The expanding utilisation of advanced imaging continues over the UK and all through the world. Inside the NHS, MRI is for some time built up as the backbone of emergency and routine diagnostic cross-sectional imaging. The applications for MRI are across the board, both for critically sick and ambulant patients, with all body parts being assessed. The utilisation of MRI has expanded significantly over the previous decade, adding to medical expenses.
Be that as it may, there is recounted proof that in the UK, investment in MRI equipment is declining, which might be because of NHS funding limitations. There is a lot of strain to “sweat the assets”, operating services for longer hours and expanding throughput, to assist make with getting to diagnostic tests ever speedier. UK’s MRI capacity is extended compared to other countries. The UK has 6.1 MRI systems per million individuals, less than the nations including Estonia and Slovenia.
The NHS is as of now confronting noteworthy pressures relating to demand and capacity in radiology. Generally, out of hours radiology services during late evenings, nights and end of the week used to be an on-call model. The government has, again and again, ensured the public a 24/7 health service. The rise in demand for radiology services brought unevenness among demand and supply. At the present time, radiology 24/7 services are open to inpatient and emergency patients only. Supply of MRI resources is static and with the uncertain rise in demand over time can result in long waiting time for outpatients.
Here are a couple of issues in the radiology department as shown by  lop-sidedness makes Mondays busier when contrasted with different days of the week. In like way,  actualised Markov chains in planning different patients group coming at different arrival rate and confronted the problem of allocation of resources for the dynamic demand.
Another issue, at NHS Hospitals in the report  and , outpatient services, for example, radiology currently run day in and day out for inpatients and emergency; however, they are just accessible to outpatients between 9 am and 5 pm.  reports uncovered that around 8% of the outpatient missed their appointments and no show is an enormous issue.  clarifies that different patient groups such as inpatient, outpatient and the emergency patient are given different priority. The emergency patient is given more priority when contrasted with inpatient and outpatient. In like manner  states that disregarding random arrival of the patient can make the model off base.
At some of the time it is hard to incorporate all the aspects of the real problems in the simulation model. The issue which NHS is facing at the moment is an increase in patient waiting time and busier Mondays. This is due to the underutilization of the resources. This has further lead to randomness in-demand and mismatch between demand and capacity. According to  , in NHS £1 bn is being squandered every year by patients missing their appointments and no show. There are various implications in changing outpatient demand from 8 hours a day to 24 hours a day.
Various methodologies are proposed for better resource utilisation. Firstly,  prescribes assigning exclusive blocks to the process with the anticipated demand and assign pool blocks to the process with less predictable demand. Also,  contends that a separate process for emergency patient helps in decreasing cancellation and overtime. Furthermore,  states that more patients booked at the start of the hour and less at the end of the hour to absorb delays. Two patients are booked at the beginning of morning and afternoon sessions and remaining patients are booked at equal interval to avoid delays.
According to  report expresses that consultants should be on a staggered rota throughout the weekend and public holidays from 9 am to 8 pm. The weekday evening rota should be 5 pm to 8 pm. The support staff should be available for extended hours. The radiographer and radiologist time should not be wasted on administrative tasks. This will help improve the utilisation of high worth equipment, for example, MRI. Moreover,  report proposes that staff rota for radiographer and consultant to be 3 days for one week and 4 days for the following week.
 DES helps with foreseeing future demand using historical patient arrival rates. Additionally,  states DES helps in assessing poor outpatient flow. It uncovers that scheduling and capacity planning in healthcare helps with improving efficiency. Moreover,  and  suggest using DES modelling in healthcare for improvement and enhancement. Also  states DES underpins in modelling, outpatient in scheduling system, number of appointments, physician time and patient flow.
 features that hospital expanded hours and opening on weekends encourages in improving access to hospital care.  diagrams that DES implemented hospitals in Sweden had improved the process quality. Moreover,  illustrates adjusting supply based on demand and time allocation for the activity assists in bringing balance. Likewise,  encourages to use DES for outpatient capacity planning, in healthcare. Similarly,  features DES to find the outpatient flow in healthcare. DES used for planning, testing and staff scheduling in a hospital facility with increased capacity.
 claims that DES is used in an outpatient clinic with batch arrivals to take care of the no shows problem. The other solution, to give same-day appointment in which the patient is less likely for no show. In like manner,  states that overbooking helps in utilising healthcare resources for the no shows. Likewise,  highlights that outpatient cancellation and no shows can be settled using overbooking of the appointments, to amplify the utilisation of radiology capacity.
The objectives focused on solving the problem using DES to simulate the demand for MRI services across different scenarios, each with different hours of operation, to decrease of waiting time, queue length and patient stay time in the system, streamlining of resources allocation on the basis of demand, formation of crisis and most extreme demand scenarios, identification of congestion bottlenecks, the examination of the effect of other no show on the existing system, and improvement of the current system operations and functions which can be utilized to reconfigure the existing frameworks so as to improve system performance.
2. Performance Measures
Key performance metrics KPI are occupancy rate, clinic utilisation, staff utilisation (radiographer, clerk, nurse), patient throughout time, average waiting time, diagnostic procedure count.  approves using DES for demand and capacity model which will assist in identifying the key performance indicator. The other KPI can be resources average use, percentage of the patient leaving the system is under 120 min.
Input parameters shown in Figure 1 will be MRI service time, number of MRI, number of staff, patient process, patient arrival rate. As indicated by  key to classify the patient as each could have different processing time. Thus, the fitting of distribution for each group is very important. Understand the patient path and time to run the simulation for the model is significant. DES should be used to forecast capacity over time based on outpatient demand. Patient characteristics such as age, diagnosis, sex, the patient category should be taken into consideration. I have included patient inter-arrival time (dynamic random arrival), service time, servers. I have included a number of radiologists, radiographer, clerk. I have classified patient based on age, gender, type of patient. The fitting of the outpatient arrival data is done by Pearson V distribution.
 and Figure 1 and Figure 2(a) clarify that the process chart is imperative to understand the problem, objectives, input, and output of the system. It is separate from the simulation model. Likewise,  notices to use activity-based the
Figure 1. Illustration of conceptual model of MRI services.
Figure 2. (a) Illustration of conceptual model of MRI services (process mapping); (b) Methodology.
diagram in healthcare for service delivery processes. Also,  proposes changing hospital process flowchart into the DES model which assists in analysing how much resources of the hospital are being utilised. Additionally,  features simulation assists in incorporating different customer arrival rates and service time for modelling without affecting the real system of the radiology department. The process includes such as patient scheduling by the clerk, scanning by a radiographer and report interpretation by a radiologist. Figure 2(b) shows the methodology adopted for simulation.
· No travel time for any resources taken into consideration;
· Preparation time is included in the waiting area time;
· Patients are always coming in time;
· Outpatient is coming with an appointment;
· Emergency patient care given priority;
· The lateness of staff is zero;
· The capacity of 20 in the reception and waiting room queue;
· The capacity of 25 in the MRI reading room queue;
· Radiographer takes the patient from the waiting room;
· Availability of resources (staff and machines)—90% of the time;
· 3 shifts morning 9 am to 5 pm, evening 5 pm to 1 am and night 1 am to 9 am;
· Figure 3 shows Radiographer morning 4 nos, evening 3 nos, night 2 nos;
· Figure 3 Clerk morning, evening, night 1 no for each shift;
· Figure 3 Consultant morning, evening, night 1 no for each shift;
· We are not taking into consideration MRI report preparation time but considering consultant MRI report interpretation time;
· Evening demand calculated from 50% of the total outpatient demand and Night demand calculated from 25% of the total outpatient demand;
· Constraints are morning, evening, and night shifts.
Figure 3. Resource assignment matrix.
6. Pros Cons of Different Modelling Techniques
 uncovered that DES results are better for nonlinear systems as compared with system dynamics and agent-based modelling (ABM). DES takes into consideration patient arrival rate, staff scheduling and resource constraints. In like manner,  clarifies that DES is used for operational and strategic purposes. It is likewise called a dark grey box, where clients can link different processes in the model easily. DES is the best solution to this problem. System Dynamics (SD) is good to see the holistic view and for this problem, a detailed view is essential consequently, DES is applied.
7. Key Data
 DES is in high demand in healthcare for resource planning, capacity estimation and evaluating alternatives. Key resources in healthcare are nurses, consultants, and physicians. Data for the simulation can be collected through primary sources such as survey and current records of the hospital. The other means of collecting data is secondary source such as a literature review.
Different service time is recommended for MRI. Moreover,  states that service time for MRI is 33.2 minutes with a minimum of 10 minutes and a maximum 120 minutes. Also,  states that around 55% patient goes to the preparation area and for the contrast, preparation time is a triangular distribution (3, 4, 5) and patient preparation in the MRI room is 6 minutes. MRI process time for changing room is Gamma (3.41, 0.86), setting patient and MRI machine is Gamma (2.08, 2.01), MRI scanning is Gamma (7.86, 2.67), after scan activities Gamma (1.66, 1.81). Furthermore,  states that MRI total process time is normal distribution (26.46, 20.47). Additionally,  states that service time for the critical patient is more as compared to the normal patient. As well,  states that an old patient scan takes more time as compared to the young patient as young are very responsive. In addition,  states service time using lognormal (4.15, 0.335) distribution.
The input parameters are listed in Table 1.
· 8% of the total outpatient is no show;
· 57% outpatient, 43% inpatient & emergency;
Table 1. Input parameters.
· 56% inpatient, 44% emergency;
· Figure 4 shows age distribution of 0 to 19 ages 12%, 20 to 39 ages 35%, 40 to 59 ages 25%, 60 to 79 ages 21%, above 80 ages 7%;
· Figure 5 shows gender distribution of 42% men, 58% women;
· Patient inter arrival time follows Pearson V distribution;
· MRI waiting room & patient preparation time follows triangular distribution (4, 5, 6);
· MRI reading room time follows a uniform distribution 6 min to 12 min;
· MRI service time follows a normal distribution;
· Reception service time follows exponent distribution 8 min.
· Increased the standard deviation of MRI processing times for inpatient of 5 min and emergency patient of 10 min;
· Warmup period of 4320 minutes (1/10 of the total run period);
· Simulation run 1 month;
· No of runs 20;
· Figure 6 shows the precision with 20 runs;
· Random Sampling 17.
Figure 4. Patient age distribution.
Figure 5. Gender distribution.
Figure 6. No. of run for precision.
7.3. Fitted Distribution
Different statistical distributions can be applied using Lognormal, Normal, Exponent, Gamma, Pearson V and Weibull. The input parameters are estimated and fitted using chi-square goodness of fit. Fitted distributions help the model incorporate the stochastic nature of the hospital system. In case, seasonal data is not available  suggests using Poisson distribution means static distribution for patient arrival. I had only daily data, so I divided it by 24 hrs and then by 60 min—get interarrival times in minutes. I have used Pearson V distribution for patient arrival time and the patient arrival during the morning, evening, night.  highlights in the radiology department Pearson distribution is used. The input parameter fitted distributions type and value is given in Table 2.
Figure 7 and Figure 8 show the histogram and Q-Q plot demonstrated patient arrival data is not normally distributed. I have also used a Chi-Square test to check the normality of the patient arrival data and found P value less than 0.05 which means poor fit. I have tried to fit data using Chi-square goodness of fit and found P value greater than 0.05 which means each category has the same proportion.
I have used Simul8 for the creation of the model. Figure 9(a) demonstrates the final model snapshot in which outpatient is given exclusive blocks and inpatient
Table 2. Input parameter fitted distributions.
Figure 7. Histogram of patient arrival data.
Figure 8. QQ plot of patient arrival data.
Figure 9. (a) Discrete event simulation incorporated in Simul 8; (b) Time bounded distribution for noshow; (c) Time Absolute distribution for noshow.
& emergency patient is given a different route to access the MRI services. In this, a separate queue is given for inpatient & emergency. No-show problem of outpatient is resolved by overbooking shown in Figure 9(b) and Figure 9(c). Outpatient gave access for the reception and further going to the waiting room for MRI.
9. Experimentation & Output Analysis
Table 3 exhibits in scenarios 1, 2, 3 outpatient arrival rates changed with a change in time. In scenarios 4, 5, 6 different distributions were experimented for the MRI service time. In scenario 7, to resolve the problem of no show, overbooking was implemented during normal hours. In scenario 8, no show was further fixed using overbooking at the start and end of the hour and this resulted in long queues. In scenario 9, exclusive resources were allocated to the emergency patient. In scenario 10, exclusive resources were allocated to inpatient & emergency patient. In scenario 11, staff changes were conducted according to the demand.
9.1.1. Simulation Type
Implement non-terminating simulation to evaluate the system behaviour in the long run which is called steady state. It starts with the warmup period which is one-tenth (4320 min) of the simulation run period. I have not used the warmup period data. I have done statistical analysis on steady-state data to find the system behaviour.
Table 3. Different scenarios input parameters.
9.1.2. Run Length and Replication
To get precise and narrower confidence interval, I have run the simulation for one month with 46 replications for each scenario. I have used Simul8 to find the precision of 46 runs.
Validation of the Model
· The total demand in February 2018 for MRI scans was 2089 (historical data).
· Our model simulates a demand of approximately 1828 to 1930 scans, so is between 85% and 90% accurate in terms of demand.
· Figure 10 display that outpatient flow of 8 hr, 16 hr, 24 hr was validated in Simul8 and there is an upward trend from 9 am to 5 pm for 8 hr. There is a rising trend from 9 am to 1 am for 16 hr and uphill trend for 24 hr.
9.3. Output Analysis
After running different scenarios, Figure 11 and Figure 12 and Table 4 show scenarios 9, 10, 11 gives the best result, throughout time for the patient in the system is less. More outpatients have been treated as well. There are a higher percentage of patients leaving the system in less than 120 minutes. Furthermore, in scenarios 9, 10, 11 approximate 1900 outpatient are treated with reasonable average time in the system.
Figure 11 shows that scenario 8, more overbooking as compared to scenario 7, resultant to increase in average time in the system for inpatient and outpatient.
Figure 12 shows that there is a trend to be seen with an increase in average time in the system for the outpatient results to a smaller number of outpatient being treated.
Figure 12 shows that scenarios 4, 6 outpatient average times in the system dramatically shoots up due to slow processing at the MRI machine.
In Figure 13 elaborates that in scenarios 9, 10, 11 outpatient, inpatient &
Figure 10. Outpatient inflow trend in Simul8.
Figure 11. Patient throughout time in the system.
Figure 12. Outpatients exit number and average time in the system. X axis is scenarios (experiments) and Y axis is No. of Outpatients/Time (in minutes).
emergency exit numbers are steady. The results are better as compared with scenarios 1, 2, 3, 4, 5, 6. The exit numbers of scenario 8 are more but adversely affecting the other KPIs. Therefore, scenario 8 was ignored. Additionally, more outpatients are treated in the system. Furthermore, in scenario 11, there is an upward slope which states the percentage of patients leaving the system has increased for the outpatients, steady for the emergency and inpatient.
Table 5 shows statistical significance using one-way Anova and Tukey test to find the variation between different scenarios.
Figure 14 shows that Report reading, Reception and MRI waiting room queue time is reduced dramatically.
Table 4. Output analysis of different scenarios.
Figure 13. Outpatients exit number.
Table 5. One-way Anova for variation check in different scenario.
Figure 14. Average queue time.
The things I learnt in the model is that the scenarios in which resources are idle, patients are treated slowly. This model really helped in finding out resource utilisation patient throughout. It also helped in identifying the bottlenecks in patient flow. It also demonstrates with the increased outflow of outpatients, resources such as MRI and radiographer utilisation increased. Waiting Room MRI Average queue time dropped from 17 min to 5 min. Outpatient exit average time in the system is reduced by 20 minutes in scenario 11. Also, I learnt to match demand with capacity in different hours.
We can also take into consideration that the cost as the KPI and agent-based modelling can be implemented for it, in which patient, radiographer, clerk, radiologist as a separate agent can be classified, and it takes a little bit more time to build. The hybrid model which is the combination of DES and agent-based modelling can also be applied for the planning and finding cost in healthcare.
10.3. Difficult to Model
· Gather more evidence for demand at night through a survey of family and friends.
· DES is difficult to model interactions between the large diversity of staff.
10.4. Model Limitations
· Restriction only to MRIs, rather than the whole Radiology service.
· Using resources that are presumably shared with other scans or services.
· Only limited data from NHS, and lots of data taken from literature or assumed.
· Demand at night which has been assumed and needs more evidence to support it.
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