Modeling and Simulation of Oncology ClinicOperations in DEVS

Michelle M. Alvarado, Tanisha G. Cotton and Lewis Ntaimo†

Department of Industrial and Systems Engineering, Texas A&M University3131 TAMU, College Station, TX 77843, USA

Eduardo PerezIngram School of Engineering, Texas State University

601 University Drive, San Marcos, TX 78666, USA

William R. Carpentier, MDBaylor Scott and White Health System, 2401 31st Street, Temple, TX 78666, USA

†Corresponding author:Tel: 979-458 2360 Fax: 979-458 4299 Email: ntaimo@tamu.edu

Abstract

Oncology clinics are often burdened with scheduling large volumes of cancer pa-tients for chemotherapy under limited resources such as nurses and chemotherapychairs. Chemotherapy is a cancer treatment method that is administered orally orintravenously at an outpatient oncology clinic. Chemotherapy patients require atreatment regimen, which is a series of appointments over several weeks or monthsprescribed by the oncologist. The timing of these appointments is critical to theeffectiveness of the chemotherapy treatment on cancer. This motivates the needfor new methods for making efficient appointment schedules and for assessing clinicoperation performance from both patient and management perspectives. This workuses a classic modeling approach based on systems theory to develop a discrete eventsystem specification (DEVS) simulation model for oncology clinic operations calledDEVS-CHEMO. DEVS-CHEMO is configurable to any oncology clinic and providesseveral capabilities for oncology clinic managers. For example, it can simulatescheduling of chemotherapy patients, clinic resources, and the arrival process ofthe patients to the clinic on the day of their appointment. This model simulatesoncology clinic operations as patients receive chemotherapy treatments and thusallows for assessing scheduling algorithms using both patient and managementperspectives. DEVS-CHEMO has been tested and validated using historical datafrom a real outpatient oncology clinic and simulation results reported in this paperprovide several insights regarding oncology clinic operations management.

Keywords: Discrete-event simulation, system modeling, healthcare, oncology clinicoperations, chemotherapy scheduling, DEVS.

1 Introduction

Outpatient oncology clinics often face the challenge of scheduling large volumes of cancerpatients under limited resources such as nurses and chemotherapy chairs. Chemotherapy

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is a commonly used treatment method for cancer and is often administered orally orintravenously at outpatient oncology clinics. Chemotherapy patients require a treatmentregimen which is a series of appointments over several weeks or months that is prescribedby the oncologist. The timing of the appointments and the increasing demand forchemotherapy treatment at outpatient oncology clinics motivates the need for efficientappointment schedules and clinic operations. The effectiveness of chemotherapy on canceris strongly tied to the timing of the appointments.

Cancer costs in the U.S. exceeded $124 billion in 2010 and are expected to increase27% by 2020 [1]. The demand for oncology services is projected to increase by 48%between 2005 and 2020 [2] and there is a need to improve patient wait times in oncologyclinics [3]. It is understood that the way oncology resources are managed has a directimpact on the quality of service to the patient in terms of wait time, pain management,and recovery time. However, increased demand for chemotherapy coupled with thecomplexity of the treatment regimens make managing patient service and resources inoncology clinic very challenging.

Chemotherapy appointment scheduling involves a complex problem setting for severalreasons. For example, each patient’s treatment regimen requires a series of appointmentsover several weeks, and for each appointment limited clinic resources (nurse, chemother-apy chair, chemotherapy drug, etc.) must be available. Also, patient appointmentrequests and actual patient arrivals to the clinic on the day of appointment are stochastic.Furthermore, nurse availability is also uncertain (e.g. nurse is sick), not to mention thatthe number of nurses can be the bottom-neck for clinics with high volumes of patients.Consequently, oncology clinic managers often find it challenging to schedule patients aswell as being able to assess the impact of their scheduling decisions on overall clinicoperations and performance. Therefore, modeling and simulation (M&S) provides aviable approach to addressing this aspect of the chemotherapy appointment schedulingproblem. This paper considers the design, verification, and testing of a simulation modelfor an outpatient oncology clinic using the discrete event system specification (DEVS)formalism [4]. The simulation model, termed DEVS-CHEMO, involves modeling thescheduling process of clinic resources and chemotherapy patients, the arrival process of thepatients to the clinic on the day of their appointment, and the oncology clinic operationsas patients receive their chemotherapy treatment. DEVS-CHEMO is configurable andis designed to be tailored to any oncology clinic to enable clinic managers to evaluatedifferent patient and resource scheduling algorithms using performance measures basedon both patient and management perspectives.

This work uses the DEVS formalism because it allows for modular and hierarchicalconstruction of models and uses well-defined concepts for coupling model components.The modular construction enables the user to design and construct models independentof the simulation engine. DEVS-CHEMO is designed to be a simulation model forevaluating different appointment scheduling algorithms and implementation policies.This paper specifically focuses on how patients are scheduled and the impact of thenumber of available nurses on clinic performance. DEVS-CHEMO captures performancemeasures from both patient and management perspectives to identify scheduling policies

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that achieve high levels of patient service while at the same time satisfying the businessobjectives of the clinic.

The contributions of this paper include the following: providing a classic modelingapproach based on systems theory to develop a configurable discrete event simulationmodel for outpatient oncology clinic operations; a simulator for assisting oncology clinicmanagers in determining appointment scheduling and operational policies, and assess-ment of clinic performance from both patient and management perspectives; and acomputational study based on real clinic data that provides useful insights for oncologyclinic managers on how to schedule chemotherapy appointments and determine staffingneeds. DEVS-CHEMO provides an advance toward simulation models for managingoncology clinic operations with the goal of attaining higher levels of patient service inhealthcare.

The rest of the paper is organized as follows: Closely related work is reviewed inSection 2. A description of the outpatient oncology clinic setting is given in Section3. The DEVS-CHEMO simulation model is presented in Section 4. This includesmodel abstraction, performance measures, design, and software implementation. Acomputational study based on a real oncology clinic is reported in Section 5. Concludingremarks and directions for future research are given in Section 6.

2 Closely Related Work

Discrete event simulation is now a well-known approach for modeling complex systemsfor various applications including healthcare. In this work, we use the discrete eventsystem specification (DEVS) formalism [4, 5] to build a discrete event simulation modelof oncology clinic operations. The DEVS formalism has since been extended and appliedto various applications. It is based on dynamical systems theory and includes M&S ofdiscrete time, discrete event, and continuous complex dynamical systems. It providesadvantages of developing mathematically sound models that can easily run on severalcomputer platforms. DEVSJAVA, a software implementation of DEVS, allows for devel-oping DEVS simulations in Java [6]. The DEVS-CHEMO simulation model presented inthis paper was implemented in DEVSJAVA.

Research in the area of scheduling of chemotherapy appointments has only receivedattention in the last decade, beginning with classification-based approaches. Some ofthese approaches are based on acuity level classification [7, 8], next-day scheduling [9, 10],and on patient classification systems [11]. The concept of acuity is usually referred toas patient acuity and is commonly used in the health science literature but withoutspecificity of definition or measurement. In general, patient acuity refers to the measureof the intensity of care required for a patient accomplished by a nurse. Studies in theliterature show that patient acuity is useful for estimating nurse staffing allocationsand budget determinations, is very important to patient safety, and promotes promotesequitable nurse patient assignments or nurse load balancing [12, 13].

It was not until about the last few years that optimization techniques have alsostarted being applied to chemotherapy appointment scheduling [2, 14–17]. Algorithms

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for scheduling patient appointments while considering treatment regimen specificationsand infusion times to minimize patient waiting time and optimize chair utilization havebeen introduced [18]). Mixed-integer programming (MIP) to optimize nurse schedules ona weekly and monthly basis has been considered for a combination of full-time and part-time nurses to minimize the number of nurse shortage hours [19]. Dynamic optimizationhas been used in chemotherapy appointment scheduling to capture uncertainty of real-time requests for appointments and uncertainty due to last-minute scheduling changes[17].

The work that is closely related to this paper in terms of the simulation approach isthat of [20, 21], who develop a DEVS model for outpatient nuclear medicine clinics. Thispaper takes a dynamical systems approach to abstract and build a generic simulationmodel of a given oncology clinic. In addition, this work devises and tests several patientand resource scheduling algorithms within the DEVS-CHEMO simulation, which in turnallows to generate appointment requests, simulate oncology clinic resource activities, andevaluate scheduling algorithms and operational policies.

Other discrete event simulation approaches have been used in modeling outpatientclinics in general [22–25] but is only relatively recently that it has been applied to model-ing oncology clinic operations. For example, an ARENA simulation model was developedand used to analyze the layout of an outpatient oncology clinic [26], while anotherARENA model was built to compute the performance of a scheduling template by [24].Another ARENA simulation model included modeling blood exams, oncologist visits, andchemotherapy infusions [27], and another was developed to sample expected patient waittimes for the objective function of an MIP model for weekly and monthly nurse scheduling[19]. Other discrete event simulation models include a Microsoft SQL simulation modelfor scheduling and postponement of patient laboratory tests and infusion appointments[18]. GAMS simulation was used to build a model to evaluate scheduling policies forchemotherapy appointments [28]. This work considers a Markov decision process anddynamic programming model to schedule patient appointments within specific timewindows. Next,the real outpatient oncology clinic setting is described.

3 Outpatient Oncology Clinic Setting

This section describes the outpatient oncology clinic setting with a focus on the patientand resource scheduling process, patient flow in the clinic, and performance measures.The performance measures of interest include both patient and clinic management per-spectives.

3.1 Patient Scheduling Process

When a patient is diagnosed with cancer, an oncologist usually prescribes a uniquetreatment regimen (e.g. Table 1) based on the type and state of cancer, and the patient’scurrent state of health. The oncologist also specifies an earliest start date to beginchemotherapy treatment so that the treatment can be successful. Delaying starting

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treatment (e.g. due to limited clinic resources, too many patients, and/or ineffectivescheduling methods) may result in poor treatment outcomes for the patient as the cancermay spread beyond what was expected. The start date is the number of days into thefuture that the patient’s oncologist recommends for the first treatment to begin. As shownin Table 1, a chemotherapy treatment regimen is a series of chemotherapy appointmentsand consists of the frequency of appointments (Days), drug name for each appointment(Drugs) and corresponding dosage (Dosage), the amount of time to perform the infusion(Infusion Times), and the expected relative attention the patient will require from thenurse (Acuity Levels). Treatment days specify the spacing between each appointment. Inthe example in Table 1, the patient has a total of seven treatments on days 1, 2-5, 8 and15, and rest days 6-7, 9-14 and 16-21. Infusion time is the expected time that the druginfusion is expected to take but is stochastic and may vary from patient to patient basedon whether or not the patients get an adverse reaction or is a ‘hard stick’ (difficulty toget the drug intravenously (IV) into the patient). Patient acuity is a relative measure ofthe nurse’s attention required by a patient during an appointment and is also subject touncertainty.

Table 1: Example chemotherapy treatment regimen.Days Drugs Dosage Infusion Times Acuity Levels

1 CISplatin, Etoposide, 20 mg/m2, 100 mg/m2, 8 hours 1Bleomycin 30 units

2-5 CISplatin, Etoposide 20 mg/m2, 100 mg/m2 7 hours 26-78 Bleomycin 30 units 1 hour 3

9-1415 Bleomycin 30 units 1 hour 3

16-21

A typical chemotherapy appointment after a patient has being diagnosed with cancerinvolves the following: First, the treatment regimen prescribed by the oncologist issent to a scheduler to determine the appointment schedule for each appointment in thetreatment regimen, and to allocate clinic resources such as a nurse and chemotherapychair (special seat for the patient when receiving chemotherapy) for each appointment.All appointments in the treatment regimen need be scheduled right away to guarantee theavailability of the later appointments. To maximize the effectiveness of the treatment,the appointments should be scheduled as close to the state date recommended by theoncologist as possible. Delay from the prescribed start date to the actual start date willbe referred to as type I delay and can result in the cancer progressing and hence reducingthe effectiveness of the chemotherapy treatment. Second, the patient typically has anappointment for laboratory ‘blood work’ and afterward meets with the oncologist todiscuss the lab results and whether or not to proceed with the scheduled chemotherapytreatment. Although this is common practice, many oncology clinics have a separatelaboratory for ‘blood work’ or use next-day scheduling, which allows the appointmentfor the chemotherapy treatment to be considered independent of the laboratory ‘bloodwork’ appointment.

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Figure 1 gives a depiction of chemotherapy patient flow in an outpatient oncologyclinic on the day of an appointment. When a patient arrives for a chemotherapy ap-pointment, the patient first checks-in with a receptionist and then waits in the waitingroom for an available nurse and chemotherapy chair. Once both a chair and a nurse areavailable, the nurse escorts the patient to the chair, orders the patient’s chemotherapydrug from the pharmacy, and checks the patient’s vital signs. While waiting for the drugto be prepared in the pharmacy, the nurse prepares and inserts the IV in the patient.When the chemotherapy drug is ready at the pharmacy, the patient’s identity is verifiedand the nurse starts the patient’s chemotherapy drug infusion through the IV. The entireprocess (escorting the patient to starting the infusion) takes about 15 minutes and thenurse is fully dedicated to a single patient during this time. Therefore, nurses can onlystart one patient during this 15 minute time period. Afterwards, the nurse is free toeither continue monitoring patients or start a new patient as the chemotherapy druginfusion can take anywhere from 30 minutes to eight hours. Finally, stopping an infusionand discharging a patient generally takes a few minutes.

Patient Check-In

Vitals Taken

Drug Ordered

Chemotherapy Administration

Patient Discharge

Chemotherapy Drug Prepared

Patient ID Verification and

Infusion Start

Pharmacy

Waiting

Room Treatment

Area

0.5-8 hours

Patient Seated

Drug Picked-Up

2 minutes

15 minutes 1 minute

Oncology

Clinic

Figure 1: Example chemotherapy patient flow on day of appointment.

The delay a patient experiences in the waiting room after arriving at the clinic willbe referred to as type II delay, while the time from when the patient is seated in thechemotherapy chair until the drug infusion begins will be referred to as the type III delay.To schedule patients and clinic resources effectively, the scheduler uses a policy, model,or algorithm to make a chemotherapy scheduling decision, which allocates a specific date,time, and set of clinic resources (chair and nurse) to each appointment in the patient’streatment regimen. Then the scheduler gives the appointment schedule to the patientand the chair and nurse resource schedules are made available for the oncology clinicoperations manager.

Chemotherapy scheduling decisions are challenging for several reasons. For example,the nature of the patient flow (Figure 1) in the oncology clinic requires the availability ofa nurse and chair. However the availability of the nurse and chair are stochastic. Nursessometimes get sick and do not report for work. On the other hand, a drug infusion may

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take longer than planned. This is because chemotherapy treatments are well-known forhaving nauseating side-effects and deteriorating a patient’s state of health. The side-effects can occur suddenly during chemotherapy administration. Depending on the typeand intensity of the treatment, nurses must pay close attention to patients in order tomonitor the patient’s condition and reactions to these side-effects. It is possible for eachnurse to simultaneously monitor the chemotherapy treatments of several patients at thesame time. However, it is crucial that the nurses are not over-utilized since they mustbe available to assist patients experiencing adverse reactions to the chemotherapy drugs.To account for this, the aforementioned concept of patient acuity, which is a relativemeasure of the nurse’s attention required by a patient during an appointment, is used.Acuity levels are assigned a value of say 1, 2, or 3, where an acuity level of 3 (or thelargest number used) represents the maximum attention required by the patient from thenurse. Each nurse can monitor several patients at once, provided that the sum of theacuity levels for all patients is less than or equal to a pre-determined maximum acuitylevel for that nurse.

3.2 Oncology Clinic Performance Measures

This work aims to improve oncology clinic management by using a classic modeling ap-proach based on systems theory to develop a simulation model for evaluating patient andresource scheduling rules/algorithms from both patient and management perspectives.Table 2 gives a summary of the patient and management performance measures usedin DEVS-CHEMO. Part of patient service satisfaction in oncology clinics is to improvethe patient’s overall experience. The first performance measure of interest from thepatient’s perspective is type I delay. This performance measure is measured in days andis important because the timing of the chemotherapy treatment regimens is crucial to thepatient’s health status and recovery. Scheduling algorithms aim to begin the treatmentregimen on or close to the start date prescribed by the patient’s oncologist. Thus typeI delay captures how well the scheduling algorithm was able to accomplish this task.Type II delay and type III delays are performance measures that capture the delay thatpatients experience at the oncology clinic on the day of an appointment. System timeis the overall time a patient spends at the clinic. Cancer patients are typically very sickand often weak, thus minimizing these delays can improve the overall patient serviceexperience in the oncology clinic.

In addition to providing a high quality of service to patients, oncology clinics mustalso operate from a business perspective. Table 2 also lists four management per-formance measures used in DEVS-CHEMO: Patient throughput, chair utilization, andnurse utilization. These performance measures are used to assess the performance ofthe oncology clinic. Nurse overtime, the amount of time each nurse must work beyondnormal clinic operating hours, is a performance measure that was particularly importantto the oncology clinic that collaborated on this paper. Clinics with low nurse overtimecan keep overhead costs down and increase employee satisfaction.

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Table 2: Oncology clinic performance measures.Patient Perspective

Type I delay Time (days) between the first scheduled appointment startdate and the state date recommended by the oncologist

Type II delay Time (minutes) between the patient arriving to waitingroom and the patient being called by the nurse to start theappointment

Type III delay Time (minutes) the patient waits in the chemotherapychair before the nurse starts the patient’s chemotherapytreatment

System time Time (minutes) the patient spends at the oncology clinicfrom arrival to the waiting room to discharge from the clinic

Management PerspectivePatient throughput Number of patients served in the oncology clinic in a dayChair utilization Percentage of time the chair is occupied during clinic

operating hoursNurse utilization Percentage of time the nurse has one or more patients

during clinic operating hoursNurse overtime Time (minutes) that the nurse must work beyond normal

clinic operating hours

The variables that can be altered in an attempt to improve performance measuresinclude patient appointment start times and the number of nurses available each day.Patient appointment start times depend on the scheduling algorithm being used and welater experiment with different scheduling algorithms to improve performance. We alsoperform a computational study of the ideal number of nurses required to achieve a certainlevel of performance.

4 DEVS-CHEMO Simulation Model

To derive the DEVS-CHEMO simulation model, first a description of the entities in areal oncology clinic setting is given. This is followed by model abstraction using anobject-oriented approach to define DEVS atomic and coupled models that represent thedifferent entities in the oncology clinic. Details of the DEVS-CHEMO model are givenincluding the system entity structure and software implementation. Finally, a descriptionof patient and resource scheduling algorithms used in DEVS-CHEMO is given.

4.1 Entities in a Real Oncology Clinic

The entities or objects in a typical real oncology clinic include human resources, patientsand clinic stations. Examples of these types of entities is listed in Table 3. Humanresources are individuals who are part of the oncology clinic staff. There are five types of

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human resources in an oncology clinic: oncologist, scheduler, receptionist, charge-nurse,and registered nurse (RN ). The oncologist is the physician who treats cancer patientsand prescribes treatment regimens along with start dates. The oncologist is not presentduring the chemotherapy treatment and thus is not modeled in DEVS-CHEMO. However,the rest of human resources are modeled. The scheduler receives patient appointmentrequests and schedules each patient’s treatment regimen based on the availability of clinicresources. The receptionist assists patients upon arrival at the clinic for an appointment.The RN performs many tasks during the patient’s chemotherapy treatment includingseating the patient, ordering the drug, checking vitals, starting the drug infusion, etc.The charge-nurse is considered the “head nurse” and oversees the clinic operations andavailability of the two primary clinic resources, the RNs and chemotherapy chairs.

Table 3: Example entities in a real oncology clinic.

Human Resources

OncologistSchedulerReceptionistRegistered Nurse (RN)Charge Nurse

Patients Chemotherapy Patients

Clinic Stations

Waiting RoomPharmacyChemotherapy ChairsOncology Clinic

The second type of entity is patients, which represents the patients in the oncologyclinic. Each patient entity has a patient identification number, treatment regimen, andappointment schedule. The third type of entity is clinic stations. These are simplylocations within the clinic where a specific activities or services take place. The oncologyclinic is composed of three clinic stations: waiting room, pharmacy, and chemotherapychairs. Waiting room is the location where patients wait after check-in with the recep-tionist before the nurse assists them to a chemotherapy chair. Pharmacy is the locationwhere drug orders are received from the RN and prepared for the patient by a pharmacist.Chemotherapy chairs are special seats located in rooms where patients sit to receive druginfusions.

4.2 DEVS-CHEMO Model Abstraction

The objects identified in the previous section will now be abstracted and modeled usingDEVS. In DEVS, these objects are modeled as atomic models, coupled models, or simply,entities. Table 4 gives a list of the atomic and coupled models that are abstractions ofthe real oncology clinic and make up DEVS-CHEMO. An object in DEVS represents areal or abstract thing with attributes and operations that define the object’s behavior.Atomic models are the simplest and form the building blocks of DEVS models. Coupled

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models link atomic models in a hierarchical manner using couplings. Atomic and coupledmodels are used when the behavior, or current state and reaction to events in the system,of the object is needed in the simulation. An entity is used when the behavior of theobject is not relevant to the simulation. Atomic models are used for simple objects withbehavioral properties while coupled models are used when the object has relatively morecomplex behavior and is composed of atomic and/or coupled models.

Table 4: Atomic and coupled models in DEVS-CHEMO.Type of DEVS Model Name Description

CoupledEF CHEMO DEVS-CHEMO modelEF Experimental FrameCHEMO Oncology Clinic model

Atomic

CGENR Call GeneratorSCHED SchedulerPGENR Patient GeneratorTRANSD TransducerRECEPT ReceptionistWAITROOM Wait RoomPHARM PharmacyCHARGENURSE Charge NurseREGNURSE Registered Nurse (RN)

The atomic models are coupled in a hierarchical manner to create the coupled modelsresulting in EF CHEMO at the highest level of the hierarchy. Thus DEVS-CHEMOsimulation model is defined by the EF-CHEMO coupled model which is composed ofEF (experimental frame) and CHEMO (oncology clinic) coupled models connected asshown in Figure 2. Detailed depiction of the two models are given in Figures 3 and 4,respectively. The EF coupled model defines the environment for testing and evaluatingCHEMO, the oncology clinic simulation model. As can be seen in Figure 3, it comprisesatomic models CGENR, SCHED, PGENR, and TRANSD coupled as shown in the figure.CGENR generates and sends calls to the clinic for appointment requests while SCHEDmimics the scheduling of the appointments. In turn, PGENR is responsible for generatingpatient arrivals to the clinic on the day of the appointment. Finally, TRANSD isresponsible for computing patient and management performance measures of interest.Details of the atomic models comprising EF now follow.

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EF_CHEMO

EF

CHEMO

out_Wait3Time

out_PatientDepart out_NurseTime

out_PatientAppt

out_Wait2Time

out_WaitRoomCapacity

in_Wait2Time in_Wait3Time in_NurseTime

in_PatientDepart in_WaitRoomCapacity

in_PatientAppt

Figure 2: EF CHEMO coupled model.

EF

TRANSD

PGENR

SCHED

CGENR

out_PatientAppt

out_ApptRequest

out_ApptTimes

in_Wait1Time

out_Wait1Time

in_ApptTimes out_PatientAppt

in_ApptRequest

in_Wait2Time in_Wait3Time in_NurseTime

in_WaitRoomCapacity in_PatientDepart

in_Wait2Time in_Wait3Time in_NurseTime

in_WaitRoomCapacity in_PatientDepart

Figure 3: Experimental frame EF coupled model.

CGENR atomic model represents the oncologist identifying a new cancer patient,prescribing a unique treatment regimen, and the patient requesting a series of appoint-ments for the prescribed treatment regimen. In DEVS-CHEMO, CGENR creates a newchemotherapy patient and sends a message to the scheduler requesting an appointmentschedule for the new patient. CGENR has one output port for sending information tothe SCHED atomic model and has two states, “Idle” and “Generating”. The model is

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CHEMO

PHARM

RECEPT

REGNURSE1

in_PatientAppt out_PatientAppt

out_PatientAppt1

out_NurseTime

out_PatientDepart

out_WaitRoomCapacity

out_NurseTask

CHARGE NURSE

out_Wait2Time

out_Wait3Time

WAITROOM

out_DrugOrder

out_PatientApptn

.

.

.

.

.

.

out_DrugOrdern

out_PatientSeated

in_PatientAppt

in_PatientAppt in_PatientSeated

out_Wait2Time out_WaitRoomCapacity

in_PatientAppt

in_NurseTask

out_DrugOrder1 in_DrugOrder

in_PatientAppt1

in_DrugOrder1 out_NurseTime out_Wait3Time out_PatientDepart

.

.

.

REGNURSEn

Figure 4: Oncology clinic CHEMO coupled model.

initialized in the “Idle” state and a state transition to the “Generating” states occurswhen the time for generating a new patient call is due.

SCHED atomic model schedules all patient appointments in the treatment regimenusing a scheduling algorithm selected by the user. It has one input port and two outputports. The “out ApptTimes output port sends information to the PGENR atomic modeland the “out Wait1Time” output port sends information to the TRANSD atomic model.SCHED has two states, “Idle” and “Scheduling”. The model is initialized in the “Idle”state and a state transition to the “Scheduling” state occurs when the model is in the“Idle” state and a message ApptRequest is received at the “in ApptRequest” input port.A method (function), Algorithm(), takes the information provided by the patient andperforms the scheduling using the algorithm chosen by the user. Upon completion of thistask (processingT ime time has elapsed) and if there are no more appointment requests(schedQueue.isEmpty() == true), the model transitions to the “Idle” state.

Two scheduling algorithms were implemented in SCHED, As-Soon-As-Possible (ASAP)algorithm and Chair and Nurse (CN) algorithm. The ASAP algorithm mimics howpatients were scheduled at the oncology clinic that collaborated on this work (describedin Section 5) at the time of this study. In this algorithm, patients are scheduled usingonly chair availability to assign a chair to each patient for each of their appointments in

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the treatment regimen without considering nurse availability. The algorithm finds therecommended date of the appointment, considers each chair resource one-at-a-time untila chair with an adequate number of time slots is found. If the chairs are unavailablefor the date, then all appointments are moved forward one day and the search processis performed again. In the CN algorithm patients are scheduled using both chair andnurse availability. Thus a chair and nurse are assigned for each patient appointment.The algorithm uses the same search procedure as the ASAP to find an available chairand once a chair is selected, the algorithm then searches for a nurse who can start theappointment and handle the additional patient acuity. The latter constraint requiresthat the sum of the acuity levels of all patients assigned to the nurse is less than or equalto a specified maximum acuity level. If the constraint is satisfied, then the appointmentschedule is kept; otherwise, the nurse search process is resumed or another time slot isselected based on chair availability. Due to space limitations, mathematical descriptionsof the algorithms are omitted.

PGENR atomic model generates patient arrivals to the oncology clinic at their sched-uled appointment date and time. PGENR has one input port and one output port. The“in ApptTimes” input port receives information from the SCHED atomic model whilethe “out PatientAppt” output port allows for transmitting information to the RECEPTatomic model. Like CGENR, PGENR also has two states, “Idle” and “Generating”.TRANSD atomic model captures data points from other atomic models and computespatient and management performance measures. TRANSD has six input ports and nooutput ports. The “in Wait1Time”, “in Wait2Time”, and “in Wait3Time” input portsreceive information from the SCHED as well as the WAITROOM and REGNURSEatomic models (describe next). The “in WaitRoomCapacity” input port receives infor-mation from the WAITROOM while the “in NurseTime” and “in PatientDepart” receiveinformation from the REGNURSE atomic model. TRANSD has two states, “Idle” and“Processing”.

The CHEMO coupled model is composed of RECEPT, WAITROOM, PHARM,CHARGENURSE, and REGNURSEi atomic models coupled as shown in Figure 4.CHEMO captures the daily operations of the oncology clinic as patient’s attend theirappointments. Since an oncology clinic typically has more that one RN, CHEMO assumesthat there are n RNs. Thus we have REGNURSE1, · · · , REGNURSEn, indexed by i.Details of each of the atomic models in CHEMO now follow. RECEPT atomic modelreceives each patient who arrives at the oncology clinic for an appointment, directs thepatient to the waiting room, and notifies the charge-nurse of the patient’s arrival to theclinic. RECEPT has one input port and one output port. The “in ApptTimes” inputport receives information from the PGENR atomic model and the “out PatientAppt”output port sends information to the CHARGENURSE and WAITROOM atomic models.RECEPT has three states, “Available”, “ServingPatient”, and “Closed”.

WAITROOM atomic model holds patients after they have left the receptionist untila REGNURSEi calls the patient to begin their chemotherapy treatment. WAITROOMhas two input ports and two output ports. The “in ApptTimes” input port receivesinformation from the RECEPT atomic model and the “in PatientSeated” input port re-

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ceives information from the REGNURSEi. The “out Wait2Time” and “out WaitRoom-Capacity” output ports send information to the TRANSD. RECEPT has three states,“Open”, “Processing”, and “Closed”. PHARM atomic model receives drug orders fromREGNURSEi, prepares the chemotherapy drugs, and notifies the REGNURSEi whenthe drugs are ready. PHARM has one input port and n output ports of type “out Drug-Ordern”, where n is the number of RNs in the oncology clinic. The “in DrugOrder”input port receives information from REGNURSE and each “out DrugOrderi” outputports send information to the corresponding REGNURSEi atomic model. PHARM hastwo states: “Idle” and “PreparingOrder”.

CHARGENURSE atomic model represents the charge-nurse and manages patientsand clinic resources. The primary responsibility of the CHARGENURSE is to as-sign patients who are ready for treatment to an available chemotherapy chair and RN.CHARGENURSE has two input ports and n output ports of type “out PatientApptn”,where n is the number of RNs in the oncology clinic. The “in PatientAppt” input portreceives information from the RECEPT atomic model while the ”in NurseTask” inputport receives information from the REGNURSE atomic model. Each “out PatientAppti”output port sends a message to the corresponding REGNURSEi atomic model to notifythe nurse that a patient is available to begin their appointment. The model has threestates, “Available”, “ProcessingPatient”, and “ChairAvailable”.

REGNURSE atomic model is the most involved atomic model in DEVS-CHEMO.This model captures the behavior of an RN: retrieves a patient from the waiting room,seats the patient in their assigned chemotherapy chair, orders drugs from the phar-macy, checks the patient’s vital signs, picks up drugs from the pharmacy, starts thepatient’s chemotherapy drug infusion, monitors the patient, and stops the patient’schemotherapy drug infusion. REGNURSE has two input ports and six output ports.The “in PatientAppt” input port receives information from the RECEPT atomic modeland the ”in DrugOrder” input port receives information from the PHARM atomic model.The “out DrugOrder” output port sends information to PHARM, the “out NurseTask”output port sends information to the CHARGENURSE, the “out PatientSeated” and“out PatientDepart” output ports sends information to WAITROOM and TRANSD,respectively. Finally, the “out NurseTime” and “out Wait3Time” output ports sendmessages to the TRANSD. REGNURSE has twelve states and its behavior is depictedusing the statechart in Figure 5.In the statechart, “==” denotes equality comparisonand & denotes logical AND.

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Figure 5: Statechart depict behavior of REGNURSE.

In Figure 5, REGNURSEi is initialized in “Home” state and a transition to the“Available” state occurs when the oncology clinic opens. A message received on the“in PatientAppt” input causes the REGNURSEi to transition to the “CheckingWaitList”state. In the “CheckingWaitList” state, if there is a patient waiting to start treatmentand there is adequate time and capacity to start the patient’s treatment, then theREGNURSEi transitions to “GettingPatient”. From here, the REGNURSEi transitionsto a series of phases based on elapsed times including “SeatingPatient”, “OrderingDrug”,and “CheckingVitals”. If REGNURSEi is in the “CheckingVitals” state and the drugorder from the pharmacy (PHARM) is ready, then REGNURSEi transitions to “Starting-Infusion”. Otherwise, REGNURSEi transitions to “WaitingOnDrug” until a message isreceived on the “in DrugOrder” input port before transitioning to “StartingInfusion”.After the infStartT ime has elapsed, REGNURSEi returns to “CheckingWaitList”.

When REGNURSE is in the “CheckingWaitList” state and there are existing pa-tients and the REGNURSE is unable to start a patient’s treatment regimen, the modeltransitions to “MonitoringPatients”. If the model is “MonitoringPatients”, an input on“in PatientAppt” triggers a transition back to “CheckingWaitList”; otherwise, the nurseeventually needs to discharge a patient, transition to “StoppingInfusion” and then to“CheckingWaitList”. If REGNURSEi is in “CheckingWaitList” and there are no patients,no patients are waiting, and no patients were recently discharged, then the model tran-sitions to “Available”. If the model is in “CheckingWaitList” and there are no patientsand no patients are waiting but one or more patients were recently discharged, then themodel transitions to “UpdateTRANSD”. After updating the transducer, REGNURSEitransitions to “Available” if the clinic is still open or transition to “Home” if the clinic isclosed. Finally, if REGNURSEi is already in the “Available” state when the clinic closes,then REGNURSEi transitions to “Home”. Since REGNURSE is critical to the operation

15

of DEVS-CHEMO, the DEVS mathematical description of the atomic is included in theAppendix for the interested reader.

4.3 System Entity Structure and Software Implementation

System entity structure (SES) is used in designing simulation-based systems and showsthe hierarchy associated with software models. Using the SES, a DEVS modeler canvisualize the relationships between atomic and coupled models. Figure 6 shows the SESfor DEVS-CHEMO. In the figure, “x dec” implies that model x can be decomposedinto smaller models. For example, “ef chemo dec” shows that EF CHEMO can bedecomposed into EF and CHEMO. Also in the figure, “y multi-dec” shows a specialdecomposition called multiple decomposition. This decomposition is used to representan entity whose number in the system may vary. This means that model y can have0, 1, 2, or more model y ’s. In Figure 6 REGNURSES model can have 0, 1, 2, or moreREGNURSEs.

EF CHEMO appears at the top of the SES which indicates that it is the highestlevel coupled model and can be decomposed into two other coupled models EF andCHEMO. The EF coupled model can be decomposed into four atomic models, TRAND,PGENR, CGENR, and SCHED. The CHEMO coupled model decomposes into five atomicmodels, RECEPT, CHARGENURSE, REGNURSES, PHARM, and WAITROOM. Themultiple decomposition node “regnurse multi-dec” shows that REGNURSES can havezero or more REGNURSEs atomic models. The benefit of using an SES is to provide astructural knowledge representation of the possible structures of a system that can beused in a model base, which is an organized software library of component models.

EF_CHEMO

ef_chemo_dec

CHEMO

chemo_dec

EF

ef_dec

TRAND PGENR CGENR SCHED RECEPT CHARGENURSE

REGNURSES

PHARM

WAITROOM

REGNURSE

regnurses_multi-dec

Figure 6: System entity structure (SES) of DEVS-CHEMO

DEVS-CHEMO was designed based on SES in Figure 6 and implemented usingDEVSJAVA [6], a Java-based M&S software using the DEVS formalism. The model

16

was implemented using the Eclipse Standard/SDK (Kepler release version) environment.Each atomic and coupled model was tested individually using DEVSJAVA SimulationView Version (SimView) 1.2. SimView allows the modeler to visually inspect the modelbehavior using test inputs and starting, stopping, or slowing the simulation run to viewthe simulation clock and parameter values.

5 Application

The DEVS-CHEMO simulation model was implemented and applied to the outpatientoncology clinic at Baylor Scott & White Hospital in Temple, Texas, USA. Historicaldata for a five-month period was made available to test and validate DEVS-CHEMO.This then allowed for conducting computer simulation experiments using alternativescheduling algorithms to gain insights into the clinic operations and management andto study the impact of the number of nurses on clinic performance. At the time of thestudy, the oncology clinic operated Monday through Friday from 8:00 a.m. to 5:00 p.m.and was closed on Saturday and Sunday. The clinic typically had one charge-nurse andfour to eight RNs on duty at any given time. There were 20 chemotherapy chairs inthe oncology clinic, but three were reserved for emergency and special appointments.Therefore, only 17 chairs were actively used for scheduling purposes. The clinic treatedabout 24 patients a day on average and had at least one receptionist and scheduleravailable during operation hours.

The historical data contained 505 patients that were scheduled over a five-monthperiod totaling 2070 appointments. The data also included actual appointment times andeach appointment contained information on the patient’s appointment date, appointmenttime, arrival time, IV start time, IV stop time, drug name(s), and each individual drugstart and stop time(s). Data on type II and type III delay was only available as thesum of the two measures in the historical data, and is reported as type II + III delayin 5. The number of chairs and number of nurses available each day was also available.Data on type I delay, resource assignments, and resource utilization were not availablefor analysis. A summary of the historical data statistics for a five-month period is givenin Table 5. The table lists the performance measures and their corresponding mean,standard deviation (St.Dev.) and units used.

Table 5: Oncology clinic historical data statistics over a five-month period.Performance Measure Mean Stdev Units

Total throughput 2070.0 AppointmentsDaily throughput 23.5 PatientsNurse overtime 2.20 7.91 MinutesNurse overtime+ 19.00 14.91 MinutesType II + III delay 50.41 6.21 MinutesSystem time 206.87 21.94 Minutes

Nurse overtime+ excludes zero entries

17

At this clinic, each day was divided into 15-minute time slots for scheduling purposes.Patient and resource scheduling was done as follows: When a patient calls the schedulerto get an appointment, the patient provides their treatment regimen and start date. Thescheduler then uses the ASAP algorithm based on the availability of the 17 chemotherapychairs to schedule the patient’s appointment. RN availability is ignored in this schedulingalgorithm. The scheduler begins with the recommended start date and ensures that thefirst appointment and all subsequent appointment dates can be accommodated by theavailability of the chemotherapy chairs. If any appointment in the treatment regimencannot be satisfied, the scheduler moves all appointments by one day and checks again.This process is repeated until all appointments in the treatment regimen are successfullyscheduled. Next, the design of experiments is described.

5.1 Design of Experiments

The design of experiments was aimed at understanding how patients and clinic resourcesshould be scheduled and how the number of nurses impacts clinic performance. Toaddress these issues, three different experiments were designed and conducted. The firstexperiment (Experiment 1 ) was aimed at testing and validating DEVS-CHEMO usinghistorical data so as to recreate what had happened over a five-month period. Thesecond experiment (Experiment 2 ) was a comparative experiment to study the impact ofusing the ASAP and CN algorithms on clinic performance. Finally, the third experiment(Experiment 3 ) used the ASAP algorithm to assess the effect of the number of availablenurses on clinic performance with a goal of determining the appropriate number of nursesfor the clinic.

The performance measures listed in Table 2 were used to analyze simulation resultsfrom the patient and management perspectives. To account for the stochastic natureof several simulation parameters, 100 replications were performed for each experiment.Furthermore, clinic operations were simulated for a five-month period based on thehistorical data. For each experiment, the mean, standard deviation, and 90% confidenceinterval for all performance measures were computed and reported. The simulations wereconducted on a Dell Precision T7500 with an Intel(R) Xeon(R) dual processors runningat 2.40GHz with 12.0GB RAM.

Even though simulation runs in DEVS-CHEMO used the chair and/or nurse as-signments for scheduling purposes, due to the stochastic nature of patient arrivals andtreatment duration at the clinic, it was unrealistic to rigidly apply these rules on theactual day of the appointment in the simulation. Instead, the assigned nurse and/orassigned chair were used only to schedule the appointment times for the patient. However,those assignments were not necessarily kept during the actual appointment. If thescheduling algorithm contained a nurse or chair assignment, DEVS-CHEMO first tried touse that assignment if the assigned resource was available. Otherwise, DEVS-CHEMOre-assigned the patient to the next available resource. This policy was implementedbecause initial experiments showed that maintaining the resource assignments resultedin high idle times for some resources, over-utilization for other resources, and high levels

18

of clinic overtime.The stochastic nature of patient treatment duration means that when a patient has

a longer treatment duration than expected, their assigned chair will still be occupiedwhen the next patient arrives to the clinic. Although a second chair may be available forthe instances where other patients had a shorter treatment duration than expected, thegoal of maintaining chair and nurse assignments requires that the second chair remainempty and the next patient must continue to wait for the first patient to finish treatmentand for their assigned chair to become available. Under such a rigid assignment policy,most subsequent appointments will continue to be delayed and the clinic will stay openovertime to accommodate all scheduled appointments, even though other resources mayhave been available for use.

Table 6 lists the parameters that were set to be stochastic in the simulation withthe corresponding probability distributions that provided the best fit based on the clinichistorical data. In the table, the empirical distributions for number of nurses availableon a given day and appointment duration were constructed using historical data. The‘empirical’ distribution for patient acuity was simply based on discussions with the clinicstaff. The rest of the distributions were the ones that provided the best fit based onhistorical data using standard statistical software. The amount of time used to scheduleand allocate time for each appointment is the planned time. The planned time wasobtained from the drug infusion time sheets that the clinic used for scheduling purposes.The drug infusion time sheet tells the scheduler how much time to allocate for eachappointment (appointment duration), depending on the drug used. The simulation usedthe planned time from the drug infusion time sheet to schedule patients, but the actualappointment duration was stochastic based on analysis results from the historical data.

Table 6: Stochastic parameters and type of distribution used in DEVS-CHEMO.Stochastic Parameter Distribution Parameters

Number of nurses Empirical [(4, 0.131), (5, 0.273), (6, 0.394),(7, 0.182), (8, 0.020)]

Early arrivals Gamma(α, β) (1.184, 25.060)Late arrivals Weibull(α, β) (0.863, 18.847)Appointment duration Empirical †

Type II + III delay Gamma(α, β) (2.893, 13.203)Treatment start date Uniform(L,U) [1, 7]Patient acuity Empirical [(1, 0.7)(2, 0.2)(3, 0.1)]

†Different for each type of chemotherapy drug

The stochastic parameters and corresponding distributions listed in Table 6 were usedin the simulations runs for Experiments 2 and 3. The oncology clinic was assumed tooperate nine hours each day to allow for nurse overtime. The clinic had one charge-nurse,one receptionist, one scheduler, and three pharmacists in the pharmacy. The number ofchemotherapy chairs was set to 17 and stopping an infusion was assumed to take twominutes. Even though the each patient’s acuity level was stochastic, the maximum acuitylevel for a nurse was set at five.

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5.2 Simulation Results

The simulation results for all the experiments will now be reported. The results aresummarized using tables and graphs and a discussion of the results is given later in thenext subsection.

Experiment 1: DEVS-CHEMO Testing and Validation

The first experiment was designed to test and validate DEVS-CHEMO based on historicaldata. This was done by simulating the actual 2070 patient appointments from thehistorical data. In this experiment, patients arrived at the clinic at their appointmenttimes and historical values for the appointment duration and arrival time to IV were usedin the simulation runs. The historical number of chairs and number of nurses availableeach day was also used. All patients were assumed to have an acuity level of one while themaximum acuity level for a nurse was five. Since data type I delay, resource assignments,and resource utilization were not available in the historical data, these were assumedto be stochastic in the simulation. Thus 100 replications were performed to accountfor these uncertain parameters in the simulation. In each simulation run, the charge-nurse randomly assigned patients to any available RN. Consequently, the patient-nurseassignments, nurse overtime, type II+III delay, and system time values were different foreach simulation run.

The results of Experiment 1 are summarized in Table 7. The table reports for eachperformance measure the mean (Mean), standard deviation (Stdev), and 90% confidenceinterval (90% CI). The mean values for all the performance measures except nurseovertime are within the 1% of the historical values reported in Table 6. The mean nurseovertime has a deviation of about 24% from the historical mean. This is a relatively largedeviation but is not surprising since the historical mean has a relatively large standarddeviation. Overall, the Experiment 1 results reproduced identical results to the historicalvalues and thus demonstrate that DEVS-CHEMO reproduce the events in the historicaldata with relative accuracy.

Table 7: DEVS-CHEMO model testing and validation results.Performance Measure Mean Stdev 90% CI

Total throughput (appointments) 2070.0 0.00 [2070.0,2070.0]Daily throughput (patients) 23.5 0.00 [23.5,23.5]Chair utilization (%) 51.22 0.05 [51.21,51.22]Nurse utilization (%) 77.28 0.32 [77.23,77.34]Nurse overtime+ (minutes) 32.47 2.75 [32.02,32.92]Nurse overtime (minutes) 6.24 0.68 [6.13,6.36]Type II delay (minutes) 14.93 0.70 [14.82,15.05]Type III delay (minutes) 39.59 0.15 [39.56,39.61]System time (minutes) 210.56 0.69 [210.45,210.68]

Nurse overtime+ excludes zero entries

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Experiment 2: Scheduling Algorithms

The next set of experiments were designed to study the comparative performance ofdifferent scheduling algorithms. The two algorithms described in Section 4.2, ASAP andCN algorithms, were implemented within the SCHED atomic model. Recall that theASAP algorithm mimics how the oncology clinic scheduled patients using an as-soon-as-possible procedure based only on chair availability. The CN algorithm was implementedas an alternative and schedules patients based on both chair and nurse availability. Foreach algorithm, 100 replications of simulation runs were made with the stochastic dataparameters set according to the probability distributions listed in Table 5.

The results of the simulation runs for the five-month period are summarized in Table8. The table lists the algorithm, performance measure, mean, standard deviation, and90% confidence interval. Throughput is reported as the total number of appointmentsserved as well as the daily throughput, which is the number of patients served in a singleday on average. Nurse overtime is reported in two different ways: “Nurse overtime+” isthe average nurse overtime without including zero entries whereas “Nurse overtime” isthe average overtime among all nurses during the five-month period. Nurse overtime+

gives averages nurse overtime across all days when there was overtime. Nurse overtime+,type II delay, type III delay, and system time are also plotted in the bar graph in Figure7. The graph also shows for each performance measures the difference between the ASAPalgorithm result and that of the CN algorithm. Finally, computer simulation time for asingle simulation run was 7.0 seconds on average.

21

Table 8: Scheduling algorithms simulation resultsAlgorithm Performance Measure Mean Stdev 90% CI

ASAP Total throughput (appointments) 2640.4 76.3 [2627.8, 2652.9]Daily throughput (patients) 23.8 0.69 [23.7, 23.9]Chair utilization (%) 49.87 1.58 [49.61, 50.13]Nurse utilization (%) 84.57 1.86 [84.27, 84.88]Nurse overtime+ (minutes) 105.60 6.41 [104.55, 106.65]Nurse overtime (minutes) 41.24 3.61 [40.65, 41.83]Type I delay (days) 1.33 0.04 [1.32, 1.34]Type II delay (minutes) 21.86 2.04 [21.52, 22.20]Type III delay (minutes) 32.06 0.43 [31.99, 32.13]System time (minutes) 210.19 4.35 [209.48, 210.91]

CN Total throughput (appointments) 2612.5 70.54 [2600.9, 2624.1]Daily throughput (patients) 23.5 0.64 [23.4, 23.6]Chair utilization (%) 49.30 1.46 [49.06, 49.54]Nurse utilization (%) 83.82 1.80 [83.52, 84.12]Nurse overtime+ (minutes) 100.37 6.19 [99.35, 101.39]Nurse overtime (minutes) 38.11 3.72 [37.50, 38.72]Type I delay (days) 1.44 0.07 [1.42, 1.45]Type II delay (minutes) 12.54 1.14 [12.35, 12.73]Type III delay (minutes) 31.94 0.38 [31.88, 32.00]System time (minutes) 200.81 3.75 [200.19, 201.43]

Nurse overtime+ excludes zero entries

0

25

50

75

100

125

150

175

200

225

Nurse overtime+ Type II delay Type III delay System time

Minutes

ASAP

CN

Difference:

Figure 7: Time-based performance results for ASAP and CN algorithms.

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Experiment 3: Performance Versus Number of Nurses

The third and last experiment was designed to assess oncology clinic performance versusthe number of nurses available in the clinic each day. This experiment was motivated bythe fact that the daily number of nurses was said to be the most limited resource for theoncology clinic in this study. In particular, clinic management was interested in knowinghow many nurses would be required to provide adequate service without compromisingpatient service, while assuming a 20% increase in patient appointments. The historicaldaily average number of nurses in the clinic was 5.6. Therefore, in this experiment thenumber of available nurses each day was fixed in each simulation run, assuming a five-month period and using the ASAP and CN algorithms, respectively, to schedule theappointments. The number of nurses was varied from five to 10. Thus six simulationruns each with 100 replications were performed. The results of this experiment are givenin Table 9. The table reports the mean for each performance measure. The average nurseutilization, nurse overtime, and system time are also plotted in the bar graph in Figure8. The figure shows the trends in these performance measures as the daily number ofnurses is increased from five to 10.

Table 9: Performance measures (mean values) versus number of available nurses.Performance Measure Number of Nurses

ASAP 5 6 7 8 9 10

Total throughput (appointments) 3095.3 3093.8 3087.1 3084.7 3080.2 3089.0Daily throughput (patients) 27.9 27.9 27.8 27.8 27.8 27.8Chair utilization (%) 58.32 58.55 58.21 58.5 58.52 58.65Nurse utilization (%) 95.33 88.92 84.07 80.74 77.76 75.42Nurse overtime+ (minutes) 60.09 45.69 42.14 41.17 41.35 40.68Nurse overtime (minutes) 37.02 24.21 19.47 17.41 16.23 14.89Type I delay (days) 0.76 0.76 0.75 0.76 0.74 0.75Type II delay (minutes) 30.52 19.49 15.68 14.29 13.39 13.00Type III delay (minutes) 31.79 32.12 32.36 32.65 32.99 33.29System time (minutes) 218.45 208.27 203.78 203.46 202.91 202.39

CN

Total throughput (appointments) 3092.6 3135.4 3092.0 3063.6 3141.4 3057.2Daily throughput (patients) 27.9 28.3 27.9 27.6 28.3 27.5Chair utilization (%) 58.55 58.48 58.41 57.91 59.19 58.33Nurse utilization (%) 98.88 89.82 82.83 75.68 71.87 65.37Nurse overtime+ (minutes) 55.54 40.37 33.89 31.4 27.69 24.88Nurse overtime (minutes) 106.3 96.61 97.6 100.18 97.68 97.67Type I delay (days) 1.53 1.51 1.47 1.37 1.47 1.4Type II delay (minutes) 15.36 11.44 10.05 10.01 10.01 9.95Type III delay (minutes) 31.92 31.91 32.54 32.85 32.68 32.94System time (minutes) 204.19 197.68 198.32 198.47 197.94 200.31

Nurse overtime+ excludes zero entries

23

0

50

100

150

200

250

5 6 7 8 9 10

Number of Nurses

Nurse utilization (%)

Nurse overtime+ (minutes)

System time (minutes)

Figure 8: Performance versus number of nurses for ASAP algorithm.

5.3 Discussion

The results of the three computer simulation experiments using DEVS-CHEMO provideinsights into how patients should be scheduled and how the number of nurses impactsclinic performance. The experiments were designed to first test and validate DEVS-CHEMO (Experiment 1) and then to assess performance of the scheduling algorithms(Experiment 2) as well as the impact of the daily number of nurses on overall clinic per-formance. Replications were made for simulation runs to guard against any pathologicalcases since several parameters in the simulation were stochastic. Thus 100 replicationsand a 90% confidence interval were arbitrarily selected. The results of Experiment 1show that DEVS-CHEMO can mimic oncology clinic operations and provide results thatare within relative accuracy of the historical values. This experiment was an initial steptowards validating DEVS-CHEMO and was limited by the five-month historical clinicdata that was available at the time of this study. More data is needed to fully validateDEVS-CHEMO under data conditions that may be different from what was observed inthat five-month period.

Two different scheduling algorithms were implemented and tested in Experiment 2.The results show that the clinic’s scheduling procedure of using the ASAP method whichonly considers future availability of chemotherapy chairs in scheduling a patient, actuallyprovides better throughput performance compared to the CN algorithm. However, it hascomparable performance on most of the other performance measures. Recall that theCN algorithm considers both the chair and the nurse availability. From Figure 7 it can beobserved that the CN algorithm provides better performance over the ASAP algorithmfor type II delay. This is the waiting time of the patient from their arrival at the clinicto the time they get attended to by a nurse. The CN algorithm provides patient waittime of about 13 minutes while the ASAP algorithms gives about 22 minutes on average.Consequently, the CN algorithm also provides slightly better system time. Thus a clinic

24

concerned about patient wait time type II should consider the CN algorithm over theASAP algorithm. It should also be pointed out that chair utilization for this clinic isabout 50% on average, while nurse utilization is about 85%. Thus the number of nursesat this clinic can be increased in order to reduce nurse utilization to be below 85% ifdesired.

The results of Experiment 3 amply demonstrate that the number of nurses availablein the clinic can indeed have a significant impact on patient and clinic performance. Theresults reported in Table 9 show that increasing the number of nurses for a fixed levelof patient demand results in decreased nurse utilization, nurse overtime, type II delay,and system time. The results also reveal (Figure 8) the diminishing returns of increasingthe number of nurses from five to 10. The gains are significant for up to about sevennurses for this oncology clinic. It can be seen that from eight to 10 nurses most of theperformance measure values remain almost constant. Thus these results indicate thathaving seven or eight nurses each day would provide relatively better performance thanhaving less than seven. Also, observe that Figure 8 shows that increasing the numberof nurses beyond seven leads to reduction in nurse utilization even though the otherperformance measures do not show significant gains.

6 Conclusion

Increased demand for chemotherapy coupled with the complexity of the treatment regi-mens make managing patient service and limited resources in oncology clinic very chal-lenging for several reasons. For example, chemotherapy patients require a series ofappointments over several weeks or months based on their treatment regimen as pre-scribed by the oncologist. Furthermore, the timing of these appointments is critical tothe effectiveness of the chemotherapy treatment on cancer. This work uses the DEVSformalism to derive DEVS-CHEMO, a generic simulation model for oncology clinicoperations that considers both patient and management aspects. DEVS is a formalM&S framework based on dynamical systems theory and provides well-defined conceptsfor hierarchical and modular model construction. DEVS-CHEMO was implemented inDEVSJAVA, tested and validated based on data for a real oncology clinic. DEVS-CHEMO provides oncology clinic managers with a model based on systems theory foranalyzing operational policies within the oncology clinic.

DEVS-CHEMO allows for computing various performance measures from the pa-tient’s perspective (type I delay, type II delay, type III delay, and system time) and fromthe management’s perspective (throughput, chair utilization, nurse utilization, and nurseovertime). Simulation results involving implementation of two scheduling algorithms, oneused at Baylor Scott & White oncology clinic (ASAP) and one that was devised in thiswork (CN), reveal several insights. For example, the results show that although theASAP and CN algorithms provide similar performance for most performance measures,the CN algorithm which considers both chair and nurse availability reduces type II delay,that is, patients wait less to get their treatment upon arrival at the clinic. The resultsalso reveal that the ideal number of nurses is seven when demand for oncology clinic

25

services is increased by 20%. Future work include extending DEVS-CHEMO to includelaboratory and blood work scheduling. This will allow for determining whether or notpatient appointments get rescheduled or treatments modified based on blood work results.Finally, modeling and simulating the health status of the patient in response to treatmentscan be incorporated in DEVS-CHEMO. This can play a role in estimating appointmentduration and patient acuity levels for each nurse.

Acknowledgments. The authors wish to thank Theresa A. Kelly, RN of Baylor Scott& White Oncology Clinic, Temple, Texas, for providing the data used in the experiments.The authors are also grateful to Valerie Oxley, RN, for sharing her expert knowledge inoutpatient oncology clinic operations.

Appendix

Mathematical Expression of REGNURSE in DEVS

The following notation will be used to mathematically define REGNURSE: == denotesequality comparison, ∧ denotes logic AND, and × denotes the Cartesian product. Also,following DEVS notation [4, 6, e.g.], σ will denote time delay in a given state, and ewill denote the elapsed time. In the mathematical expressions that follow, we use phaseto denote one of the possible state variables. The REGNURSE atomic model, whosestatechart is given in Figure 5, can be expressed in DEVS as follows:

DEV SREGNURSE = (XM , YM , S, δext, δint, δcon, λ, ta)

where, XM is the set of inputs, YM is the set of outputs, S is the set of states, δext is theexternal transition function, δint is the internal transition function, δcon is the confluencefunction, λ is the output function, and ta is the time advance function. More specifically,these artifacts are defined as follows:

XM = {(p, v)|p ∈ IPorts, v ∈ Xp} is the set of input ports and values, IPorts ={“in PatientAppt”, “in DrugOrder”}, and Xin PatientAppt = V1 and Xin DrugOrder = V2are arbitrary sets.

YM = {(p, v)|p ∈ OPorts, v ∈ Yp} is the set of output ports and values, OPorts ={“out DrugOrder”, “out NurseTime”, “out Wait3Time”, “out PatientChair”, “out -NurseTask”}, and Yout DrugOrder, Yout NurseTime, Yout Wait3Time, Yout PatientChair, andYout NurseTask are arbitrary sets.

S = {“Available”, “CheckingWaitList”, “GettingPatient”, “SeatingPatient”, “Or-deringDrug”, “CheckingVitals”, “WaitingOnDrug”, “StartingInfusion”, “Monitor-ingPatients”, “StoppingInfusion”, “UpdateTRANSD”, and “Home”}×R+,0×V1×V2is the set of sequential states.

External Transition Function :

26

δext((phase, σ,msg), e, (p, v))

= (“CheckingWaitList”, checkT ime,RN), if phase == “MonitoringPatients”∧ p ==“in PatientApppt”;

= (“CheckingWaitList”, checkT ime,RN), if phase == “Available” ∧ p ==“in PatientAppt”;

= (“StartingInfusion”, infStartT ime,RN), if phase == “WaitingOnDrug”∧ p ==“in DrugOrder”;

= (phase, σ − e, RN), otherwise.

Internal Transition Function :

δint(phase, σ,msg)

= (“Available”, openT ime,RN), if phase == “Home”, where openT ime is theremaining time the clinic is open for the day;

= (“GettingPatient”, gettingT ime,RN), if phase == “CheckingWaitList”∧WaitList.isEmpty() == false ∧ inadT imeCap() == false;

= (“SeatingPatient”, seatingT ime,RN), if phase == “GettingPatient”;

= (“OrderingDrug”, orderT ime,RN), if phase == “SeatingPatient”;

= (“CheckingVitals”, vitalT ime,RN), if phase == “OrderingDrug”;

= (“WaitingOnDrug”,∞, RN), if phase == “CheckingVitals”∧vitalsT ime elapsed ∧DrugReadyList.isEmpty() == true;

= (“StartingInfusion”, infStartT ime,RN), if phase == “CheckingVitals”∧vitalsT ime elapsed ∧ DrugReadyList.isEmpty() == false, where vitalsT imeelapsed indicates completion of checking patient vitals and DrugReadyList is thelist of chemotherapy drugs on patient’s treatment regimen;

= (“CheckingWaitList”, checkT ime,RN), if phase == “StartingInfusion”;

= (“MonitoringPatients”, nextT ime,RN), if phase == “CheckingWaitList”∧numPatients > 0 ∧ (WaitList.isEmpty() == true||(WaitList.isEmpty() ==false ∧ inadT imeCap() == true));

= (“StoppingInfusion”, infStopT ime,RN), if phase == “MonitoringPatients”;

= (“CheckingWaitList”, checkT ime,RN), if phase == “StoppingInfusion”;

= (“UpdateTRANSD”, updateT ime,RN), if phase == “CheckingWaitList”∧WaitList.isEmpty() == true ∧ numPatients == 0 ∧ stopInf == true;

= (“Available”, openT ime,RN), if phase == “UpdateTRANSD” ∧ openT ime > 0;

= (“Home”, homeT ime,RN), if phase == “UpdateTRANSD” ∧ openT ime <= 0where homeT ime is the time until the clinic opens on the next business day;

= (“Home”, homeT ime,RN), if phase == “Available”.

Confluence Function :

27

δcon((s, ta(s), x) = δext(δ(s), 0, x).

Output Function :

λ(phase, σ,RN)

= (“out NurseTask, NurseTask), if phase == “StoppingInfusion”, whereNurseTask is the message sent to CHARGENURSE;

= (“out PatientDepart, PatientChair), if phase == “StoppingInfusion”, wherePatientChair is the message sent to TRANSD;

= (“out PatientSeated, PatientChair), if phase == “GettingPatient”, wherePatientChair is the message sent to WAITROOM;

= (“out DrugOrder, DrugOrder), if phase == “OrderingDrug”, whereDrugOrder is the message sent to PHARM;

= (“out NurseTime, NurseT ime), if phase == “UpdateTRANSD”, whereNurseT ime is the message sent to TRANSD;

= (“out Wait3Time,Wait3Time), if phase == “StartingInfusion”, whereWait3Time is the message sent to TRANSD.

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Michelle M. Alvarado is a visiting professor at Texas A&M University, Departmentof Industrial and Systems Engineering, College Station, Texas, USA. She obtained herPh.D. in Industrial and Systems Engineering from the Texas A&M University in 2014.

Tanisha G. Cotton obtained her Ph.D. in Industrial and Systems Engineering fromTexas A&M University in 2013.

Lewis Ntaimo is an associate professor at Texas A&M University, Department ofIndustrial and Systems Engineering, College Station, Texas, USA. He obtained his Ph.D.in Systems and Industrial Engineering from the University of Arizona in 2004. He hasbeen with Texas A&M University since 2004.

Eduardo Perez is an assistant professor at Texas State University, Ingram School ofEngineering, San Marcos, Texas, USA. He obtained his Ph.D. in Industrial and Systemsfrom Texas A&M University in 2010. He has been with Texas State University since

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2012.

William R. Carpentier, MD is a retired radiologist and nuclear medicine physicianfrom Baylor Scott and White Health System, Temple, Texas, USA. Dr. William Carpen-tier was chief physician for the Apollo 11 crew and is acknowledged as one of the greatestcontributors to the field of space life science.

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