Improving service use through prediction modelling: a case study of a mathematics support centre
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IMA Journal of Management Mathematics (2021) 00, 1–12 https://doi.org/10.1093/imaman/dpab035 Downloaded from https://academic.oup.com/imaman/advance-article/doi/10.1093/imaman/dpab035/6377514 by guest on 04 January 2022 Improving service use through prediction modelling: a case study of a mathematics support centre Emma Howard† School of Psychology, University College Dublin, Dublin, Ireland † Corresponding author. Email: emma.howard@ucd.ie and Anthony Cronin School of Mathematics and Statistics, University College Dublin, Dublin, Ireland [Received on 29 October 2020; accepted on 26 August 2021] In higher education, student learning support centres are examples of walk-in services with nonstationary demand. For many centres, the major expenditure is tutor wages; thus, optimizing tutor numbers and ensuring value for money in this area are key. In University College Dublin, the mathematics support centre (MSC) has developed a software system, which electronically records the time each student enters the queue, their start time with a tutor and time spent with a tutor. In this paper, we show how data analysis of 25,702 student visits and tutor timetable data, spanning 6 years, is used to identify busy and quiet periods. Prediction modelling is then used to estimate the waiting time for future MSC visitors. Subsequently, we discuss how this is used for staffing optimization, i.e. to ensure there is sufficient coverage for busy times and no resource wastage during quieter periods. The analysis described resulted in the MSC reducing the number of queue abandonments and releasing funds from overstaffed hours to increase opening hours. The methods used are easily adapted for any busy walk-in service, and the code and data referenced are freely available: https://github.com/ehoward1/Math-Support-Centre-. Keywords: staffing optimization; mathematics support; nonstationary demand; predictive modelling. 1. Background A central part of management for any service is the effective staffing of trained personnel. In walk- in services, where customer arrival is nonstationary, the issue of staffing can be complex. Defraeye & Van Nieuwenhuyse (2016) provide a literature review of the research on staffing and rostering for services with nonstationary demand. Komarudin et al. (2020) discuss the difference between staffing and rostering optimization problems. They explain that staffing is ‘concerned with making decisions regarding the quantity and characteristics of human resources in the organisation’ (p. 254), whereas rostering involves assigning work shifts to the available personnel while taking into account predetermined constraints. For example, Duenas et al. (2008) discuss the nurse roster problem whereby nursing staff need to be scheduled for different work shifts (day, evening, night) in a hospital setting according to specific constraints such as a nurse cannot work a night shift and then subsequently work a day shift. Saccani (2012) focuses on the staffing optimization problem. He used an action research approach to examine the problem in a call centre—forecasting call volumes using the time series HoltWinters exponential smoothing method with additive trend and multiplicative seasonality. Overall, he emphasizes the need for transparency in forecasting processes, evaluation of the implementation © The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4. 0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
2 E. HOWARD AND A. CRONIN and involvement of managers. In our paper, we examine the staffing problem for a busy academic support centre with nonstationary demand, focusing on the quantity of staff needed to satisfy that demand. Downloaded from https://academic.oup.com/imaman/advance-article/doi/10.1093/imaman/dpab035/6377514 by guest on 04 January 2022 The mathematics support centre (MSC) has become an essential academic support component for students of higher education in Ireland, the UK, Australia, Germany and elsewhere (Lawson et al., 2020). While some MSCs offer bookable appointments, the most common form of student support is the dedicated drop-in space where students of the university can access expert tutors for help with mathematical queries from their programme. MSCs tend to use a first-come first-served or skill-based routing queuing policy (Defraeye & Van Nieuwenhuyse, 2016). MSCs are complementary to regular timetabled teaching activities such as formal lectures, tutorials and laboratories. However, unlike these timetabled activities, students’ visits to an MSC do not occur at a regular rate, and this is one of the most challenging problems MSC managers face. For example, in University College Dublin (UCD), the number of students attending the MSC oscillates as each semester progresses (12 weeks of teaching followed by one revision week and two examination weeks) with peaks in Weeks 7 and 10–13 of both semesters, coinciding with the mid-term and end-of-semester examinations, respectively. However, the service is well utilized from Week 1 and therefore meeting students’ needs requires sufficient tutors with the relevant mathematical backgrounds to be on duty when students access the centre. Without sufficient tutors, learners can experience lengthy waiting times and overcrowding of the centre. Similar to other walk-in services subject to nonstationary demand, this in turn may lead to learners leaving without receiving tuition (abandonment of the queue) and conflicts arising between disappointed students and overloaded tutors. These factors can result in students developing negative perceptions of the service that can affect word-of-mouth recommendations and service promotion. In a survey of mathematics support practitioners in Ireland (Cronin et al., 2016), the top two suggestions for enhancing provision were ‘longer opening hours’ (39% of respondents) and ‘more tutors’ (26% of respondents). However, hiring more staff and extending opening hours increases costs. Hence, an MSC service must look to maximize its current offering in terms of minimizing waiting times for students and staffing appropriately qualified tutors at relevant times. This requires the accurate identification of busy and quiet periods within the MSC. There has been limited research investigating usage patterns of MSCs (Edwards & Carroll, 2018) and subsequently staffing or rostering optimization. How students make use of the MSC space and resources affects the length of time they spend there and their waiting times. For example, in addition to regular attendees, the MSC can be suddenly ‘flooded’ by students prior to assessments (Wilson & Gillard, 2008). As this ‘flooding’ of MSCs tends to be infrequent, Lawson et al. (2020) [p.13] note that ‘to double staff at all times simply for these peaks would be wasteful’. Using computational approaches for the staffing of tutors in MSC settings is rare. An example, by Gillard et al. (2016), uses queueing theory to reformulate the problem of rostering 8 tutors over 10 MSC opening hours as a finite-source queueing model. Here the students represent machines breaking down where a breakdown corresponds to a student requiring assistance from a tutor. Using their MSC service data, they calculate that students on average sought support twice per hour and that tutors spent on average 10 min with a student. They add further complexity by considering the skills of the tutors versus the queries asked by the students. They treat the assignment of staff as ‘an optimization problem, the objective [being] to maximise a linear cost function to ensure that as many fields of mathematics... are covered as possible within each shift’ (p. 205). A limitation of this method is the scalability. We approach the staffing problem by examining historic MSC data of student wait times and by using prediction modelling to estimate student wait times over the course of a semester; the chosen
IMPROVING SERVICE USE THROUGH PREDICTION MODELLING 3 prediction method, K-nearest neighbours, achieves a mean absolute error of 8.2 min using 10-fold cross- validation. We show how the MSC manager uses predictions of student wait times for the next semester to staff tutors for that semester. This has resulted in the MSC reducing the number of abdonments of Downloaded from https://academic.oup.com/imaman/advance-article/doi/10.1093/imaman/dpab035/6377514 by guest on 04 January 2022 the queue and releasing funds from overstaffed hours to extend opening hours. Additionally, we use prediction modelling in two further ways. Firstly, when a student enters the MSC, they can see on the projector screen their expected waiting time as well as their current queue position. This prediction can be important in assisting a student to prepare for their visit appropriately and to inform them of how long they can expect to wait before engaging a tutor. The second instance is through the implementation of an RShiny app (Chang et al., 2019) hosted on the UCD MSC website, which allows students (external to the centre) to look up the current waiting time and see predicted waiting times for the semester by day and semester week. This allows students to plan their MSC visit for quieter periods. In order to analyse students’ use of an MSC, and subsequently use prediction modelling for staffing, accurate historical data on when student visits occurred are needed. A limiting factor to the utilization of data analytics in an MSC is the limited use of electronic systems to capture engagement data within MSCs (Cronin et al., 2016). However, provided a robust record of client waiting times is captured, the methods used in this paper can be utilized by any busy walk-in service to reduce waiting times and improve client satisfaction, e.g. call centres, airports, motor tax office, academic writing centres, vaccination centres, hospital A&E, etc. The structure of our paper is as follows: in Section 2, we describe the MSC data collected and analysis conducted. In Section 3, we show how data analytics can be used to identify busy and quiet periods in a MSC and discuss how this knowledge impacted staffing decisions. We also provide details of an application developed for students’ use which incorporates prediction modelling. In Section 4, we discuss the performance metrics used to evaluate the impact of the prediction modelling and the limitations of the approach taken. 2. Method 2.1 Overview of the electronic system The UCD MSC regular opening hours operate on a first-come, first-served drop-in basis (similar to walk-in customer service centres). The MSC uses a bespoke session management system, developed in-house, to electronically record the time each student uses the MSC via them logging into the queue on a computer at the MSC entrance. We will refer to this as ‘the system’ from now on. Using the system, each MSC tutor can initialize, pause or end a student–tutor session, and all these time points are recorded on the system. In addition, the tutor can categorize the mathematics query, both at a high level (e.g. Linear Algebra) and granular level (e.g. addition of matrices) and describe the help provided through logging free-form feedback comments on the session (Cronin & Meehan, 2016, 2020). Through the weekly automated sending of these comments to the relevant lecturer, the feedback loop is closed. The software system and details on how a tutor operates a session with a student can be viewed at: https://www.youtube.com/watch?v=pbswG50OuCs&feature=youtube. 2.2 Participants In UCD, the MSC supports in excess of 5,500 student visits per year from over 250 distinct modules across all 6 colleges of the university. The MSC has been using the system since Semester 2 of the 2014/15 academic year. When students log in, they are given the option to consent or not to their
4 E. HOWARD AND A. CRONIN Table 1 Data extracted from the system Downloaded from https://academic.oup.com/imaman/advance-article/doi/10.1093/imaman/dpab035/6377514 by guest on 04 January 2022 Start Wait Tutor_time Wall_time 13 October 3,660 233 833 2017 13:02 17/ October 295 3,374 3,375 2017 16:39 17 October 136 2,130 4,959 2017 16:41 17 October 30 1,096 4,536 2017 15:45 visit data being used for research and evaluation purposes. To date, in excess of 99% of all visitors have consented to this request. For this study, we are interested in students’ waiting time to see a tutor. A number of visitor entries on the system were removed from analysis where their waiting time was deemed not applicable. For example, the MSC runs a number of workshops called ‘Hot Topics’. These are a proactive way of supporting a significant minority of students within a module who may be lacking some prerequisite material. Hot topic groups range in size from 8 to 35 students, run more like a traditional tutorial session and are booked in advance. Thus, while these students log in on the system for the purposes of maintaining the total visits record, their waiting time is not related to the regular drop-in MSC waiting time. In other cases, the waiting times were beyond normal expectations, defined as anything in excess of 90 min, and likely to have been caused by tutor error. For example, tutors may not have logged students into the system upon sitting with a student, thus extending their recorded waiting time. Removing these instances gives 25,702 student visits as historical data for analysis from the period of Semester 2 of 2014/2015 to Semester 1 2019/2020 inclusive. 2.3 The data Table 1 gives an extract of the data retrieved from the system. The ‘start’ variable is the time when a student logs into the MSC queue with their student number. The ‘wait’ variable denotes how many seconds have elapsed until a tutor logs the student into their interface, i.e. when the tutor is available to support the student. This signals the beginning of the period that the tutor spends with the student. The ‘Tutor_time’ variable is the amount of time in seconds that the tutor spends with a student providing support. The ‘Wall_time’ variable is the amount of time the tutor spends with a student, in addition to any paused time when a tutor leaves the student to work on their own independently or a paused period of time when the student is swapped between attending tutors. For the purposes of conducting data analysis and prediction modelling, we wish to extract the maximum amount of information from these four variables (see Table 2). In addition, the number of tutors on duty in the MSC can be calculated for each time period from the MSC records and has been included in Table 2. ‘New System’ refers to the time period from October 2015, when the MSC moved from supporting all university students to supporting only those students from preparatory, first- or second-year programmes. Hence, from October 2015, third- and fourth-year undergraduate students in addition to postgraduate students were no longer assisted at the MSC unless they were registered to earlier stage modules more typical of a first- or second-year student (e.g. an elective module). ‘Tutor start time’ is considered to be a student’s start time with their wait time added on. For example, if a student logs into the system at ‘13 November 2019 11.21’ and waits 480 s, or 8 min, the ‘Tutor Start
IMPROVING SERVICE USE THROUGH PREDICTION MODELLING 5 Time’ is ‘13 November 2019 11.29’. ‘Tutor End time’ is considered to be the ‘Tutor Start Time’ with the time spent with a tutor added on. Continuing with the same example, if this tutor supports the student for 720 s, or 12 min, then the ‘Tutor End Time’ is ‘13 November 2019 11.41’. Downloaded from https://academic.oup.com/imaman/advance-article/doi/10.1093/imaman/dpab035/6377514 by guest on 04 January 2022 2.4 Data analysis To identify busy and quiet periods in the MSC, we are interested in the length of time students wait until they start a session with a tutor, i.e. their waiting time. To investigate this, we initially ran descriptive statistics, predominantly boxplots, of the waiting time controlling for specific variables from Table 2. In a boxplot, the middle line of each box represents the median waiting time, and the upper and lower lines of the boxes represent the upper and lower quartiles, respectively. The code for further descriptive analysis and figures to those shown in Section 3 are available at https://github.com/ehoward1/Math- Support-Centre-. To identify future waiting times, prediction modelling was employed using historical MSC data from the 12-week teaching period of the semester, i.e. not including revision week (Week 13) and examination weeks (Weeks 14 and 15). The revision and examination weeks are excluded as waiting times have unusually high variance during this period and the tutor timetables also change significantly over this period. The prediction methods compared were random forests (Breiman, 2001), principal components regression (Ilin & Raiko, 2010), K-nearest neighbours (Hechenbichler & Schliep, 2004), support vector machines (Karatzoglou et al., 2004) and splines (Friedman, 1991). The accuracy of these methods was compared using 10-fold cross-validation and mean absolute error. K-nearest neighbours achieve the lowest mean absolute error at 8.2 min, with 50% of errors between -1.7 min and +7.4 min. At the time of implementation of the RShiny app (2017/18), random forests gave the best prediction and was subsequently implemented for the prediction modelling. To predict future waiting times, a dataset was created for every time point in the following semester. The prediction modelling analysis was approved by the university ethics committee. As mentioned, for this dataset, the two best methods for prediction modelling have been K-nearest neighbours and random forests. K-nearest neighbours calculate a predicted waiting time (response variable) for a test case by identifying the ‘k’ training cases that are the most similar to the test case and averaging the waiting time of the ‘k’ test cases. Here, k = 5 is used. In the case of a non- numeric response variable, the prediction is made based on a voting approach. K-nearest neighbour is a nonparametric method (Hechenbichler & Schliep, 2004). Random forests is an ensemble method, which constructs multiple decision trees and averages the waiting time across the decision trees constructed. To allow trees to be independent from each other, for each tree, a bootstrap sample of data is chosen and a random subset of variables is considered at each split of the tree. 3. Results 3.1 Distribution of waiting times Initially, we investigated the waiting times from 2014/2015 Semester 2 until 2019/2020 Semester 1 using a histogram (see Fig, 1). The average waiting time is 14.5 min with the median waiting time being 7.6 min. As the waiting times are exponentially distributed, they were log-transformed for the prediction analysis. This truncated exponential pattern is persistent for the waiting times for every year and semester. Of the 25,702 student visits to the MSC, 62% occurred in Semester 1. Also, Semester 1 has on average a longer waiting time of 14.9 min as compared to 13.7 min in Semester 2. Historically, 10%
6 E. HOWARD AND A. CRONIN Downloaded from https://academic.oup.com/imaman/advance-article/doi/10.1093/imaman/dpab035/6377514 by guest on 04 January 2022 Fig. 1. Distribution of waiting times in the MSC with a truncated exponential distribution fitted (λ = 0.07). Table 2 Data variables extracted from the system data New variables Year Week in year Tutor start time Month Semester week Tutor end time Day Semester Number in queue Hour New system Number of tutors of student visits have occurred in both Week 7 and Week 12 of the semester, and 44% of student visits occurred in the first 3 h of opening for the MSC (10 am–1 pm). The average waiting time for students is longest on Fridays (at 17.7 min) and shortest on Mondays (at 12.5 min). The longer waiting time for Friday is likely a reflection of the shorter opening times on Friday coinciding with the morning peak. Waiting times could also be examined based on any variable from Table 2. For example, Fig. 2 shows the waiting times and the number of student visits based on the number of tutors working in the MSC at any given time. The number of student visits is given above the upper left of each box. For example, during periods when five tutors were on duty concurrently in the MSC, there have been 518 student visits to the UCD MSC. Unsurprisingly, as the number of tutors increased, the waiting times decreased. For example, the median waiting time when two tutors are on duty is 10 min, whereas when five tutors are on duty, it decreases to approximately 3 min. The difference between the waiting times when four or five tutors are on duty is marginal. Examining the waiting times based on different variables gives MSC management greater insight into when long waiting times may be expected and how best resources can then be managed. Examining waiting times for specific periods can also prove useful for management. For example, Fig. 3 displays the waiting time for Weeks 1–12 of Semester 1 of 2018/2019 and 2019/2020 based on the day of the week. For 2018/2019, Tuesdays had a longer waiting time in comparison with the other days. Compared to Wednesdays, the MSC on Tuesdays had an additional 109 student visits.
IMPROVING SERVICE USE THROUGH PREDICTION MODELLING 7 Downloaded from https://academic.oup.com/imaman/advance-article/doi/10.1093/imaman/dpab035/6377514 by guest on 04 January 2022 Fig. 2. Boxplot of 2014/2015–2019/2020 waiting times based on number of tutors on duty. However, on Mondays, the MSC had 37 more student visits than Tuesdays and the lowest average waiting time. Since university timetables tend to stay consistent between academic years, this type of information can be used by MSC management for staffing for the corresponding semester in the next academic year. To reduce the longer waiting times on Tuesdays, more tutor hours were assigned to Tuesdays in Semester 1 of 2019/2020 in the UCD MSC. The median waiting time for Tuesdays reduced substantially from 16 min in 2018/2019 to 7.5 min in 2019/2020; on average a 8.5-min reduction in waiting times (See Fig. 3). While the coordinator assigned an increased number of tutor hours to Tuesdays in 2019/2020, the waiting time would presumably have also been impacted by the decrease in MSC visits (658 reduced from 754). The reduced waiting time is likely a combination of both of these factors. Of note, for MSC management, is the change in attendance for Mondays for the 2 years. It would be interesting to observe whether this was owing to a change in module timetabling or a random effect. UCD MSC management could investigate this on the system by examining the topics of the queries and the module type logged by the tutors. 3.2 Incorporating prediction modelling into the MSC Prediction modelling has been incorporated into the MSC in three ways. The first instance occurs in the MSC itself. When a student enters the MSC, the student can see on a projector screen: the expected
8 E. HOWARD AND A. CRONIN Downloaded from https://academic.oup.com/imaman/advance-article/doi/10.1093/imaman/dpab035/6377514 by guest on 04 January 2022 Fig. 3. Waiting times for Weeks 1–12 of the 2018/2019 and 2019/2020 Semester 1 by the day of the week. waiting time of the next person to see a tutor; how long the queue currently is (in terms of number of students in the queue) and the mathematical strengths of the tutors on duty (see Fig. 4). Unlike the two other uses of prediction modelling discussed later, this prediction is built into the system design. It is based on live MSC visitor and tutor information of: the number of students working by themselves; the number of students working with tutors; the number of student groups working by themselves; the number of student groups working with tutors; the number of students waiting for a tutor (i.e. current queue size) and how long the student at the top of the queue has been waiting. Both tutors and students in the MSC benefit from these predictions. Tutors can take a glance at the projector screen to see if and how the queue is building, and also how many other tutors are on duty with them and their relative strengths should they need to transfer a student to one of them. In comparison, students benefit by checking the screen to see if they have time to wait to see a tutor. If their time is limited, the student can decide to come back later. If they join the MSC queue, they have an estimate of how long they have to prepare at an MSC table before they start a session with a tutor. Prediction modelling has also been incorporated through a RShiny application on the UCD MSC website. This was trialled in 2017/2018 and proved popular with students evidenced by the increase in traffic to this part of the MSC website and via the embedding of this app into the university’s central Student Desk suite of apps. Through accessing the application, students were informed of the current estimated waiting time to see a tutor. Also, students could see a graph of the estimated waiting time
IMPROVING SERVICE USE THROUGH PREDICTION MODELLING 9 Downloaded from https://academic.oup.com/imaman/advance-article/doi/10.1093/imaman/dpab035/6377514 by guest on 04 January 2022 Fig. 4. Queue image from the MSC projector. for that day. Students had the option of seeing the predicted waiting time for any day and week in the semester (see Fig. 5). The aim of this application was to allow students, particularly students who lived off campus and needed to make considerable journeys to campus, to plan their study day more effectively. Finally, prediction modelling has been fitted over the waiting times for every time point of the semester of interest. Thus, allowing the MSC manger to identify periods of longer/shorter waiting times and to schedule tutors accordingly. 4. Discussion We have described a number of ways that prediction modelling can be used to introduce both cost and resource effective measures in a busy student learning support setting. Defraeye & Van Nieuwenhuyse (2016) provide a list of performance metrics such as number in system/queue, waiting time, abandonments/throughput, length of stay, and utilization. To evaluate the impact of this current work, we consider the metrics of waiting times for visitors, length of time for tutor–student interactions and change in the number of visitors left without being seen. Descriptive statistics of these metrics are basic indicators, and subsequently, the next phase of research will involve more formal assessment of how to evaluate the impact of using the prediction models. Firstly, using the historical data for the teaching semester, the median waiting time to see an MSC tutor reduced from 7 min in 2015/2016 (n = 4, 112) to 5 min in 2016/2017 (n = 4, 681). In 2017/2018 and 2018/2019, the waiting time was 7 min (n = 4, 970) and 8 min (n = 4, 864), respectively. While there was a marginal increase in waiting time over the past 2 years, there was also an increase in the number of student visits to the MSC. Balancing the waiting time and time spent with tutors is a challenge for a busy walk-in service. The median time spent with a tutor for the teaching semester has remained steady over these years. In 2015/2016, this was 16.9 min; in 2016/2017, it raised to 17.5 min before dipping to 15.6 min in 2017/2018 with a further increase to 17 min in 2018/2019. This again despite the increase in annual student visits and no extra expenditure on tutors. It should be noted that this statistic refers strictly to the time that a student spends with a tutor receiving support and does not include the
10 E. HOWARD AND A. CRONIN Downloaded from https://academic.oup.com/imaman/advance-article/doi/10.1093/imaman/dpab035/6377514 by guest on 04 January 2022 Fig. 5. MSC app for estimating waiting times. time durations when a student is paused to do work independently of the tutor or when their session is paused while a tutor tends to another student/table. The implementation of the predictive models has accrued savings of over e12,000 as tutor expenditure was utilized in a more efficient way, i.e. less tutors utilized in quieter periods. While the number of annual tutor hours remained the same, the allocation of these hours changed. For example, opening hours were extended to 7.30 pm Monday to Thursday in Semester 1 2017/2018 and to 8 pm in 2018/2019, and until 7.30 pm Monday to Thursday for Semester 2 of both 2017/2018 and 2018/2019. Friday opening hours were also extended from 10 am–1 pm to 10 am–2 pm in both 2017/2018 and 2018/2019 using this model. Spreading the tutor allocation in a more efficient manner using the model has also meant we have been able to hire more tutors (with a more diverse array of specialisms), from 21 tutors in 2017/2018 to 28 tutors in 2018/2019 albeit using the same number of annual tutor hours (Cronin, 2020). Lastly, we analysed the number of visitors who left the MSC without being supported by a tutor. In 2015/2016, 2016/2017, 2017/2018, 2018/2019 and 2019/2020, the number of visitors who left without
IMPROVING SERVICE USE THROUGH PREDICTION MODELLING 11 being seen were 335, 280, 212, 306 and 193, respectively. While it is regrettable that any student leaves a support centre without receiving assistance, the use of such models to optimize staffing has helped minimize this event. Downloaded from https://academic.oup.com/imaman/advance-article/doi/10.1093/imaman/dpab035/6377514 by guest on 04 January 2022 There are limitations in using prediction modelling for staffing, for example accurate and robust visitor records are needed and this requires buy-in from all staff. This prediction modelling approach is in some ways reliant on the static nature of module timetabling and on the knowledge that a large number of MSC visits arrive prior to assessments (Edwards & Carroll, 2018). In UCD, modules tend to be timetabled at the same time slots each year for convenience, and module assessment due dates also tend to be consistent. If there was substantial change to the timetabling of modules and/or their assessments, we would expect poorer predictions. Other academic changes such as new modules being formed, changing of the module format, new continuous assessment regime and the offering of a module being switched from Autumn to Spring would also impact the accuracy of the predictions. The effect of academic changes to a module on MSC visits can potentially be reduced via maintaining strong communication links with the heads of teaching and learning, module coordinators and the MSC coordinator, see Cronin & Meehan (2020). The authors would be interested if any improvements can be made to further utilize the model. For example, unlike our model, the approach taken by Gillard et al. (2016) considered tutors’ mathematical strengths. The next phase of this research will also involve examining the impact that a student’s background has on their time spent with an MSC tutor in terms of their programme, stage in their degree, the specific module and subject with which they are seeking help, in addition to their gender, international status, prior mathematical learning and other potentially determining demographics. Predicting student length of stay in an MSC is vital because it may be considered a reliable and valid proxy of measuring the consumption of resources. 5. Conclusions While each customer/student walk-in service centre has its own requirements and demands, there is a certain amount of commonality when it comes to meeting the needs of customers/students to ensure satisfaction with the service. Obviously, long queues, excessive waiting times and clients leaving the service without being supported by tutors will reflect negatively on a service’s reputation and success. Also, the assignment of sufficient tutors with requisite skills at the required times avoids resource wastage in quieter times and in our experience can prove useful when applying for sustained or increased funding. Thus, we hope by sharing our experiences and the efforts made to minimize these issues in the MSC context we can help other busy academic support centres and customer-facing services do the same. As mentioned, we have provided the (anonymized) data and code in a GitHub repository, which is flexible in that it can be easily adapted to suit the conditions (the number of staff, opening hours, etc.) of other such services including academic support centres and customer call centres. In terms of supporting decision-making for budget planning, staffing levels and other plans around expected peak waiting times, we hope this paper and the complementary code can help ease the management of walk-in support services in planning for and providing the best support experience for those who use the service. Acknowledgements We would like to thank Dr Raja Mukherji for all his support with designing, creating and maintaining the UCD MSC session management system. We would also like to thank the editor and the anonymous reviewers for their very helpful comments on the previous version of this paper.
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