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Hospital deals with human lives, which are often at risk and where everything depends on quick response to diverse medical conditions. Thus, the need for efficient and effective management of patient care flow processes in a hospital is being one of the main leading goals in health sector.In this paper,a Timed Coloured Petri Nets (TCPN) formalism i...

## Contexts in source publication

**Context 1**

... hospital under study consist of registration, admission and discharge unit and two inpatient areas: one for male and the other for female withtwelve inpatient beds each. The health centre works three (3) shifts a day with four(4) medical attendants, four(4) nurses and three(3) doctors.Patient arriving at the health centre follows a flow processes depicted in Figure 1. The flowchart depicted in Figure 1 is based on the observation of the processes, studying and surveying the health centre at the current situation. ...

**Context 2**

... health centre works three (3) shifts a day with four(4) medical attendants, four(4) nurses and three(3) doctors.Patient arriving at the health centre follows a flow processes depicted in Figure 1. The flowchart depicted in Figure 1 is based on the observation of the processes, studying and surveying the health centre at the current situation. The process of service started when a patient arrives at the medical record area and ends when a patient is admitted or discharged. ...

**Context 3**

... statistical analysis of the results shown in Figure 9was carried out usingSPSS (Statistical Package for the Social Sciences) software, version 17.0. The result (Figure 10) of the statistical analysis shows that there were no significant differences between the outputs of the simulation and the actual data at 5% significance level. Hence, the developed TCPN model is valid and accurately represents the actual system. ...

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## Citations

... In order to model and simulate a multi-phase traffic light-controlled intersection for the T-type junction with an accompanying fixed signal timing plan to lessen traffic congestion and guarantee greater safety, [31] used the Timed Coloured Petri Nets (TCPN). Again [32] proposed a solution to the issue of patient-health-care break-continuity using the TCPN modeling approach to improve the flow process thereby saving lives. [33] applied the Hierarchical Coloured Timed Petri Net to simulate the Point of Sale (POS) cash deposit and Deposit Slip processes in Nigerian banks. ...

A food system is composed of a complex network of activities and processes for production, distribution, transportation and consumption, which interact with each other, thus leading to changeable behaviour. Most existing empirical studies on cassava processing have focused on the technical efficiency analysis of the cassava crop processing techniques among processors indicating that the modelling of the events and operations involved in the processing of the cassava crop is highly limited. In this context, different strategies have been used to solve difficult environmental and agro-informatic systems model-based problems such as system dynamics, agent based, rule-based knowledge and mathematical modeling. However, the structural comprehension and behavioral investigation of this modeling are constrained. In this regard, formal computational modeling is a method that enables modeling and simulation of the dynamical characteristics of these food systems to be examined. In this study, the system specification is designed using Unified Modelling language (UML) to show the structural process and system design modelled and simulated using Coloured Petri Net (CPN), a formal method for analyzing the behavioural properties of complex system because of its efficient analysis. For the purpose of observing and analyzing the behaviour of the cassava food process, a series of simulation runs was proposed.

... This CPN model combined elements from a series of strategies on cloud systems and resource allocation, which we developed [9][10][11][12][13]. Other fields of PN and CPN applications are mentioned below: parallel processing [14], grid computing applications [15,16], traffic control [17], analysis of safety-critical interactive Systems [18], manufacturing [19], everyday applications [20], supply chain management [21], medicine [22], industry [23], project management [24], fuzzy systems [25], and communication protocols [26,27]. ...

The Colored Petri net (CPN) has evolved into a complete modeling language, which is based on the object-oriented paradigm. Although this language is quite complete and can be used to accurately model a wide variety of systems, it seems that there is a lack of certain modeling rules, which can be used to generate models based on real datasets. This paper is a first attempt to incorporate sequences of real system events and translate them into sequences of Petri net transitions. Then, well-defined modeling rules control the model generation based on these transitions. The specific entities that take part in each of the real system events, as well as their attributes are also considered. The models produced using real data are structured because, in the majority of real systems, each incurring event usually affects a part of the system. Then, this effect is propagated to the entire system. Therefore, it is much easier to divide the entire model into distinct parts when real data are used and then interconnect these parts to build an entire model. This is a very important aspect when modeling very large systems. To test our approach, we used the real data from a courier company to generate its model. Our simulation results have shown that we managed to obtain quite accurate results through the model produced by the actual data.

... In order to study and improve performance of a shared memory system in terms of global memory utilization rate and its waiting time before it can be accessed by core(s) of a processor, simulation models are necessary. Petri Net (PN) is a graphical and mathematical modeling language that can be used to develop a simulation model for a system characterized as being synchronous, asynchronous, deterministic, stochastic, concurrent, distributed and parallel in nature [6]. A Timed Coloured PetriNet (TCPN) model is the introduction of time concepts into a Coloured Petri Net model; thereby making it possible to calculate performance measures, such as the speed by which a system operates, mean waiting time and throughput [5]. ...

A shared memory multi-core computer system is a computing paradigm in which processors have more than one core to process requests and also have access to a common memory. Most existing works are limited to modeling of a shared memory single-core computer system and thus the models are not flexible enough to study the operations of multi-core computer systems. Hence, in this paper, a high-level Petri Nets formalism (Timed Coloured Petri Nets) was used to develop a simulation model for a shared memory multicore computer system. Intel HP core i5 was used as a case study in developing the TCPN model for a shared memory multi-core computer system. The developed TCPN model was simulated using Coloured Petri Net (CPN) tools. One hundred and fifty simulation runs were carried out in order to obtain average utilization rate of the shared memory and average waiting time of the processor’s cores in accessing the shared memory. The developed TCPN model was validated based on both real and simulated average memory utilization of the shared memory multi-core computer system. The validation result of the developed TCPN model showed that there was no significant difference between the simulated and real average memory utilization of the shared memory multi-core computer system.

... Besides, Petri Nets (PN) as a discrete event simulation modelling language is better suited for modelling multiprocess systems which include food manufacturing systems. PN is a graphical and mathematical tool for describing and studying systems which are characterized as being synchronous, asynchronous, concurrent, parallel, distributed, deterministic, non-deterministic and or stochastic [8,9]. PN approach can be extended by colour, hierarchy and time concepts [10]. ...

... PN approach can be extended by colour, hierarchy and time concepts [10]. The inclusion of colour and hierarchy to the classical PN results in a high-level PN called the Hierarchical Timed Coloured Petri Nets (HTCPN) [11,12], which combines the strength of PN with the strength of functional programming language Standard ML [10,9]. ...

Numerous efforts are being made yearly by researchers to improve the production flow, planning and scheduling of food manufacturing systems through the use of modelling to meet both current and future market demands. In this paper, a Hierarchical Timed Coloured Petri Nets (HTCPN) model was developed for bakery production system using Ladoke Akintola University of Technology (LAUTECH) Bakery, Ogbomoso, Nigeria, as a case study. The HTCPN model was developed consisting of main module and five sub modules. The sub-modules named mixing, fermenting, rolling, cutting and baking modules modelled the sequential processes of converting flour into bread. The model was simulated using Coloured Petri Nets Tools to determine the average production processing times for processing of 50, 100, 150 and 200 kg of flour into bread. The simulation was also extended to determine the utilization rates required at varying units (manual mixing process, the rolling machine, manual cutting process and baking) for processing of 50 and 100kg bags of flour. The model was validated by comparing the simulated and the actual processing times at 5% significance level using statistical t-Test. The simulation results revealed that the production processing times for processing of 50, 100, 150 and 200 kg of flour starting from the mixing process till baking process were 217, 314, 411 and 508 minutes respectively. The utilization rates required at the mixing process unit, the rolling machine unit, the cutting process unit and baking unit were 0.138; 0.115; 0.046; 0.147 respectively for processing of 50kg bags of flour and 0.191; 0.159; 0.064; 0.203 respectively for processing of 100kg bags of flour. Statistically, there were no significant differences between the simulated and the real processing times. This model could be employed to study worker and machine utilization rates as well as production time required to produce bread from a given quantity of flour in the considered bakery production system or other related ones.

... A model is a description or a representation of the operations of a real system either mathematically or symbolically. Petri Nets is a graphical and mathematical tool for describing and studying systems that are characterized as being concurrent, synchronous, asynchronous, distributed, parallel, deterministic, nondeterministic and/or stochastic [9]. Coloured Petri Nets (CPN) is an example of high-level Petri Nets which combines the strength of Petri Nets with the strength of functional programming language Standard ML [10,4,11]. ...

Inbound call centres are centralized offices which are operated by modern organizations to administer incoming product supports or information inquiries from consumers. In this paper, a model for an inbound call centre, which is characterized by agent utilization and call abandon rates, was developed using Hierarchical Timed Coloured Petri Nets (HTCPN). The inbound call section of SN Nigeria Ltd., Lagos, Nigeria, was used as a case study in developing the HTCPN model. Data were collected and analyzed statistically using ARENA simulation software to determine the model parameters. These parameters were used as inputs in developing the HTCPN model which consists of Call Arrival, Hang up Processes, Sales Processes, Customercare and Enterprise Process modules. The model was simulated using Colour Petri Nets tools and validated by carrying out a statistical analysis (t-Test) between the simulated and the real number of abandon calls and agents utilization rates at 5% significance level. The simulation results of the developed HTCPN model revealed that increase in number of agents utilized resulted into decrease in abandon calls from 71, 7 and 108 to 35, 4 and 102 in customer care, enterprise and sales departments, respectively. Correspondingly, increase in number of utilized agents led to reduction in agents’ utilization rates from 96, 50 and 96% to 84, 40 and 92% for customer care, enterprise and sales departments, respectively. The result of the validation showed that there were no significant differences between the simulated and the real number of abandoned calls and agents utilization rates.

... For the correctness and credibility of the model, validation of the developed model was carried out. Validation is to determine that the developed model is a representation of the real system [24]. Thus, the proposed Hierarchical Timed Coloured Petri Net model was validated by comparing the output of the simulation of the developed model (i.e. ...

During Nigerian 2015 general elections, in an attempt to exercise their civic rights in voting for the candidates of their choices, many electorates exercised the limitations of their patience by tiredly waiting on queue for their turn at the poll centers. In order to study the aforementioned scenario, this paper carried out a simulation based analysis of a Hierarchical Timed Coloured Petri Net (HTCPN) model, which abstracted the Re-Modified Open-Secret Ballot System (REMOBS) adopted in the 2015 Nigerian general elections. Using CPN Tools, ten simulation runs were carried out on the HTCPN model to experiment the effect 300 and 750 voters on service time, queue length and average waiting time while dedicating Assistant Polling Officers I, II and III (APOI, APOII and APOIII) or four polling officers (two APOI and two APOII) to each polling unit. The validation of the HTCPN model was determined by carrying out a statistical analysis (T-Test) between the simulated and observed voters' arrival times. By employing three polling officers (APOI, APOII and APOIII) at the polling unit, the simulation results revealed that service times of 5 hours and 13 hours 57 minutes would be required to accredit 300 and 750 intending voters, respectively. The simulation results also established that a maximum queue length of 105 and 480 voters was reached during accreditation of 300 and 750 voters, respectively. Similarly, a maximum waiting time of 1 hour 20 minutes and 10 hours was recorded in the process of accrediting of 300 and 750 voters, respectively. With four polling officers (two APOI and two APOII) per polling unit, the simulation results revealed that service times reduced from 13 hours 57 minutes to 6 hours 47 minutes to completely accredit 750 voters. The simulation results also established that average queue length reduced from 240 to 155 voters during accreditation of 750 voters. Similarly, the maximum waiting time was reduced from 13 hours 53 minutes to 1 hour 14 minutes in the process of accrediting of 750 voters. Statistically, there were no significant differences between the simulated and observed number of the voters arriving at the polling unit at 5% level. Thus, the results obtained from the simulation based analysis of the HTCPN model could serve as a basis for decision makers to improve and manage the issues of prolonged queue which often disfranchise intending voters during elections.

... Les réseaux de Pétri ont été utilisés par exemple par Celano et al. (2006) dans le cadre département de radiologie. Ganiyu et al. (2015) a utilisé un réseau de Pétri coloré pour modéliser l'accueil d'un centre de santé (l'enregistrement et la salle d'attente). Un réseau de Pétri coloré permet de faire une distinction entre les entités, dans ce cas les patients ambulatoires (qui ne restent que la journée) et les autres. ...

Le nombre croissant de personnes âgées dépendantes est un des enjeux majeurs en France pour les prochaines années. La prise en charge du sujet âgé est complexe car de nombreux facteurs peuvent venir perturber les diverses prises de décision. En effet la dépendance, les maladies chroniques ou même l’environnement social sont à prendre en compte lors d’une hospitalisation ou un placement sur le long terme. Le parcours de soins des personnes âgées se divise en deux volets : (i) les hospitalisations dans le cadre des évènements aigus et (ii) la prise en charge des soins de longue durée. Nous avons étudié dans un premier temps les problèmes liés à l’hospitalisation aiguë avec des études de cas en collaboration avec le CHU de Saint-Étienne. Un premier sujet concerne l’organisation des services gériatriques, nous utilisons la simulation à évènements discrets pour évaluer la pertinence d’une intégration des deux services en un seul. De la même manière nous évaluons la mise en place d’une hotline permettant de mettre directement en contact les médecins de ville et du CHU, le but étant d’éviter les passages aux Urgences. Nous étudions ensuite les parcours de soins sur le long terme en modélisant les états de santé des personnes âgées selon 3 critères (degré de dépendance, degré des pathologies chroniques et degré d'isolement social). Une chaine de Markov est utilisée pour représenter les transitions entre les états. Un modèle de simulation est utilisé pour déterminer le dimensionnement d’un territoire. Enfin nous nous intéressons au pilotage des flux de patients dans les structures résidentielles de soins de longue durée (EHPAD, USLD) avec un modèle d’optimisation stochastique.

... For the correctness and credibility of the model, validation of the developed model was carried out. Validation is to determine that the developed model is a representation of the real system (Ganiyu et al. 2015). Thus, the proposed Hierarchical Timed Coloured Petri Net model was ...

Voting systems are combination of activities that take place before, during and after election
whose interactions are complex. Most of the existing voting system models are non-modular, and
hence could not accommodate future modifications. This research developed a modularized model
for a voting system using Hierarchical Timed Coloured Petri Nets (HTCPN).
The Re-Modified Open-Secret Ballot System (REMOBS) adopted in the 2015 Nigerian
general election was used as a case study in developing the modularized HTCPN model. This
consists of Accreditation and Voting modules. Each of the modules has two sub-modules
(Polling_unit and Voting_station). The Polling_unit sub-module abstracted the arrival and departure
of voters. Voting_station sub-module modelled the queuing of voters, the operation of the presiding
officers and the voters’ behavioral patterns (balking and reneging). Voters’ arrival rate, average
polling officers’ response time, average voters’ response time and expected voters’ population were
used for model simulation. The developed HTCPN model was simulated using Coloured Petri Net
Tools. Ten simulation runs were carried out to experiment the effect of 300 and 750 voters on
service time, queue lengths and waiting times while dedicating Assistant Polling Officers I, II and
III (APOI, APOII and APOIII) or four polling officers (two APOI and two APOII) to the polling
unit. The validation of the HTCPN model was determined by carrying out a statistical analysis (T-
Test) between the simulated and observed voters’ arrival times.
By employing three polling officers (APOI, APOII and APOIII) at the polling unit, the
simulation results revealed that service times of 5 hours and 13 hours 57 minutes would be
required to accredit 300 and 750 intending voters, respectively. The simulation results also
established that a maximum queue length of 105 and 480 voters was reached during accreditation
of 300 and 750 voters, respectively. Similarly, a maximum waiting time of 1 hour 20 minutes and10 hours was recorded in the process of accrediting of 300 and 750 voters, respectively. With four
polling officers (two APOI and two APOII) per polling unit, the simulation results revealed that
service times reduced from 13 hours 57 minutes to 6 hours 47 minutes to completely accredit 750
voters. The simulation results also established that average queue length reduced from 240 to 155
voters during accreditation of 750 voters. Similarly, the maximum waiting time was reduced from
13 hours 53 minutes to 1 hour 14 minutes in the process of accrediting of 750 voters. At p<0.05,
there were no significant differences between the simulated and observed number of the voters
arriving at the polling unit.
This research has been able to develop a modularized HTCPN model that can be easily
modified through its associated modules to suit any future modification in the voting system. The
HTCPN model could serve as a reference model for decision makers to study and manage the issues
of prolonged queue which often disfranchise intending voters during elections

... In this paper, a Timed Coloured Petri Net (CPN) formalism stated in (1) was used to develop an executable model for the voting system under consideration. A Coloured Petri Nets and Timed Coloured Petri Nets are tuples defined as [10,11,12]; CPN = (Σ, P, T, A, N, C, G, E, I) Where: (i) Σ is a finite set of non-empty types, called color sets. (ii) P is a finite set of places. ...

Voting systems are complex systems that involve activities that take place before, during and after election. The world over, automation of voting systems has attracted the attention of academia and industry because voting system is fundamental to the success of any democratic process. In this paper, Hierarchical Timed Coloured Petri Nets (HTCPN) formalism is explored to develop an executable model for the Re-Modified Open-Secret Ballot System (REMOBS) adopted in Nigerian 2015 general election. The developed HTCPN model for REMOBS is made up of two modules representing the Accreditation Process and the Voting Process. Each of the modules comprises two sub-modules (voting_station and voting_booth). These sub-modules are made up of another layer of sub-modules that abstract key activities while each sub module in this layer is made up of several transitions and places. Thus, the developed HTCPN model can be easily modified through its associated modules to suit any future modification in voting systems.

... In this paper, a Timed Coloured Petri Net (CPN) formalism stated in (1) was used to develop an executable model for the voting system under consideration. A Coloured Petri Nets and Timed Coloured Petri Nets are tuples defined as [10,11,12]; CPN = (Σ, P, T, A, N, C, G, E, I) Where: (i) Σ is a finite set of non-empty types, called color sets. (ii) P is a finite set of places. ...

Voting systems are complex systems that involve activities that take place before, during and after election. The world over, automation of voting systems has attracted the attention of academia and industry because voting system is fundamental to the success of any democratic process. In this paper, Hierarchical Timed Coloured Petri Nets (HTCPN) formalism is explored to develop an executable model for the Re-Modified Open-Secret Ballot System (REMOBS) adopted in Nigerian 2015 general election. The developed HTCPN model for REMOBS is made up of two modules representing the Accreditation Process and the Voting Process. Each of the modules comprises two sub-modules (voting_station and voting_booth). These sub-modules are made up of another layer of sub-modules that abstract key activities while each sub module in this layer is made up of several transitions and places. Thus, the developed HTCPN model can be easily modified through its associated modules to suit any future modification in voting systems.