1 Introduction

Common law criminal justice systems are composed of complex subsystems, such as police, courts, and corrections, operating in an interconnected yet autonomous fashion. These complex subsystems both contribute to, and respond to the operational fluctuations amongst their own elements, in other subsystems and across the system as a whole. Criminological analysis that focus on single components of a justice system are often unable to predict the effects of the changes in the policies or operations, on the other subsystems or divisions of the system (see [8, 12, 15]).

This chapter is based on a recent application of systems thinking to the Criminal Justice System (CJS) in British Columbia, Canada [11], and its purpose is to illustrate how systems thinking can be used to assist the process of strategic decision-making in complex managerial situations.

The main goal of this article is to develop a general high-level system dynamics model of the CJS by analyzing and examining the effect of changes to the system as entities move through it over time. The system dynamics approach models entities as they move through the various stages of the CJS through a network of flow pipes. System dynamics is an ideal approach to modeling in such cases in comparison to other modeling approaches, because the data requirements are minimal and much of the behavior of the system can be constructed using expert knowledge of the system.

Developed in the early 1960s, system dynamics models are based on the economics concepts of stocks and flows. The strength of the system dynamics modelling lies largely on the fact that it is both qualitative and quantitative in nature. The qualitative nature of the system dynamics comes from the fact that it builds upon a systems thinking model approach. Thus the original model can be created using minimum data, by solely focusing on the qualitative nature of the system. This is best obtained based on the experience and the insights of professionals and managers. This knowledge base, although qualitative, is the foundation of the actual decision process in the system, and as such is considered more comprehensive.

The proposed system dynamics simulation model could be used to examine the impact of the management decisions on the performance of various components of a justice system, such as prosecution services, court services, and corrections. Furthermore, it could be used to determine the impact of other factors—both internal and external—on the performance of the various components of a criminal justice system. This model further addresses an important operational need for a simulation tool which can incorporate measures of workload. For example, how would a change in the number of court appearances will impact the efficiencies within the system? This model could be used to address questions such as:

  • What is the impact of police resources on crime in general?

  • How to allocate police resources in order to balance the workload across a criminal justice system?

  • How does the distribution of police resources affect specific crime types, such as impaired driving or organized crime?

  • What is the impact of changes in upstream practices on corrections — especially with regards to community versus institutional sentences?

  • What is the interdependence between increases in pending cases and the workload for actors within a criminal justice system?

  • What is the relationship between remand counts and average time to disposition for those in remand?

Furthermore, this model can help with understanding the principal drivers of resource consumption within a criminal justice system. It could be used to develop good metrics for resource consumption by answering questions such as: how to determine when resources are being used efficiently? how does resource consumption relate to dollar costs? and what is the best granularity with which to track resource consumption?

Many stakeholders will benefit from this model by running “what/if” scenarios. Policy makers, governmental agencies, police, justice department, and many private firms are among institutes that can use this model to make better decisions.

The rest of this article organized as follows: next section is an introduction to the criminal justice systems. In Sect. 3 the historical background of the research in the domain of modelling criminal justice systems are reviewed. Section 4 contains the description of the sub-systems in the proposed model, and the assumptions that are considered in this model. In Sect.  5 some simulation details such as the data and the verification and validation of the model are discussed. Section  6 contains examples of two scenarios that are studied using the proposed model. Finally, Sect. 7 covers the conclusions and the related future works.

2 Criminal Justice System

A criminal justice system (CJS) is a set of legal and social institutions for enforcing the criminal law in accordance with a defined set of procedural rules and limitations. CJSs include several major sub-systems, composed of one or more public institutions and their staffs: police and other law enforcement agencies; trial and appellate courts; probation and parole agencies; custodial institutions (jails, prisons, reformatories, halfway houses, etc.); and departments of corrections (responsible for some or all probation, parole, and custodial functions). Some jurisdictions also have a sentencing guidelines commission. Other important public and private actors in this system include: defendants; private defense attorneys; bail bondsmen; other private agencies providing assistance, supervision, or treatment of offenders; and victims and groups or officials representing or assisting them (e.g., crime victim compensation boards). In addition, there are numerous administrative agencies whose work include criminal law enforcement (e.g., driver and vehicle licensing bureaus; agencies dealing with natural resources and taxation).

The notion of a “system” suggests something highly rational and carefully planned, coordinated, and regulated. Although a certain amount of rationality does exist, much of the functioning of criminal justice agencies is unplanned, poorly coordinated, and unregulated. Most jurisdiction do not reform all (or even any substantial part) of its system of criminal justice. Existing systems may include some components that are old (e.g., jury trials) alongside others that are of quite recent origin (e.g., specialized drug courts). Moreover, each of the institutions and actors listed above has its own set of goals and priorities that sometimes conflict with those of other institutions and actors, or with the goals and priorities of the system as a whole. Furthermore, each of these actors may have substantial unregulated discretion in making particular decisions (e.g., the victim’s decision to report a crime; police and prosecutorial discretion whether and how to apply the criminal law; judicial discretion in the setting of bail and the imposition of sentence; and correctional discretion as to parole release, parole or probation revocation, prison discipline, etc.).

Nevertheless, all of the institutions and actors in the CJS are highly interdependent. What each one does depends on what the others do, and a reform or other change in one part of the system can have major repercussions on other parts. It is therefore very useful to think about criminal justice as a system; not only to stress the need for more overall planning, coordination, and structured discretion, but also to appreciate the complex ways in which different parts of the system interact with each other.

3 Simulation Modeling in Criminal Justice Systems

Mathematical modeling and simulation of the CJS date back to 1970s. During that time there was a surge of activity using system dynamics model to represent CJSs (see [3, 5–7]). Some of the researches emphasized on modelling the court process [8, 12, 13]. In the recent years in parallel to the computer technology, mathematical modeling and simulation techniques in criminology and CJS are developed and expanded [1, 4, 9].

Previous studies on modelling the CJS have mainly focused on one of the subsystems in the CJS. Much of the simulation modeling focuses on police and its resources [16]; on the court system or components of the court system [8, 10, 14] or corrections, primarily prison systems [2, 17].

New interest in the use of system dynamics models in the CJS has blossomed among academics and professional in recent years for at least four separate, but related reasons. First, the continuing expansion of computing power has made it possible to construct and use large-scale simulation models that were simply not possible before. Second, the development of large electronic data archives have made model calibration and validation possible in ways that were not previously feasible. Third, the growing sophistication of criminal justice professionals has led them to ask researchers to explore policy impact questions of increasing complexity. Fourth, the software packages available today that can be used to construct system dynamics models were not readily available to researchers a couple of decades ago.

Next section describes the major components of the contemporary CJS in British Columbia. It presents a system dynamics model for better understanding of how these components typically operate in practice, and examines the various uses of the system concept.

4 Description of the System

In any modeling project the goals and assumptions of the model are inter-related. It is important to outline the assumed conditions and purpose of the model, as these affect the nature of the predictive “what-if” questions that a model is able to address, the level of model detail to consider and the data requirements of the model.

The first assumption of our model is that we are dealing with aggregate flows of entities over a unit of time. For instance, these entities can be crime incidents, reports to Crown Council, cases, persons, etc. System dynamics analyzes input data and examines the effect of changes to the system as these aggregate entities move through it over time. The system dynamics approach models entities as they move through the various stages (represented as boxes) of the CJS through a network of flow pipes (arrows).

The second assumption of this model is that it is a high-level model of a CJS. As a result, a) each of the parts of the system are modeled as stages where entities continue through the system or leave the system in various ways. This means that the full complexity at each stage might not be modeled, and b) this model is linear which means that feedback behavior is not modeled. An example of feedback behavior occurs when a stock (e.g., Pending Cases — see Sec. 4.3) has a capacity or limit. Once that limit is reached or exceeded the behavior of other system components or stocks changes over time.

Figure 1 shows the process flow of the CJS understudy. In this section we describe the details of each sub-system. The description of the model starts with the police sub-system, moves to the Crown and courts sub-system, continues with the corrections 1 process and concludes with corrections 2 sub-system. The details of these sub-systems are depicted in Figs.  2, 3, 4, 5, 6 and are explained in Sect.  4.1 to 4.4. The complete detailed flowchart can be found in Appendix A.

Fig. 1
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Main sub-systems of the B.C. criminal justice system

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Fig. 2
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Police sub-system of the B.C. criminal justice system

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Fig. 3
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Crown sub-system of the B.C. criminal justice system

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4.1 Police Sub-System

In the police sub-system, monthly inputs of Uniform Criminal Reports(UCR) reported offences enter the system as founded offences into the Substantiated offences stock. A certain proportion of the UCR offences leave the Substantiated offences stock as not cleared and the remaining offences are either cleared by charge or are cleared by other means. Currently, the cleared by other means flow is a system exit point. The monthly flow of offences cleared by charge is converted into the flow of Report to Crime Council from police (RCCs from police). Figure  2 shows the police sub-system.

Fig. 4
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Courts sub-system of the B.C. criminal justice system

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Fig. 5
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Corrections 1 sub-system of the criminal justice system

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4.2 Crown Sub-System

Flows of Report to Crime Council RCCs enter the model from two sources: (1) regulatory agencies, and (2) police agencies. These reports proceed to the Crown Charge Assessment stock. This stock determines the monthly flow of RCCs not approved to court or sent to alternative measures and RCCs approved to court. The Crown Charge Assessment stock provides a mechanism to track the number of people approved to court. The RCCs approved to court flow from the Crown Charge Assessment stock to the Informations Sworn stock. The flow of RCCs approved to court is used to determine the monthly values for remand, bail and Released On Own Recognizance (ROOR), while the RCCs not approved to court dictates the flow of people into alternative measures. RCCs approved leave the Informations Sworn stock and flow into the Pending Cases stock. In order to reflect the reality of the process and the data provided RCCs leaving the Informations Sworn stock are converted into new cases that flow into the Pending Cases stock. Cases exit the Pending Cases stock each month and flow into the Court Decision stock. Figure  3 shows the Crown sub-system.

Fig. 6
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Corrections 2 sub-system of the B.C. criminal justice system

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4.3 Court Sub-System

The Court Decision stock is not a separate stock in reality and merely represents a decision branch where cases may be resolved in one of four manners. They may be Found Guilty (either through a plea or trial), they may be Found Not Guilty, cases may be Stayed, or cases may proceed to an Other outcome. For the purposes of interpreting this model, the stocks of Found Not Guilty, Stayed and Other are system exit points. Cases in the Found Guilty stock flow into the Sentencing stock where they have one of five possible paths. The three sentencing flows that have an impact on the Corrections sub-system are: Custody Sentences, Probation Sentences and Conditional Sentences. The All Fine Sentences and Other Sentences flows are considered system exit points in the model. Figure  4 shows the court sub-system.

4.4 Correction Sub-Systems

The Correction subsystems have two main components, pre-conviction statuses and past-conviction statuses.

4.4.1 Corrections 1— Pre-Conviction Statuses

This sub-system in the justice model is the remand, bail or ROOR sub-system (termed the Corrections Sub-system 1: Pre-conviction Statuses) where accused not yet convicted of an offense, but detained by the police, have a status that precedes a court decision. Currently, this sub-system occurs in the flow of RCCs approved to court to the Informations Sworn stock before new cases enter the Pending Cases stock. This sub-system tracks the number of people approved to court in each of the three pre-conviction corrections stocks: Remand, Released on Bail and ROOR in each month. Each month a given number of people, determined through a formula, enter and leave each of these stocks. Additionally, the sub-system models the non-conviction based outcome Alternative Measures. This stock is derived from the flow of RCCs not approved to court leaving the Crown Charge Assessment stock. The Alternative Measures stock tracks the number of people on an alternative measures program and those that finish a program in each month.

4.4.2 Corrections 2 — Past-Conviction Statuses

The final sub-system is the corrections sub-system (referred to as the Corrections Sub-system 2: Post-conviction Statuses). This sub-system contains a non-conviction based outcome and conviction-based outcomes. The non-conviction outcome is a Peace Bond stock that has a separate input not linked to the rest of the model. This stock calculates the number of people under a peace bond and those that finish a peace bond each month. The conviction-based outcomes in the Corrections sub-system are composed of three stocks. The first stock is In Custody and it calculates the number of people in custody per month as a function of the number of people sentenced to custody and the number of people who have completed a custodial sentence. The second and the third ones are On Probation and On Conditional Sentence stocks which they operate in an identical fashion. Each of these stocks calculate the number of persons under each of these sentencing outcomes in a given month and, at present, do not account for resources.

5 Simulation Development

To develop the model, many meetings with different stakeholders have been organized. The initial step was to define the problem, in which the goals and the needs of the study was clarified. Next, the details of the components of the system was defined. We spent numerous hours understanding the actual behavior of the system, and mapping the process flow as described in the previous section. Determining the basic requirements of the model was necessary in developing the right model. Then, the required data was identified and collected. The model was translated to the simulation package. Our model has been subjected to rigorous verification and validation, in which we confirmed the model behave as intended, and ensured that no significant difference exists between the model and the real system (considering the assumptions).

We used the software package iThinkFootnote 1 for simulation of the CJS model. This simulation contains the Police, Crown, Courts and Corrections subsystems as described in Sect. 4. It covers the flow of all activities, from the reporting of offences to the disposition of matters according to their many possible outcomes. For example, Fig. 7 presents the iThink model of the courts subsystem of the CJS as described in Section 4.3.

Fig. 7
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iThink model of the courts sub-system of the B.C. criminal justice system

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The model showed it is effective in producing quality results, and computationally efficient in-terms of the time required to generate the results. The simulation is done on a dual processor Apple G5 computer and the estimated computation time is about 30 s for each simulation run. In the following sub sections, we discuss examples of the efforts in gathering the data, and the verification and validation of the model.

5.1 Data

Once the agreed upon structure for the model was implemented, 5 years of aggregate system data for police, Crown, courts and corrections was used to populate the model, and to develop formulae for system behaviour. The data, provided by the Working Group of the Ministry of Public Safety and Solicitor General and the Ministry of Attorney General (PSSG/AG) in British Columbia, was a monthly count of entities in each stock from January 2003 to December 2007. The input data used in the model includes offences reported to police, RCCs from other agencies, and admissions to peace bond. The following is the list of the data fields that were used to construct and populate the model.

  • The Police Data Fields

    1. 1.

      UCR Data: Number of UCR Reported Offences.

    2. 2.

      Clearance Data: Number of UCR Cleared by Charge and UCR Cleared By Other Means.

  • The Crown Data Fields

    1. 1.

      RCC Data: Crown Total RCCs, Crown RCCs Approved to Court, Crown RCCs Not Approved to Court.

    2. 2.

      Person Data: Crown Total Persons, Crown Persons Approved to Court, Crown Persons Not Approved to Court.

  • The Court Data Fields

    1. 1.

      Court Case Data: Courts Provincial Criminal New Cases, Courts Provincial Criminal Completed Cases, Courts Provincial Criminal Pending Cases.

    2. 2.

      Court Case Decision Data: Courts Provincial Criminal Guilty Findings, Courts Provincial Criminal Not Guilty Findings, Courts Provincial Criminal Other Findings, Courts Provincial Criminal Total Findings.

    3. 3.

      Court Sentencing Data: Courts Provincial Criminal Custody Sentences, Courts Provincial Criminal Probation Sentences, Courts Provincial Criminal Fine Sentences, Courts Provincial Criminal Other Sentences, Courts Provincial Criminal Total Sentences, Total Sentences as a percentage of Guilty Findings.

  • The Corrections Data Fields

    1. 1.

      Monthly Admissions to BC Corrections Data: Alternative Measures, Recognizance/Peace Bond, Bail, Remand, Custodial Sentences, Probation, Conditional Sentences.

    2. 2.

      Average Daily Counts Per Month: Alternative Measures, Recognizance/Peace Bond, Bail, Remand, Custodial Sentences, Probation, Conditional Sentences.

5.2 Verification and Validation of the Model

Verification is the process of ensuring that the model behaves as intended. Throughout the development phase, we constantly checked the elements of the model with the system, to ensure it behaves as intended. One of the verification check performed on this model was a steady-state analysis. In the absence of changing influences, we would expect that over time the average number of RCCs, people, and cases in each part of the system would approach to a constant value. This equilibrium arises because competing influences in a stable system eventually reach a balance. Verifying that the model exhibits this behaviour demonstrates that the key competing influences are incorporated in the model. Steady state analysis requires the development and analysis of differential equations for each stock. It was evident that the stocks in the model for which this analysis is conducted reach a steady state rapidly.

After verifying step, we validated the model. Validation ensures that no significant difference exists between the model and the real system. This is an important step to show that the model reflects reality and can be used to accurately address “what-if” questions, and to forecast the future behaviour of the system over time. We used historical system data to develop the mathematical functions and formulae to represent the behaviour of the stocks incorporated in the system dynamics model. The results are then tested against real data to determine the level of the fit between the simulation results and the reality from the data. A good fit make us confident in the quality of the future predictions derived from the changes to the model parameters.

6 Simulated Scenarios

Here, we illustrate how the model can assist policy makers and mangers to assess potential inteventions by simulating them before executing them. In this section, we present two different scenarios and compare each to the status quo. Scenario 1 involves changes to UCR clearance practices; Scenario 2 involves changes to the volume of UCR offences reported to the police.

We were required to keep all data confidential. Accordingly, the vertical scales on all graphs have been eliminated.

6.1 Scenario 1: The Development of a Large Task Force

An integrated gang homicide task force is created in the metro Vancouver area of British Columbia in June of Year 1 to respond to a recent surge of gang-related homicides. As a result, police agencies in the Lower Mainland are under pressure to close as many open cases as possible and to free up resources for assignment to the task force. The result is that clearance rates double (non-cumulatively) in the months of June, July, August and September of Year 1. The simulation of this scenario illustrates the predicted downstream effect on the number of accused offenders in remand when the number of offenses cleared by charge doubles in each of the four months in question.

Figure  8 shows the “intervention” being simulated, that is, the flow of offences cleared by charge under the status quo and when such activity doubles during the four month period.

Figure 9 shows one downstream effect of the intervention, the impact on the number of accused offenders in remand. Figure 9 illustrates how a short-term change in an upstream activity (offences cleared by charge) has a prolonged effect on a downstream variable (accused offenders in remand). The model projects that the doubling of clearances over four months results in a significant increase in offenders in remand over an entire year. Over this year, on average, there are about 9 % more offenders in remand as compared to the status quo. The strongest effect is in September of Year 1 when about 20 % more offenders are in remand.

Fig. 8
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A four month increase in UCR cleared by charge events

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Fig. 9
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The impact on remand of a four month increase in UCR cleared by charge events

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Fig. 10
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The effect a 40 % increase in drug, mischief and other property damage offences on the number of UCR cleared by charge events

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Fig. 11
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The impact of a \(40\,\%\) increase in drug, mischief and property damage offences on the number of accused on bail

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6.2 Scenario 2: A Broken-Windows Policy

In January of Year 1, police agencies in across British Columbia embark on a strategy that incorporates the “broken windows” thesis, targeting drug, mischief, and other property damage offences accordingly. Officials estimate that the strategy will lead to a 40 % increase in UCR reported offences of these types over the subsequent three years. The simulation of this scenario illustrates the predicted downstream effect on (all) offenses cleared by charge and accused offenders on bail.

Fig. 12
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Flowchart of the B.C. criminal justice system

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Figure 10 shows the effect on the flow of all offences cleared by charge under the status quo and when the reporting of the above mentioned offenses increases by 40 % every month (non-cumulatively). Offences cleared by charge each month increase by about 12 %.

Figure  11 shows the effect of 40 % more drug, mischief and other property damage offences being reported on the number of accused offenders on bail. The impact on the stock of accused offenders on bail is cumulative. 40 % more reports of the above mentioned offences leads to about 12 % more offenses cleared by charge which leads to a cumulative 1.8 % per month increase in offenders on bail.

7 Conclusions and Future Works

This chapter is restricted to the development of a high-level model of a CJS containing the main sub-systems police, Crown, court and corrections. Clearly it is very important to incorporate queues in the model to more accurately represent “wait-time” behaviour. This provides a more accurate method for estimating wait-time behaviour and delay in a CJS. In the model described in this paper resourcing is not incorporated so in future research resourcing model can be developed for the different sub-systems.

The current model is linear, meaning it possesses no feedback. Feedback is a critical characteristic of dynamical systems, such as CJSs. Feedback occurs when certain stocks have limits that, when approached, necessitate a system response or adaptation. To accomplish this requires the identification of the “stocks” in the model where these limits exist. Subsequently, the stocks that are the most crucial to system functioning can be determined. The next step in this process necessitates an understanding of the types of adaptations that can and do take place when a critical stock reaches capacity. This means that in the process a qualitative description of which other “stocks” change their behaviour in response to a capacity limit of a critical stock is pivotal. This qualitative description, which should be gleaned from the expertise of system managers, can then be transformed into a mathematical representation of feedback behaviour. An example might be, what happens at the various stages in a CJS when Pending Cases reaches a limit?

The model in this paper deals with overall UCR reported offences. As a result, there is no prioritization of UCR reported offences in this model. It is important that a prioritization scheme be implemented to reflect the dynamics of the input data. This prioritization scheme could be set at a general level (i.e., summary conviction/indictable or major crime groupings — violent, property, drug and other) or a highly specific level of detail (homicide offences, assault offences, robbery, other violent offences, theft offences, break and enter offences, mischief offences, drug possession offences, drug trafficking offences, administrative offences, etc.). This type of prioritization scheme allows the model to make more detailed predictions and it enhances the detail of the “what-if” questions that may be tested.

As another future work we can assign different attributes to the entities that impact their flow through a CJS. For example, age of the offender, gender of the offender, offence location and risk classifications (i.e., low, medium, high) of offenders on probation impact the outcomes and paths in the system. These are important influences in a detailed model of the criminal justice system in British Columbia, and have a different effect on resource utilization.