Health Care Management Science 8, 213–220, 2005C© 2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands.

Length of Stay-Based Patient Flow Models: Recent Developmentsand Future Directions

ADELE MARSHALL∗Department of Applied Mathematics and Theoretical Physics, David Bates Building, Queen’s

University of Belfast, Belfast Northern Ireland, UKE-mail: a.h.marshall@qub.ac.uk

CHRISTOS VASILAKIS and ELIA EL-DARZIHarrow School of Computer Science, University of Westminster, UK

Abstract. Modelling patient flow in health care systems is vital in understanding the system activity and may therefore prove to be useful inimproving their functionality. An extensively used measure is the average length of stay which, although easy to calculate and quantify, isnot considered appropriate when the distribution is very long-tailed. In fact, simple deterministic models are generally considered inadequatebecause of the necessity for models to reflect the complex, variable, dynamic and multidimensional nature of the systems. This paper focuseson modelling length of stay and flow of patients. An overview of such modelling techniques is provided, with particular attention to theirimpact and suitability in managing a hospital service.

Keywords: health, stochastic models, simulation

Introduction

The provision and planning of hospital resources has alwaysbeen a matter of great importance. To this extent, it is critical forscientifically sound and valid methods to be employed when itcomes to developing models that can capture the complexityof health care systems. Modelling patient flow in health caresystems is considered to be vital in understanding the operationof the system and may therefore prove to be useful in improvingthe functionality of the health care system.

Hospital length of stay (LoS) of in-patients has been em-ployed as a proxy for measuring the consumption of hospital re-sources. A measure frequently used is the average LoS (ALoS),which although easy to quantify and calculate, is often not rep-resentative of the underlying distribution due to the data beingskewed in many cases [1]. It is also commonly used in moregeneric but rather simplistic models for planning and managinghospital resources and capacities. These models usually takethe form of some deterministic, spreadsheet-based calculations[2]. However, since a hospital is a complex stochastic system,simple deterministic approaches for planning and managingthe system are considered to be inadequate [3,4].

A better way of assessing the system activity is to con-sider the measurement of flow of patients through hospitalsand other health care facilities. Patient flow is an importantaspect in the systemic approach of health care services as itbrings out the temporal dimension of the system as well asthe structural dimension. An accurate and reliable model ofpatient flow would enable hospital managers to predict futureactivity on the wards. Such predictions would be extremelyuseful in assessing future bed usage and forthcoming demands

∗ Corresponding author.

on various hospital resources such as the number of beds re-quired, the length of time for which the beds are required,the case-mix of each ward—the type of beds required and thevarious associated staffing levels needed. However, in makingsuch predictions, the hospital manager will be constrained byeconomic and financial factors and would more generally needto consider fluctuations in demand due to changes in policy,population growth or decline, epidemiology and improvementsdue to changing technologies.

Cote [5] view flow from two perspectives, the clinical andthe operational. From the operational perspective, patient flowrepresents the movement of patients through a set of locationsin a health care facility. Operational models of patient flow arevery detailed and complex, usually taking the form of simulatedqueuing systems (for example, see [6,7]). Although capable ofproviding very accurate predictions for various future systemactivities, these models are very costly and time consuming tobuild. This is due to sheer complexity and the fact that most ofthe required input data are not readily available. The latter ne-cessitates expensive and time consuming on-site observations.Furthermore, such models are usually tailor made to the needsof specific health care settings and as a result, cannot be easilygeneralised.

In contrast, from the clinical perspective patient flow rep-resents the progression of a patient’s health status [5]. Mod-els developed from this perspective are considered to be lesscostly and time consuming than the operational models sinceroutinely collected data can be used for estimating the input pa-rameters. These models are of particular value to epidemiolog-ical studies where the behaviour of certain patient populationsis modelled over a long period of time and the cost effective-ness and efficiency of different interventions or screening pro-grammes is evaluated [8,9]. The problem is that most hospital

214 A. MARSHALL, C. VASILAKIS AND E. EL-DARZI

departments deal with a variety of patient populations and dis-eases thus, models developed under this perspective are notsuitable if micro-level resource allocation and capacity plan-ning activities were employed.

Alternatively, patient flow can be seen from other perspec-tives such as a strategic perspective where long term modelsare considered in terms of changing policies, population demo-graphics and demand, and behavioural perspective where staff,patients, and facilities interact with each other to form specialtyspecific, locally determined streams of flow [10]. The assump-tion behind such models is succinctly described by Snowden[11]:

“Humans, acting consciously, or unconsciously are capable of a col-lective imposition of order in their interactions that enables cause tobe separated from effect and predictive and prescriptive models to bebuilt”.

In general, the goal of most behavioural research is to inferthe underlying process that generated the observed data [12].The following observation lends support to the introduction ofan appropriate technique for modelling LoS:

“. . . despite the immense complexity of a hospital system, there isa simplicity: patients occupy beds for a measurable amount of time”[13]

Observing a health system from the behavioural perspec-tive offers, in certain cases, the correct level of simplificationand abstraction for the models. Concepts such as acute care,assessment, fast stream, continuing care and long-term, implydimensions of time as well as actual facilities. Routinely col-lected administrative data can be used and thus, expensive andtime consuming on-site observations can be avoided [14]. Ad-ditionally, models can be scaled to accommodate departmental,hospital, regional and national levels of analysis. A complicat-ing factor however, is that establishing such models is not atrivial task. Advanced and sound statistical techniques needto be employed or developed before being linked to decisionmodels from the broad OR/MS portfolio.

The scope of this paper is to bring together some recent de-velopments that are related to this particular domain of patientflow modelling. In the next section different probabilistic solu-tions for modelling LoS, namely Markov models, phase-typedistributions, and conditional phase-type distributions are pre-sented and discussed in terms of their impact and suitability inassisting with the management of a hospital service. The paperthen discusses how a mixed-exponential model can be used asthe basis for a compartmental model of patient flow, whichin turn can be converted to a discrete-event simulation model.Finally, a discussion is provided on the general merits of thesemodels before concluding with possible future directions inthe field.

Probabilistic modelling of patient flow

Markov models

Markov models are often used to represent stochastic processesin statistical theory [15]. The stochastic process is formalised

by a set of states to which the system may belong and prob-abilistic laws that govern movement between the states. Sucha model assumes a probabilistic behaviour of patients movingaround the system and therefore gives a realistic representationof the actual system.

Irvine et al. [16] describes the development of a continuoustime stochastic model of patient flow. Essentially, it is a two-stage continuous-time Markov model that describes the move-ment of patients through geriatric hospitals. The compartmentsin the model can be regarded as states and the probabilities ofpatients moving within those states can be calculated. Patientsare initially admitted to the acute state from which they transferto the long-stay state or leave the hospital completely throughthe discharge or death state. Such an approach takes into ac-count different types of patients and their corresponding lengthof stay.

McClean et al. [17] extend the previous stochastic Markovmodel to a three stage one and attaches different costs to eachof the three stages thus providing a model that can facilitateplanning of health and social services for the elderly whiletaking cost into account. Taylor et al. [18] uses the above ap-proach of a continuous time Markov model and apply it toa four compartmental model [19], where the four stages areacute, long-stay, community, and dead. The model estimatesthe expected number of patients at any time t in each stage for acohort of patients, all admitted on the same day and enables theestimation of the variances of the number of patients in eachstage at time t . Taylor et al. [20] extend these models to con-tain six stages to determine the interactions between hospitalgeriatric medical services and community care. The method-ology allows any number of compartments in the model to begoverned by the data in order to obtain a model that gives thebest representation of the system.

Markov models are based on well established statisticalmethodologies and provide a viable approach to measuringand modelling flow. The models reflect the patient journeyand give insights into the hazard rates and probabilities in-volved. However, such models rely on the developer havingknowledge of the various Markov states of care. This restric-tion may be overcome by expanding the modelling processto combine other techniques such as the compartmental mod-els of patient flow, described later in this paper. Alternatively,probabilistic networks based on phase-type distributions (theConditional phase-type models described below) can incorpo-rate prior knowledge of the internal process along with othercontributing covariates such as age, gender, and marital status.

Phase-type distributions

Another statistical model that can be employed to represent thevariable nature of LoS is phase-type distributions (Ph). Suchdistributions describe the time to absorption of a finite Markovchain in continuous time, where there is a single absorbing stateand the stochastic process starts in a transient state [21]. Theassumptions of the distributions state that the 1,. . . , n states areall transient, so absorption into the state n +1, from any initial

LENGTH OF STAY-BASED PATIENT FLOW MODELS 215

Figure 1. An illustration of the Coxian phase-type distributions.

state is certain. These models describe duration until an eventoccurs in terms of a process consisting of a sequence of latentphases—the states of a latent Markov model. For example, pa-tient LoS can be thought of as a series of transitions throughphases of the patient illness as they progress to a better statefrom say acute illness, intervention, recovery, to discharge. Inmost instances, phase-type distributions can be generalised toinclude almost all continuous distributions [22] such as theexponential, which will only have one phase, the Erlang, andmixed exponential distributions, a feature that makes them ap-pealing to use.

Phase-type models were originally introduced as a naturalprobabilistic generalisation of Erlang distributions. The keydifference is that movement between all the transient stages andthe absorbing phase can occur in the phase-type distribution.Conversely, in the case of the Erlang transitions, movementcan only occur between sequential phases. In other words, thephase-type distributions allow a patient to leave the systemcompletely at any stage and move directly into the absorbingstate. However, the generality of the phase-type distributionsmakes it difficult to estimate all the parameters of the model. Toovercome this problem Coxian Phase-type distributions wereintroduced.

Coxian phase-type distributions [23] are a special sub-classemployed to describe the probability P(t) that the process isstill active at time t [22]. They differ from general phase-typedistributions in that the transient states (or phases) of the modelare ordered. The process begins in the first phase and may ei-ther progress through the phases sequentially or enter into theabsorbing point. Such phases may then be used to describestages of a process which terminates at some stage (see fig-ure 1). For example, in the case of a patient staying in hospital,transitions through the ordered transient states could corre-spond to stages such as diagnosis, assessment, rehabilitationand long-stay care.

Faddy and McClean [24] use this model to find a suitabledistribution for the LoS of a group of geriatric patients in hos-pital. They conclude that phase-type distributions are suitablefor measuring the LoS of patients in hospital and show how itis also possible to consider other variables that may influenceit such as age on admission and year of admission. The year ofadmission may influence duration of stay as a result of policychanges implemented by the hospital, health authority or gov-ernment. The three-term mixed exponential model that will bedescribed later can be regarded as a three phase distributionwhere the patients are split into three groups, short, medium,and long-stay according to their LoS.

Coxian phase-type distributions are based on cohort dataand can identify the presence of different compartments. They

Figure 2. The Conditional Phase-Type Distribution (C-Ph).

give better insight into the reality of the two extremes of pa-tient flow where the distribution is similar in nature to thelog-normal but highly skewed forming a long tail representingthose patients in very long-term care. In addition to LoS beingrepresented in a sound mathematical sense, the model providesa useful representation for interpretation by non mathemati-cians where LoS consists of a sequence of phases mimickinga type of behaviour or property such as acute or long stay.

Conditional phase-type models (c-ph)

The conditional phase-type (C-Ph) distribution is a novel ap-proach which uses Coxian phase-type distributions condi-tioned on a Bayesian Network (BN). This approach allowsthe incorporation of discrete and continuous variables [25].Unlike previously developed models the C-Ph model can rep-resent a continuous distribution which is highly skewed whilealso incorporating causal information from inter-relationshipsbetween explanatory variables.

The incorporation of a BN into the model allows the in-clusion of statistical graphical models which provide a frame-work for describing and evaluating probabilities when thereis a network of inter-related variables representing causality[26]. Such inter-relationships are verified by conditional inde-pendence tests of the edges in the network. Figure 2 illustratesthe model as consisting of these two components where theCoxian phase-type distribution is referred to as the processmodel and the BN the causal network.

The conditional phase-type (C-Ph) model is defined as con-sisting of causal nodes C = {C1, . . . Cm} belonging to thecausal network, and process nodes Ph = {Ph1, . . . Phn} rep-resenting the phase-type distribution. The Coxian phase-typedistribution can be fitted to the patient LoS using a sequentialprocedure, as described in Faddy [22].

Marshall et al. [25,27] use the C-Ph model to model the LoSof elderly patients in hospital. The approach is illustrated us-ing data on hospital duration of stay (the process) for a numberof geriatric patients along with personal details, admissionsreasons, dependency levels and destination (the causal net-work). The final model represents patient LoS in terms of fiveof the most significant variables in the patient data set: patientage, gender, admission method into hospital, Barthel grade(dependency score) and predicted destination on departure

216 A. MARSHALL, C. VASILAKIS AND E. EL-DARZI

from hospital. The approximations of the parameters of thephase-type distributions are recorded for the optimal numberof phases in the distribution along with the appropriate jointprobability distribution of the causal network. The BN maytherefore be used to select the most likely situation for a pa-tient based on the other variables in the network. The patientLoS may then be modelled using the estimates of the phase-type distribution for that particular cohort of patients.

In summary, the C-Ph model provides a better understand-ing of resource use. It integrates probabilistic networks withCoxian phase-type distributions to prototype a forecasting toolbased on historic activity. Such models can be used to give valu-able insights into the interaction between important variables(e.g. dependency, previous illness, local social circumstances,etc.) and the probability that a patient will be short, mediumor long stay. For all of these reasons, it has the potential tobe a useful explanatory management tool. However, the con-struction methodology is more complex than using traditionalmethods hence further testing is required to ensure it is moreclinically and managerially meaningful.

Compartmental and simulation modelling

Mixed exponential distributions

Millard [27,28] observed a identifiable distribution to bed oc-cupancy that was initially assumed to be staff skill related.It was later proposed that the observed change in the distri-bution represented the interaction of the simultaneous move-ment of two or three types of patients through the system. Thehypothesis that the time pattern of bed occupancy in depart-ments of geriatric medicine is expressed by a mixed exponen-tial equation was later tested on data collected from thirteenhealth districts in the South West Thames Region, England[29]. McClean and Millard [30] used hazard functions to con-sider various models of survival of geriatric patients in hospitaland observed that the pattern of bed occupancy in departmentsof geriatric medicine could be expressed using mixed expo-nential distributions. This two-term mixed exponential modelhas shown to give a good fit for durations of occupancy ofgeriatric beds [31,32].

In general, the model also gives a reasonable approximationto the numbers of patients departing each week from hospital.The development of such a model led to a new method ofestimating the usage of hospital beds. McClean and Millard[30] use the fits of the mixed exponential models to provide amethod for predicting future behaviour of patients and identifychange. The mixed term exponential model of survival mayhelp explain why a small proportion of the people who enterlong-term care stay for a very long time. This also providesreasoning as to why the majority of beds in a long-term careunit are occupied by very long-stay patients.

A variation of the mixed exponential model is the moresophisticated lognormal and exponential mixture which couldprovide a better description of the early peak in departuresto death/discharge. However, the lognormal model requires

Figure 3. The Two-compartment model.

the estimation of an additional parameter and is hence morecomplicated to apply than the exponential [30].

Compartmental modelling

Godfrey [33] defines compartmental systems as those consist-ing of a finite number of homogeneous, well mixed, lumpedsubsystems, called compartments. These exchange with eachother and with the environment so that the quantity or concen-tration of material within each compartment may be describedby a first-order differential equation. Compartmental modelscan be linear, non-linear, deterministic or stochastic dependingon the process they represent and have additional characteris-tics such as the possibility of including feedback loops betweenlong and short stay. In recent years compartmental models havebeen applied to the movement of patients throughout hospitalsystems.

Harrison and Millard [32] suggested that the movement ofgeriatric patients around departments of geriatric medicine isbest described by a model consisting of two compartments.The model, illustrated in figure 3, describes patients who areinitially admitted to a acute state (sometimes referred to as ashort-stay state), from which they either die or are dischargedat a rate r , or are transferred to a second long-stay state at arate v from which they either die or are discharged from thehospital at a rate d. The model is deterministic with discretetime. It provides a means of estimating the numbers of acuteand long-stay patients and their expected lengths of stay.

The system may be described by two linear difference equa-tions, the solution of which is a two-term expression which caneasily be written as the two-term mixed exponential model dis-cussed earlier in the paper. The two-compartment deterministicmodel enables hospital planners to optimise the number andpotential use of geriatric beds thus giving a more realistic andintuitive insight into the movement of geriatric patients aroundthe geriatric department.

Further work on the pattern of bed occupancy in acute hos-pitals showed that some patterns of bed occupancy were bestrepresented by an equation with three exponents. Harrison [34]extends the two compartment deterministic model to incorpo-rate a third compartment thus representing patient behaviour asacute stay, rehabilitative stay and long-stay care. Taylor et al.[35] describe a four compartmental model which takes intoaccount an extra compartment for patients in the community.

LENGTH OF STAY-BASED PATIENT FLOW MODELS 217

A specially designed analysis program, called Bed Occu-pancy, Management and Planning System (BOMPS), imple-ments the mathematical model. The e-fit module of this soft-ware program generates performance statistics based upon thefit between a mixed exponential curve and bed census databy using a nonlinear least squares algorithm [36,37]. Depen-dent on whether the best-fit mixed exponential equation hasone, two or three components; one, two or three compartmentstatistics are generated respectively. The number of compart-ments used in a model is determined on the basis of the numberof exponents required to obtain the best mathematical fit to theactual data.

Given patient admission date, discharge date and censusdate, BOMPS does the following:

� estimates individual bed occupancy times,

� displays the cumulative pattern of occupancy,

� determines and displays the best fit curve, and

� generates resource utilisation statistics such as

– the number of patients in a stream,

– the estimated ALoS of patients within a stream,

– the rates of admission and release to and from a stream,and,

– the conversion rates from one stream to another.

This facilitates scenario modelling as it is possible to changethe conversion and discharge parameters in each compartment.Several examples of using the software in different areas ofhealth services have been published collectively [38,39], whilefurther applications have been reported separately [40–45].They all report successful application of the methodology todifferent hospital departments.

In summary, compartmental modelling is a well-establishedmethodology that has been validated mathematically and clini-cally. Its disadvantage is that it is based on a one-day bed censusand thus, it is highly dependent on the day of the census. It ig-nores seasonality and the cyclical effects of admissions anddischarges.

Simulation modelling

Another logical extension to the compartmental modellingframework is to consider the problem as a queuing system.Queuing systems, whether developed as analytic approxima-tions or simulations can be used to extend the capabilities ofthe compartmental models previously described. Queuing per-formance measures such as time in the system and time spentwaiting in queues can help planners to test different scenariosand avoid bottlenecks in the flow of patients.

Given the complexity of the system and the required flex-ibility in modelling terms, discrete event simulation (DES) isusually preferred to analytic approximations. DES concernsthe modelling of a system as it evolves over time by a repre-

sentation in which the state variables change instantaneously atseparate points in time, called events [46]. Events are definedas instantaneous occurrences that may change the state of thesystem. DES is widely used in modelling health care systemsas recently discussed by Jun et al. [47]. The basic componentsof a patient flow simulation model can be summarised as:

(i) entities, the simulated elements of the system e.g. patients,

(ii) activities, the operations and tasks that transform the stateof the entities e.g. compartments and queues, and

(iii) the state of the system, a collection of the variables thatdescribe the system at a certain point in time e.g. the numberof available beds, the number of patients in a queue etc.

El-Darzi et al. [48] first described the development of such aqueuing system by using DES to perform the numerical eval-uations. Initially, a steady-state simulation model with threecompartments (described as short-, medium-, long-stay) with-out capacity constraints was developed and tested against theresults of the established compartmental models. The durationof service of each compartment was exponentially distributedand the random nature of the patients’ progression through thesystem was simulated by a probabilistic node between the com-partments. A very long warming up period was observed duringwhich the system was repeatedly simulated until a steady statewas reached. Apart from having technical implications to themodel (the batch means method was preferred to the replica-tion/deletion method), this highlighted the real-life problemsassociated with very long LoS. Any changes that will affectthe flow of the long-stay patients, will take time before theirconsequences stabilise and become apparent. A constrained(capacitated) model was then used to evaluate the effect ofchanges in various model parameters and the general flow ofpatients. In line with findings of previous studies, it concludedthat the key for the smooth flow of patients in the system is theemptiness in the long-stay compartment along with the actualsize, financing and staffing levels of such systems.

The main advantages of these DES models arise from thefact that by adapting the concept of the compartmental modelto that of a queuing system, the incorporation of capacity con-straints and bed blockage in the evaluation of patient flowis made possible. By employing DES to evaluate the result-ing queuing system numerically, the stochastic nature of themodelled system is taken into account along with the requiredflexibility and adaptability for the conceptual modelling capa-bilities. This has been demonstrated by adding external com-partments (independent home and support home) to the basicconfiguration [49] and by modifying the basic model to caterfor a possible hypothesis on the causes of the winter bed crisisin English hospitals [50].

A main disadvantage of DES models is the long executiontime and the amount of output data they generate. Each scenarioand thus model set-up needs, one very long run of hundredsof thousands of simulated days even under the more efficientbatch means method of output analysis. It follows naturally thatthe modeller has to be particularly cautious when selecting thedifferent scenarios to be evaluated.

218 A. MARSHALL, C. VASILAKIS AND E. EL-DARZI

However, these problems have been partially resolved byemploying data warehousing and On-Line Analytical Pro-cessing (OLAP) techniques to handle the data generated bythe DES model [51–53]. More specifically, the proposed datawarehouse environment provides the means for automating thenecessary algorithms and procedures for estimating differentparameters of the simulation. They include initial transient insteady-state simulations and point and confidence interval es-timations. This data warehouse environment can substantiallyreduce the computational complexities in analyzing and inter-preting simulation output data and it constitutes a significantstep toward rendering simulation engines “black boxes” for theend-users.

Discussion

This paper discusses some of the methodologies that have beenrecently developed in the health care modelling domain thatseek to discern in-patient populations in two or three separateflow streams. The first probabilistic approach describes a spe-cial type of Markov model known as the Coxian phase-typedistribution and its further development into the Conditionalphase-type distribution. The Coxian phase-type distributionallows the representation of the continuous duration of stayof patients in hospital as a series of sequential phases whichthe patients progress though until they leave the hospital (thesystem) completely. Such identification of the presence of dif-ferent patient states is not only mathematically sound but alsoprovides an additional means of interpretation for the clini-cian or health care manager. Although, virtual, the phase-typerepresentation of patient length of stay can be interpreted asdifferent types of patient behaviour, for example in the caseof a three phase model these were identified by the clinicianas being equivalent to three groups of patient activity: acute,rehabilitation and long-stay. This gives a better insight into thereality of the system.

It is possible to expand the theory of Coxian phase-typedistributions to include a network of additional interrelatedvariables that may interact to influence patient LoS. This is fa-cilitated by the recent development of the Conditional phase-type distribution which conveniently allows the representationof additional variables (such as patient characteristics) to beconsidered and taken into account using a Bayesian network.Although this representation is mathematically complex, itsgraphical nature provides a visual representation that is easyfor clinicians to interpret. However the technique does requireexpert assistance in its development due to the complex fit-ting of the Coxian phase-type model to the conditional prob-abilities attached to the network variables. Nonetheless suchmathematical complexity in model fitting makes the result-ing conditional phase-type distribution a much more powerfulmodel than some of its counterparts. In fact the resulting modelis currently being applied to length of stay data in a local UKhospital with the aim of representing patient activity and facil-itating bed allocation. As such it has the potential of becominga valuable tool for clinicians and health care managers by more

realistically representing the health care systems under consid-eration.

The second general approach described in this paper usescompartmental models to provide input parameters to a DESmodel for evaluating the interaction of the different streams ofpatient flow through health care systems. By adapting the con-cept of the compartmental model to that of a queuing system,the incorporation of capacity constraints and bed blockage inthe evaluation of patient flow was made possible. By employ-ing DES to evaluate the resulting queuing system numerically,the stochastic nature of the modelled systems was taken intoaccount along with the required flexibility and adaptability forthe conceptual modelling capabilities of the model.

Although the DES models of patient flow inherit the as-sumptions of the compartmental models of patient flow (dis-charge independent of LoS, compartments operating at fullcapacity, system in stable state), they are not bound by theminsofar as their parameters can be estimated by different statisti-cal and mathematical models. These include survival analysis,phase-type distributions, and data mining algorithms. How-ever, as it has been demonstrated by several case studies re-ported in the literature, the compartmental models of patientflow give an accurate picture of the ongoing process in healthand social care services. Thus, it is safe to assume that the sim-ulation models reported here hold the same favourable charac-teristics. Furthermore, the latest developments in informationtechnology and data processing have enabled the developmentof a decision support framework that incorporates the com-partmental and DES models.

Conclusions

The management of hospital resources is a critical issue. Healthcare systems are continually being developed to try to repre-sent the bed occupancy and length of stay activity in hospitalwards and how the management of such can be modelled andimproved for future allocation of resources. It is hoped thatmodelling patient flow in health care systems can assist in theoverall understanding of the system activity and may thereforeprove useful in representing the functionality of the health caresystem.

Previously developed bed usage measures do not adequatelyrepresent the true activity or situation in the hospital ward.Therefore it is necessary to consider new models that for ex-ample, do not focus on the average measure such as the ALoS,but use other modelling techniques to represent LoS and pa-tient flow in a hospital ward. Such models would be consideredbeneficial to the hospital manager for instance a more accurateand reliable model of patient flow would enable hospital man-agers to predict future activity on the wards. Such predictionswould be useful in assessing future bed usage and forthcom-ing demands on various hospital resources such as the numberof beds required, the length of time for which the beds arerequired and the case-mix of each ward.

Current trends in health care modelling have expanded theportfolio of methods and techniques being employed to include

LENGTH OF STAY-BASED PATIENT FLOW MODELS 219

recent developments in scientific fields such as artificial in-telligence, data mining and information technology. Considerthe framework described by Harper [3] where there are vari-ous components or stages of analyses combining a preliminarystatistical analysis with a further data investigation using meth-ods such as classification and regression tree analysis (CART)and modelling techniques on patient length of stay. This iscomplemented by a final stage of modelling using simulationtechniques. In this case, various data mining, statistical andoperational research methods come together to provide oper-ational modelling for hospital resources. Another example isWalczak et al.’s [54] use of the artificial intelligence methodof neural networks to facilitate the modelling and predictionof resource utilization associated with patient LoS. There aresome drawbacks in using such an approach where the modelsare considered to be ‘black box’ in nature, however the combi-nation of such a technique with other forms of analysis couldovercome such problems thus making the method applicableto health resource allocation.

The authors believe that the future of modelling patientactivity in health care can be built on the successes of cur-rent models and the currently evolving hybrid approaches.One view is to consider the modelling techniques as forminga toolbox of data mining, data analysis, operational researchand artificial intelligence methods. This toolbox would facili-tate preliminary data preparation and initial statistical analysiswith advanced methods for modelling health care resourcesand inference techniques for providing further predictions.The reported complexities of health care systems coupled withthe availability of vast amounts of health related data neces-sitate the inter-disciplinary collaboration of research in thisarea.

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