able to take into account more numerous and more complex data, including data coming from various sensors and sources in its environment. Currently, RFID tags and readers, enabling the identification of the moving elements throughout the system are the main equipment that are implemented in the large applications [START_REF] Leitão | Intelligent products: The grace experience[END_REF]. For smaller ones, such as Lab XP for example, some sensors start to be implemented benefiting from the advances in the field of the Internet of Things for example [START_REF] Ahuett-Garza | A brief discussion on the trends of habilitating technologies for Industry 4.0 and Smart manufacturing[END_REF].

HMI: Human-Machine Interaction

The objectives of systems integration evolved in the last few years, shifting from a model where the system was intended to adapt automatically and be equipped with reasoning and decision making capabilities aiming at replacing human ones to a model where CPS are focusing on use scenarios fully involving the humans. Two possible scenarios [START_REF] Dworschak | Competences for Cyber-physical Systems in Manufacturing -First Findings and Scenarios[END_REF] were specifically designed.

In the first one (called Automation scenario), the human is guided by the CPS, i.e. the global decision making process is performed by the CPS and the human executes the operation in itself. It is also a human that is responsible of the implementation and maintenance of the CPS. In a manufacturing context, his scenario corresponds roughly to an online and pulled flow oriented transposition of the classical functions of planning and scheduling that can be encountered currently. This scenario is intended to fit well to the workshops implying a heavy manual duty in a manufacturing environment targeting a high flexibility.

Second scenario (Tool scenario) emphasizes the human in the core of the decision loop. The idea is to make the CPS being guided by a human initiated to the cooperation with the CPS, but still actively assisting the human in the decision making process. This scenario intends to fit the activities in which operations are partially or fully automated, but where the operator's expertise brings a significant contribution notably in terms of agility and quality enhancement.

In both first and second scenario, it is the combination between calculation abilities of CPS and communication with human capacities that enable the enhancement of the performance of the cooperation system. Frameworks such as HilCP²SC (Human-in-the-Loop Cyber-Physical Production Systems Control) are being developed [START_REF] Gaham | Human-in-the-Loop Cyber-Physical Production Systems Control (HiLCP2sC): A Multi-objective Interactive Framework Proposal[END_REF], in order to offer the possibility to integrate the preferences of the human in a multi-objective decision making context led by the CPS. More than a framework, it is probably necessary to modify the (manufacturing) distributed systems design paradigm, using CPS reference models that need to be anthropocentric, such as those suggested by [START_REF] Zamfirescu | Human-centred Assembly: A Case Study for an Anthropocentric Cyber-physical System[END_REF] or [START_REF] Pirvu | Engineering insights from an anthropocentric cyber-physical system: A case study for an assembly station[END_REF] for example. Whatever the scenario, a significant evolution of the tasks, qualifications and skills of the human operators in charge of the cooperation with the CPS [START_REF] Dombrowski | Mental Strain as Field of Action in the 4th Industrial Revolution[END_REF] is foreseen. Therefore, basic and professional trainings of those operators needs to adapt in order to give them the keys to efficiency in a problem resolution process, to have a more accurate conscience of process interdependencies of which they are a link and to be able to take regulated initiatives for self-organization in case of disruptions occurring in the nominal working of the system.

As it can be noticed, the CPS-Human integration is of a great matter, and considers a whole scope of situations, from the most automated ones to the most manual ones. In production systems, The same scope of situations exist, and can be characterized in the same way, although some of them are not so much disseminated for the time being. Therefore, considering this criterion, a larger list was induced from the levels suggested by [START_REF] Dworschak | Competences for Cyber-physical Systems in Manufacturing -First Findings and Scenarios[END_REF] and applied to CPPS:

• Full : the human only has a role of supervision of the CPPS, which is able to take all the necessary decisions without any intervention of the human; • Automation: the CPPS guides the human during its task by taking most of the decisions and leaves the functions of adaptation to the human; • Tool: the human guides the CPPS and is in charge of most of the decisions;

• Manual: CPPS only provides data to the human, who is in charge of all the decisions.

Example of application of the framework to a subset of current literature

The objective of this article is to introduce an innovative framework enabling the classification of cyber-physical production systems developments in literature in order to identify either the convergence between the different authors or the leads that were not explored for example. In this section, a short example of use of the framework and a preliminary analysis is performed in order to illustrate the benefit of such a framework for future potential users.

The focus of this analysis was chosen on the Agility axis. As stated before, the concept of CPPS inherits from many older fields of research, among which Intelligent Manufacturing Systems, Reconfigurable Manufacturing Systems, Holonic Manufacturing Systems, Industrial Agents. Most of these fields are targeting the Agility axis, which explains why many of the early developments of CPPS available in literature are related to this axis. This analysis was oriented towards identifying the relationship between the extent of the developments and both the cognition level of the proposed solution, which is closely related to its intelligence, and the interaction with humans.

Analysis grid of current literature regarding Agility

The articles exposed in this section are representative of the current developments currently available in literature and specifically addressing the concept of CPPS, restricted to those aiming for the Agility axis. It is obvious that a lot more applications can be encountered without clearly addressing the notion of CPPS, but these are not included in the limits of this analysis. Table 1 positions some of the most recent articles in the field relatively to all the items expressed before. The columns represent in the same order the items described in the previous section contained in the framework. 1 exhibits some values of those criteria that are not really consistent. Indeed, considering the communication protocols for example, some of them belong to the same class, while others can run on top of the rest. This apparent confusion in the list is mainly due to the lack of information that is present in the examined articles. This lack of information is a true handicap for the readers who are potentially interested in implementing its own CPPS, as this is an important matter. The same reasoning fits to the Instrumenting criterion.

The framework introduced above aims at emphasizing these criteria in order to encourage the publication of such data and disseminate the good practices in literature.

Using the framework to draw preliminary conclusions on CPPS developments targeting Agility

First conclusion that can be drawn from this table is the high density of applications between C1 and C3 (see also Table 2). Globally, it was expected to encounter relatively few applications with C5 abilities, as these cover at the time being more perspectives than actual possibilities. However, the low presence of C4 levels is surprising in manufacturing comparing to fields of application like Infrastructure [START_REF] Wang | An Integrated Scheme for Cyber-physical Building Energy Management System[END_REF] or Transportation [START_REF] Le Mortellec | Embedded holonic fault diagnosis of complex transportation systems[END_REF] for example. This can be explained by the late appropriation of the concept by manufacturing, and the high inertia of the field of application due to the current limitations of high cost hardware that is not suitable for the full integration of high cognition levels.

Most of the listed applications are currently Lab XP, which is coherent with the global state of the art. However, some POC and industrial applications are rising, which is an interesting indicator for the future developments of literature. The important presence of Learning factories is interesting, as it shows a great interest of the community towards this difficult question of training.

Crossing these criteria in Table 2 exhibits a major axis of research that is still not explored considering levels C3, C4 and C5 of cognition, even in laboratories. The current developments in artificial intelligence are probably an interesting lever for enhancing the cognition level of the various applications. [START_REF] Ahuett-Garza | A brief discussion on the trends of habilitating technologies for Industry 4.0 and Smart manufacturing[END_REF][START_REF] Gaham | Human-in-the-Loop Cyber-Physical Production Systems Control (HiLCP2sC): A Multi-objective Interactive Framework Proposal[END_REF][START_REF] Horstkemper | Employing Order Allocation Flexibility in Cyber-physical Production Systems[END_REF][START_REF] Otto | Why Cyber-physical Production Systems Need a Descriptive Engineering Approach -A Case Study in Plug & Produce[END_REF][START_REF] Rojas | Enabling Connectivity of Cyber-physical Production Systems: A Conceptual Framework[END_REF][START_REF] Merkel | Teaching Smart Production: An Insight into the Learning Factory for Cyber-Physical Production Systems (LVP)[END_REF][START_REF] Wang | Current status and advancement of cyber-physical systems in manufacturing[END_REF] After several decades of questions about the best network standards to be used in manufacturing context, classical TCP/IP (wireless or not) is now globally used for the high-level communications level. For low-level ones and the interconnection between them, the studied articles rarely give the implementation details. We hope that this framework could encourage the future authors to exhibit their communication infrastructure in order to help the community reaching a consensus. The most promising leads at the time being is probably the introduction of OPC UA or AutomationML [START_REF] Monostori | Cyber-physical systems in manufacturing[END_REF], which exhibits some service-oriented characteristics that fit well the objectives of initiatives such as Industry 4.0.

What can be finally noticed is the lack of references in Automation and manual modes (see Table 3). The Lab XP for example are generally oriented either on a fully automated system, which seems logical considering the availability of humans for experimentations, but when a human is in the loop, then it is to be in charge of the decisions (Tool mode). Considering the Automation mode, one possibility is that such a mode requires the human to trust the CPPS, which might not be the case at the time being. However, it does not presume of the future applications which might implement massively this mode.

Conclusion

This article introduces a new analysis framework for classifying Cyber-Physical Production Systems applications relatively to various items, including their cognitive abilities, their application extent, the interaction with human operators, the distribution of intelligence and the network technologies that are used. This framework was described and applied to several examples retrieved from literature. From the grid extracted from this analysis, several conclusions are drawn for each encountered application domain, noticing that this framework globally fits the main trends that can be spotted in each specific field.

This framework is meant to be the basis of future classification of future CPPS developments for researchers and practitioners in the field. The objective is to use such a classification in order to ease the relative positioning of those developments and foster their visibility towards a larger audience.

The main perspective about the use of the framework deals with its maintainability, notably considering the technological developments that might occur and modify the perception of the concept. This perspective might be incorporated by the future users of this classification in order to create new levels or even new items so that the framework fits at best the future developments.

Table 1 .

 1 Agility oriented application of the framework example

	Reference Extent	Axis	Communication Intelligence Cognition Instrumenting	HMI
	[23]	Lab XP Agility TCP/IP & USB	Machines	C2	Sensors	Full
	[26]	Lab XP Agility	TCP/IP	Machine	C2	Sensors	Tool
	[81]	Learning Factory	Agility	RFID	Products machines and	C1	Sensors	Tool
	[82]	Lab XP Agility	TCP/IP	Machines	C2	Unknown	Tool
	[83]	Lab XP Agility	TCP/IP	Products digital twin	C2	Unknown	Full
	[84]	Learning Factory	Agility	TCP/IP	Products and machines	C3	RFID & sensors	Automation
	[85]	Lab XP Agility	PROFINET	Central	C1	Sensors	Full
	[86]	POC	Agility	TCP/IP	Machines	C2	Sensors	Full
	[87]	Learning Factory	Agility	TCP/IP	Central	C1	RFID	Manual
					Machines
	[88]	POC	Agility	TCP/IP	and	C2	Sensors	Tool
					Transport
	[89]	Lab XP Agility	TCP/IP	Machines	C2	RFID & Sensors	Tool
	[90]	Lab XP Agility	TCP/IP	Machines	C1	Sensors	Tool
	[91]	Lab XP Agility	TCP/IP	Digital Twin	C2	Sensors	Full
	[38]	Lab XP Agility	OPC UA	Central	C1	Sensors	Full
	[92]	Lab XP Agility	RS232	Digital Twin	C1	Sensors	Full
	[93]	POC	Agility	Wifi	Machine	C2	Sensors	Tool
	[11]	Lab XP Agility	TCP/IP	Machine	C2	Sensors	Full
	[94]	Industry Agility	Wifi	Machine	C3	Sensors	Tool
	[95]	POC	Agility	Ethernet	Machine	C2	RFID	Tool
	[96]	POC	Agility	Ethernet	Machine	C2	RFID	Tool

Preliminary remarks regarding Instrumenting and Communication protocols

  Looking at Table1, first elements that can be emphasized concern the characteristics with an open choice. Instrumentation devices and communication protocols are indeed connected to technological aspects, that cannot be listed exhaustively at a given time.Table

Table 2 .

 2 CPPS developments positioning relatively to cognition and development extent Lab XP[74, 79, 81, 82] [9, 21, 24, 71, 72, 78, 80, 89, 90] POC

	Cognition level /	C1	C2	C3	C4	C5
	CPPS Extent
	Industry			[84]
	Learning Factory	[70, 76]		[73]

Table 3 .

 3 CPPS developments positioning relatively to human-machine interaction and development extent

	HMI /	Manual	Tool	Automation	Full
	CPPS Extent
	Industry		[84]
	Learning Factory	[76]	[70]	[73]
	Lab XP		[24, 71, 78, 79, 89, 90]		[9, 21, 72, 74, 80, 81, 82]
	POC		[77, 83, 85, 86, 87, 88]		[75]

http://www.nsf.gov/

6

References


Olivier Cardin

DETERMINATION OF AN EMPIRICAL MODEL OF AVERAGE RANK FOR MULTI-DEEP AS/RS BASED ON SIMULATION Latéfa Ghomri

We consider in this paper multi-deep automated storage/retrieval systems, where the cells capacity is strictly greater than one load. The main advantage of this class of AS/RS is a better use of space. Its main drawback is that, in order to retrieve a desired load, it is necessary to move all the loads in front of it. This is a common characteristic of all the multi-deep automated storage/retrieval systems. The number of loads to move is given by the rank of the load to retrieve. The mean value of the average access time to a given load is an important performance index for the design of such systems. This time depends on several parameters among which the average retrieval rank is the hardest to compute. It is still an open problem, even with random storage and retrieval heuristics. In this paper, our objective is to provide an empirical formula of the average retrieval rank in a multi-deep automated storage/retrieval system with random heuristics for both storage and retrieval. With this formula, it is then easy to deduce the mean retrieval time. This computation is based on multiple simulations of various AS/RS models and a regression on the obtained data. The particular case of the flow-rack automated storage/retrieval system will be considered to illustrate our contribution. It will then be possible to use this formula for other multi-deep systems.

1

INTRODUCTION

Typically, an Automated Storage/Retrieval System (AS/RS) consists of storage racks, S/R machines and pickup/drop-off (P/D) stations. They are generally classified according to their physical configurations; namely:

1. The number and capacity of S/R machines, 2. The arrangement of racks and aisles in the system, 3. The position of P/D stations, 4. The depth of racks, i.e., the maximum number of loads that could be stored in a cell.

In this paper, we consider the class of multi-deep AS/RS, also called compact AS/RS, high-density AS/RS or 3D AS/RS. Although the application of multi-deep AS/RS is still limited, they have become increasingly popular. The main particularity of this class is that the capacity of a cell (the maximum number of loads that could be stored in the same cell) is strictly greater than one load. which significantly reduces the amount of floor space. Each storage cell is independently accessible, and so any load can be stored in any storage cell. Both sides of a cell are accessible either by the same Storage/Retrieval (S/R) machine or by different S/R machines. This allows to move: (1) loads to store from the pickup/deposit stations to cells, and (2) loads to retrieve from cells to the pickup/deposit stations.

In order to explain the contribution of this paper, it is important to point out the retrieval mechanism. When the load of rank m has to be retrieved, the (m -1) preceding loads must retrieved first and stored again. The movement of these other loads here is called relocation. The operation of relocation is a part of the retrieval operation, which means that, in order to express the retrieval time of a given load, it is necessary to express the number of relocation operations to be carried out during the retrieval operation. Consequently, the rank in which the desired load is located (m) must be determined.

Obviously, a smart storage of an AS/RS improves its performance (like the mean access time). This is all the more true for multi-deep AS/RS, since the access time to a given load depends on the number and types of loads that precede it. Several works that propose storage heuristics for multideep AS/RS systematically compare the performances of the proposed heuristics with the performances of a random storage [START_REF] Cardin | Performance Evaluation of In-Deep Class Storage for Flow-Rack AS/RS[END_REF]; Le-Duc and De Koster 2007), as random storage is considered as the worst storage heuristic and therefore its performance as a classical lower bound. The purpose of this paper is to introduce a new way to evaluate this lower bound, using a calculation rather than a simulation study as commonly performed. This is meant to avoid the development of such model, which is generally time consuming. To achieve this objective, the last parameter to determine is the mean retrieval time, as expressed before. As a matter of fact, The main aim of this paper is to propose an empirical model, developed via simulation, of the average rank 𝑚 𝑖 of a load of type i, whose proportion in the system is 𝛼 𝑖 .

This paper is organized as follows: Section 2 gives a brief literature review on multi-deep AS/RS, section 3 presents a description of one kind of multi-deep-AS/RS, flow-rack AS/RS. Section 4 gives the analytic formula of the average retrieval time in the case of flow-rack AS/RS, that highlights the critical parameter considered here. Section 5 describes the simulation approach, while section 6 computes the average rank analytic formula using the simulation results. Finally, in section 7, we compare the results of the proposed empirical model to the performances obtained by simulation.

LITERATURE REVIEW

We will present in the following some of the works related to multi-deep AS/RS. [START_REF] Ghomri | Travel Time Models for Double-Deep Automated Storage and Retrieval Systems[END_REF] suggested analytic travel time models for the computation of single and dual cycle times for unit-load double-deep automated storage and retrieval systems. [START_REF] Le-Duc | Travel Time Estimation and Order Batching in a 2-Block Warehouse[END_REF] developed an optimization method to determine the average throughput time for an order-batching problem in a 2-block rectangular warehouse; they applied the well-known method of S-shape heuristic. [START_REF] Yu | Designing an Optimal Turnover-Based Storage Rack for a 3D Compact Automated Storage and Retrieval System[END_REF] derived the expected single-command cycle time under the full turnover-based storage policy and developed a model to determine the optimal rack dimensions by minimizing the cycle time. They simplified the model, and analytically determined the optimal rack dimensions for any given rack capacity and any ABC curve skewness. They proved that the cycle time was significantly reduced as compared to a random storage strategy. [START_REF] Sari | Travel-Time Models for Flow-Rack Automated Storage and Retrieval Systems[END_REF] considered the flow-rack AS/RS, which is a special configuration of multi-deep AS/RS, to see whether it can be used for the storage of a large number of load types, by using intelligent heuristics for storage and retrieval processes. [START_REF] Bessenouci | Metaheuristic Based Control of a Flow Rack Automated Storage Retrieval System[END_REF] considered metaheuristics based control of flow rack AS/RS. They investigate the scheduling of retrieval request to minimize the system response. [START_REF] Sari | Design & Modeling of a Single Machine Flow Rack AS/RS[END_REF] designed a new physical flow-rack AS/RS configuration and modeled the mean travel time of an S/R single machine. In the configuration they proposed, cells have a U form and are divided in segments; each segment is used for the storage of one unit. A single load is conveyed by a powered conveyor from the input side to the output one. For this same physical configuration, [START_REF] Hamzaoui | Optimal Dimensions Minimizing Expected Travel Time of a Single Machine Flow Rack AS/RS[END_REF] determined the optimal dimensions, i.e., the dimensions that minimize the mean retrieval time. Traditionally, bins slope in the same direction in a flow-rack in order to make unit-loads slide from the storage face to the retrieval face driven by gravity. Unit-loads are then stored to the storage face and retrieved from the retrieval face. [START_REF] Chen | A Bi-Directional Flow-Rack Automated Storage and Retrieval System for Unit-Load Warehouses[END_REF] designed a new configuration of flow rack AS/RS in which bins are bidirectional, i.e. in adjacent columns slope to opposite directions. They developed a travel time model for the configuration they suggest. [START_REF] Liu | Travel Time Model of a New Compact Storage System[END_REF] studied a new configuration of multi-deep AS/RS. This last is composed of several aisles, each aisle is served by one S/R machine. The cells are equipped by conveyors. When a given load needs to be retrieved, the S/R machine makes the horizontal and vertical movements and the conveyor of the cell makes the movement in depth. For this AS/RS, the authors develop an analytic model and present the minimum travel time for given dimensions. [START_REF] Fan | Travel Time Model of the Storage/Retrieval Machine for Multi-Deep AS/RS Based on Flexsim[END_REF] study the travel time of the S/R machine in multi-deep AS/RS based on simulation methods. A flexible model of multi-deep AS/RS with 3600 kinds of plans has been built and simulated by the authors, aiming at the S/R machines travel time. They thus obtained a large number of simulation data, which were then used in the multiple regression analysis. The fitting formulas of the S/R machines travel time has been finally built.

However, we consider here the flow rack AS/RS, which is a special physical configuration of multideep AS/RS, the average rank model we develop here can be used to express the average retrieval rank of any physical configuration of multi-deep AS/RS.

FLOW RACK AS/RS DESCRIPTION

As shown in Figure 1, flow-rack AS/RS is composed of only one multi-deep rack, consisting of a set sloping cells. Each cell can contain several loads placed one after the other. Each cell is equipped with a gravity conveyor based on rollers or freewheels inclined in such a way as to allow the loads to slide from one end of the cell to the other, and therefore from one side of the rack to the other. The items are loaded on one end of the rack, i.e. the storage face. They slide on the gravity conveyors to the other end of the rack, i.e. the retrieval face. The retrieval machine withdraws the item from the retrieval face during the retrieval process. The storage and retrieval machines travel on parallel x-y planes to reach any cell on the rack. A drop-off station and a pickup station are located at the storage face and retrieval face of the rack, respectively. A restoring conveyor links the retrieval and storage machines, as shown in Figure 1. In the case of unit-deep AS/RS, modelling average retrieval time is a rather easy problem, since all items are on the front side of the system. In multi-deep AS/RS, as flow rack AS/RS, the retrieval process is more complex to compute. The same cell is used for the storage of different types of loads with different proportions. The retrieval of an item often requires the retrieval of all the items that precede it.

Ghomri and Cardin

To retrieve an item, the retrieval machine starts by transporting, one by one, all the items that precede it in the cell, to the front end of the restoring conveyer. This last carries the items from the retrieval face to the storage face, so that the storage machine stores them again in the rack. The storage and retrieval machines move simultaneously in the horizontal and vertical directions. These movements known as Tchebychev moves allow a faster machine operation.

AVERAGE RETRIEVAL TIME IN A FLOW RACK AS/RS

In this section, we detailed the computation process of the average retrieval time. This will show the importance of the rank parameter.

Consider the retrieval time of the item stored in the rank number m of the cell whose time coordinates (X, Y). Figure 2.a shows the flow-rack AS/RS retrieval face. This face has 3 important stations, which are:

1. The dwell position of the retrieval machine located at the center of the retrieval face. 2. The AS/RS drop-off station located at the lower left-hand corner of the face. 3. The front end of the restoring conveyer located at the lower right-hand corner of the face.

Figure 2.b shows a column (a set of cells arranged one on the other) from the rack of a flow-rack AS/RS. Retrieving the item stored in the segment number m, requires from the retrieval machine to remove, one by one, all the items stored before it, i.e. the items stored in the segments from 0 to m -1, until the desired item reaches the first segment (number 0) on the retrieval face of the rack. After this, the retrieval machine retrieves it.

The retrieval machine performs three elementary travels when retrieving an item (Figure 2.a):

• 𝐸 1 𝑅 is the travel time from the dwell point of the retrieval machine to the backside of the cell containing the desired item; during a retrieval operation the machine makes the travel 𝐸 1 𝑅 once. • 𝐸 2 𝑅 is the travel time from the front end of the restoring conveyor to the cell containing the desired item; during a retrieval operation the machine makes this travel once.

• 𝐸 3 𝑅 is the travel time from the drop-off station to the cell containing the desired item; during a retrieval operation the machine makes this travel 2m times; where m is the segment containing the desired item.

The time required to retrieve the item stored in the cell (X, Y) and in segment m can be expressed as follows:

𝐸 𝑅 = 𝐸 1 𝑅 + 2𝑚𝐸 2 𝑅 + 𝐸 3 𝑅 (1)
Since the variables m and 𝐸 2 𝑅 are independent, we can write:

𝑚𝐸 2 𝑅 ̅̅̅̅̅̅ = 𝑚 ̅ 𝐸 2 𝑅 ̅̅̅̅ (2)
The average value of 𝐸 𝑅 is calculated as follows:

𝐸 𝑅 ̅̅̅̅ = 𝐸 1 𝑅 ̅̅̅̅ + 2𝑚 ̅ 𝐸 2 𝑅 ̅̅̅̅ + 𝐸 3 𝑅 ̅̅̅̅ (3)
In equation ( 3) 𝐸 1 𝑅 , 𝐸 2 𝑅 and 𝐸 3 𝑅 are time variables that depend on the physical dimensions of the flow rack AS/RS, whereas 𝑚 is an integer variable that depends on rate of existence of the item in the rack. It also depends on the number of loads in the system.

Ghomri and Cardin

The analytic computation of the average movement times 𝐸 1 𝑅 ̅̅̅̅ , 𝐸 2 𝑅 ̅̅̅̅ and 𝐸 3 𝑅 ̅̅̅̅ is well solved in the literature. The retrieval face of the rack is approximated by a continuous face. It was used by [START_REF] Bozer | Travel-Time Models for Automated Storage/Retrieval Systems[END_REF] to model the average travel time for unit load AS/RS and by [START_REF] Ghomri | Expression Analytique Du Temps de Cycle Pour Les AS/RS Multi-allees[END_REF] to model the average travel time in multi aisle AS/RS. [START_REF] Sari | Travel-Time Models for Flow-Rack Automated Storage and Retrieval Systems[END_REF] model the average travel time in the case of flow rack AS/RS under the assumption that the rack is used for the storage of a very large number of different types of loads. However, the parameter m remains to be computed.

Ghomri and Cardin

• 𝛼 𝑖 : the proportion of the load of type i in the AS/RS, it is given by the ratio of the number of loads of type i present in the system out of the total number of loads present in the system.

As shown in Figure 1, M represents the total number of segments in a cell. Then M corresponds to the mean number of items in cells. It is the first parameter in the computation of the average rank. The second parameter is 𝛼 𝑖 , it identified the product i. Performing simulations, these two parameters were found as the basic terms for the determination of 𝑚 𝑖 ̅̅̅̅, It is why our set of simulations is structured with two inputs (𝑀, 𝛼 𝑖 ) and on output the average rank 𝑚 𝑖 ̅̅̅̅.

The input 𝑀 varies from 1000 to 19000 every 1000, while 𝛼 𝑖 varies from 5% to 100% each 5%. This set of data generates 340 experiments, with various physical configurations of the rack. To cope with this set, a Rockwell Arena simulation model was created, able to generate automatically the number of cells given in a configuration file. A Microsoft Excel file was used in order to handle the set of inputs, generate the configuration file, run the model and retrieve the simulation results. This process is detailed in the sequence diagram of Figure 3. The queues creation is made in the "Runbegin" phase, i.e. before the compilation of the model. The assignment of the parameters of the simulation run is made in the "RunBeginReplication" phase, i.e. just after the compilation. The result (𝑚 𝑖 ̅̅̅̅) is estimated via a VBA procedure, calculating, for each cell containing a load i, the average value of the first occurrence of such a load in the cells. With this procedure, the simulation model in itself is extremely simple, as it is only used to store the loads in the random cells. As a matter of fact, the simulation run ends when all the loads are stored.

Running with multiple replications was chosen in order to deal with the re-initialization of random distributions. The sequence diagram of Figure 3 )Ghomri and Cardin correct number of simulations to define in the previous process. To do so, three physical configurations of racks were created: (1000 cells of 50 segments), (100 cells of 25 segments) and (25 cells of 10 segments) corresponding to a huge, an intermediate and a small rack. For each configuration low and high  (0.1 and 0.9) and 𝛼 𝑖 (0.1 and 0.5) were tested in a set of 6 configurations. For these 6 configurations, the same random heuristics were simulated on 5, 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100 replications. Considering that the highest NREP provides more accurate results, we chose to express the obtained results in the form of the error relative to the average of the values obtained for NREP=80, 90 and 100. The results are shown in Table 1. Configurations providing less than 1% error are highlighted in green. The table clearly shows that the reliability problems occur most often with small racks, which is quite logical as the number of loads is lower than in bigger configurations. In order to be secure the process, we chose to run systematically replications.

ANALYTIC DETERMINATION OF THE AVERAGE RANK

From the set of data obtained by simulation as explained above, we used regression techniques in order to obtain an analytic formula of the average rank. The general solution is complex and not unique. It depends strongly on the parameter 𝛼 𝑖 , it is why we present a set of solutions function of the range of 𝛼 𝑖 .

We have considered 3 intervals for this parameter.

1) 𝛼 𝑖 close to 0:

We represent hereafter, using the software Maple the set of points obtained by simulation. Each point gives 𝑚 𝑖 as a function of 𝜌𝑀 and 𝛼 𝑖 . From Figure 4, we can observe that for 𝛼 𝑖 close to 0, which means that there are very few loads of type i in the system, 𝑚 𝑖 has an inclined straight line. Intuitively, in this situation, the load of type i will be retrieved from the middle of the full part of the cell.

𝑚 𝑖 ̅̅̅̅ = 1 2 𝜌𝑀 (4)

In Figure 5 2) 𝛼 𝑖 close to 1:

From Figure 4, we observe that for 𝛼 𝑖 close to one (all the loads or the majority of them are of type i), 𝑚 𝑖 has a straight line. Intuitively, in this situation, the load of type i will always be retrieved from the first segment of the cell. In Figure 6 hereafter we represent the straight line 𝑚 𝑖 = 1 and the cloud of points obtained by simulation, by setting 𝛼 𝑖 to 1.

3) 𝛼 𝑖 in comprised between 0 and 1:

M (a) (b)
M M

Ghomri and Cardin

In the general case, when 𝛼 𝑖 is between 0 and 1, the shape of the curve of the function 𝑚 𝑖 is as represented in Figure 6. We have chosen a polynomial solution for its simplicity. The first tests have shown that the output depends on the square of the input parameters. The powers than 2 are neglected. By applying a linear regression on the data obtained by simulation, we found that the polynomial function that best models the relation among the average rank 𝑚 𝑖 , the load rate 𝜌 and the proportion of the load of type i in the AS/RS ∝ 𝑖 , is as follows:

𝑚 𝑖 = 6.10𝛼 𝑖 2 -10.37𝛼 𝑖 + 0.16𝜌𝑀 + 4.38 Figure 7 hereafter presents both the curve of the empirical proposed solution and the cloud of points obtained by simulation. These formulas can be used efficiently for the catalytic computation of the average retrieval time in any kind of AS/RS. This corresponds to the usefulness of our contribution.

VALIDATION OF THE EMPIRICAL MODEL

In this section we will compare the result of the empirical model with simulation results. To this purpose we have simulate several configuration, that were different from those used to the model development.

Ghomri and Cardin

We consider 1000 cells. Each cell has a capacity of 50 items. In this system we vary the load rate  between 10% and 90%, with a step of 20%. This means that M varies between 5 and 45 with a step of 10. We also vary the item existence rate  𝑖 between 10% and 90% with a step of 20%. The results summarized in Table 2 below. From table 2, we can notice that the error of the empirical model is relatively interesting. It is low when the parameter 𝛼 𝑖 is low and increases when 𝛼 𝑖 approaches 1. This can be improved by increasing the points considered during the fitting phase.

Figure 1 :

 1 Figure 1: Configuration components and dimensions of a typical Flow-rack AS/RS.

Figure 2

 2 Figure 2: a. Flow-rack AS/RS retrieval face; b. A column from the rack in a flow-rack AS/RS5 SIMULATION APPROACHThe objective of this section is to determine a set of data corresponding to the average rank of a load type i: 𝑚 𝑖 ̅̅̅̅ (equation 3). Two important parameters have to be considered:• 𝜌 : The load rate of the flow rack AS/RS, It is given by the proportion of the loads in the rack to the capacity of the rack;

Figure 3 :

 3 Figure 3: Sequence diagram of the simulation run

  exhibits the NREP parameter. This notation corresponds in Arena to the number of replications of the run. A preliminary study was run in order to estimate the

  hereafter we represent the straight line 𝑚 𝑖 = 1 2 𝜌𝑀 and the cloud of points obtained by simulation, by setting 𝛼 𝑖 to 0.05.

Figure 4 .

 4 Figure 4. Curve representing the cloud of points obtained by simulation;

Figure 6 .

 6 Figure 6. Curves representing the cloud of points obtained by simulation by setting: (a) 𝛼 𝑖 to 0.3, (b) 𝛼 𝑖 to 0.5 and (c) 𝛼 𝑖 to 0.8;

Table 1 :

 1 NREP study results.

		Cells=1000	Cells =1000	Cells =100	Cells =100	Cells =25	Cells =25
	NREP	Segments=50 =0.9	Segments =20 =0.1	Segments =25 =0.9	Segments =25 =0.1	Segments =10 =0.9	Segments =10 =0.1
		𝛼 𝑖 =0.1	𝛼 𝑖 =0.5	𝛼 𝑖 =0.1	𝛼 𝑖 =0.5	𝛼 𝑖 =0.1	𝛼 𝑖 =0.5
	5	0.35	0.77	0.68	0.09	3.33	-1.77
	10	0.19	-0.03	0.34	0.12	-1.29	2.52
	20	-0.21	-0.2	0.89	1.38	-4.7	2.57
	30	-0.18	0.16	-0.21	1.12	-1.35	2.77
	40	0.08	0.23	0.53	0.92	0.41	1.22
	50	-0.11	0.24	0.3	0.57	0.17	1.12
	60	0.01	0.25	-0.29	0.12	-0.13	0.88
	70	0	0.08	-0.74	-0.04	0.2	0.51
	80	-0.01	0.04	-0.27	-0.03	0.75	-0.38
	90	0.06	0	0.46	0.1	-0.42	0.37
	100	-0.05	-0.04	-0.19	-0.07	-0.33	0.01

Table 2 :

 2 Validation of the empirical model.

	M	∝ 𝒊	𝒎 𝒊 ̅̅̅̅	𝒎 𝒊 ̅̅̅̅	Error (%)
		0.1 0.3	(simulation) 3.95 2.47	(empirical 4.20 model) 2.62	6.49 5.95
	5	0.5	1.75	1.52	13.07
		0.7	1.34	0.91	32.19
		0.9	1.09	0.79	27.71
		0.1	6.80	5.80	14.63
		0.3	3.06	4.22	37.96
	15	0.5	1.92	2.12	10.36
		0.7	2.40	2.51	4.77
		0.9	1.80	2.39	32.79
		0.1	8.21	7.40	9.79
		0.3	5.23	5.82	11.34
	25	0.5	3.97	4.72	18.89
		0.7	3.41	4.11	20.38
		0.9	2.90	3.99	37.38
		0.1	9.09	9.00	0.90
		0.3	6.30	7.42	17.73
	35	0.5	4.99	6.32	26.58
		0.7	4.42	5.71	29.06
		0.9	4.11	5.59	36.06
		0.1	9.66	10.60	9.77
		0.3	8.33	9.02	8.23
	45	0.5	7.00	7.92	13.17
		0.7	6.73	7.31	8.64
		0.9	5.11	7.19	40.67

CONCLUSION

In this paper, we have provided an analytic formula for the computation of the average retrieval rank in a multi-deep automated storage/retrieval system. There is no mathematical solution to the general problem, hard assumptions are considered to tackle this problem. Then we have proposed a parametrized simulation associated with a regression technique to answer this problem It is then easy to deduce the mean retrieval time. Polynomial solutions have proved to be satisfactory approximations. The particular case of the flow-rack automated storage/retrieval system has been considered to illustrate our contribution. This formula can easily be used for other multi-deep systems.

AUTHOR BIOGRAPHIES

LATEFA GHOMRI is an associate professor in industrial engineering and control engineering at Tlemcen University. Her PhD thesis focuses on supervisory control of hybrid dynamical systems. Her fields of interest are: Simulation and modeling in manufacturing systems; supervisory control and discrete events systems. She is member of the Manufacturing Engineering Laboratory of Tlemcen and head of the team Simulation and Control of Systems. Her e-mail address is: mailto:ghomri@mail.univ-tlemcen.dz.

OLIVIER CARDIN is currently assistant professor in the University of Nantes, where he teaches robotics, discrete-event simulation and automated production. He received his PhD in automatic control from the University of Nantes in 2007. He is also member of the LS2N-CNRS, Nantes, France. His research interests are in the area of production activity control of flexible and agile manufacturing systems. He is a co-chairman of workgroup IMS2 ''Intelligent Manufacturing Systems and Services'' in the CNRS French research group MACS. is e-mail address is: mailto:olivier.cardin@univ-nantes.fr.