Pilkington Library Simulation Study
Simulation Study
Pilkington Library Main Issuing Desk
Abstract: This paper investigates the activity of the main issuing desk at the 3rd floor of Pilkington Library during weekdays between 5 and 6pm. The aim is to find ways of minimizing queuing times and respond to flexibility in demand. Two sets of data have been analysed and transposed into a simulation study using the Simul8 software package. The results of the simulation are presented in support of our optimization proposals.
Introduction
With more than 370,000 books issued last year, serving almost 15,000 users which made up to 600,000 enquires, the Pilkington Library is definitely one of the busiest place on campus especially when it gets near the examination period.
One …show more content…
of the library objective is:
"To support and facilitate the research, learning, teaching and administrative activities of the University, by organising, maintaining and providing access to appropriate literature and information resources in such a way as to provide optimum benefit for Library users." (Loughborough Library)
Of course, the library is a complex facility providing a range of services which far exceeds our simulation capabilities requiring the support of over 80 staff and use of specialised computer packages to track all items, users, requests and staff resources ensuring the functionality of the whole system.
The scope of our research therefore will be limited to the long-loan counter at the 3rd floor of the library which is the main contact point between the users and the library circulation system. Our aim is consistent with the library's own objective of optimizing the service for the benefit of its users. One way of doing this is by finding ways to minimize queuing times and respond to flexibility in demand.
Data Collection
In order to gain a better understanding of how the issuing desk operate we ran 2 sessions of data collection (1 hour each). We decided to collect the data on Monday and Tuesday between 5pm and 6pm. During these sessions we looked at how the system operates starting with a sketch of our conceptual model and analysing whether the scope of our project should include any other information. For example beside the main counter there is a drop-in box for returns only and there are another 2 self-service issuing machines. We decided to include these into our research since they can be often used to supplement or substitute the main counter duties. Regarding short-loan items we decided not to include them since they are organised as a self-contained system.
Since users (especially students) DO NOT come to the library in a orderly deterministic fashion there is a high level of uncertainty and the system presents a stochastic behaviour. To accommodate this problem we decided to use a diary of significant events in which we recorded the following information:
Initial length of each queue
Time when somebody joins a queue (main, self-service, drop-in box)
Time when somebody joins counter (which counter)
Time when somebody leaves counter (which counter)
We used the following tables:
N Joins queue
(main) Joins counter 1 Joins counter 2 Joins counter 3 Leaves counter
N Joins queue
(self service) Joins counter 1 Joins counter 2 Leaves counter
N Joins queue
(drop-in box) Starts unloading Leaves
* tables are provided in appendix A
The Conceptual Model
Once our data collection was over we had to develop our computer model in order to simulate the real system. According to Oakshott, 1997 "a conceptual model of a system should be developed before specifying the computer model. The conceptual model will specify the interactions between the different components of a system". Oakshott recommends the use of activity cycle diagrams in which all components of the system are assumed to have a life cycle, and the purpose of the diagram is "to show how the different life cycles combine to create the system."
Before composing the simulation model, we made some assumptions about the library system. These were as follows:
If a person had an enquiry, they would use a counter if it was available and staffed.
Once a person had finished their enquiry or action, they would move away from the counter, drop-in box or machine so it was free again.
Enquiries would be able to be solved by the member of staff behind the counter.
Both self-issue machines were in working order
Drop-in box is not full
People will queue in an orderly fashion
We believe our conceptual model gives a good representation of the library system that we observed. It takes into account the assumptions we made and therefore we took this forward as a basis for the Simul8 model.
Below is a screenshot of the model which was created. Starting from the left hand side, the first 3 icons are work entry points. They represent the entrance to the queuing systems for the counters, self-issue systems and drop-in boxes respectively. These work entry points are then joined to storage areas which represent the queues for each of the different points of service. From the first storage area there are two arrows connecting to two work centres, representing counter 1 and counter 2 at the main enquiry desk. From the second storage area there are also two arrows connecting to two work centres, and these represent the two self-issue machines. The third storage area has one arrow leading from it to the work centres representing the drop-in box. Finally each of the work centres is connected to a work exit point representing the exit from each point of service.
Analysis of the data
In order to configure the Simul8 model in such a way as to best reflect the reality we needed to find out the inter-arrival times, processing times and queuing times for each stage of the process and how these values are distributed. Below we will try to briefly analyse each of these sets of data.
Inter-arrival times have been calculated by subtracting the time between two arrivals. The results for the main counter are summarised below
Case Summaries (inter-arrival times)
N 48
Mean 1:13 min
Median 0:44 min
Minimum 0:02 min maximum 5:23 min
Range 5:21 min
Std. Deviation 1:17 min
The two diagrams above give us an idea on the distribution of the inter-arrival times. It is noticeable that the values tail off reflecting an exponential pattern.
Similar values have been calculated for the drop-in box and the self servicing machines. The exponential distribution has been chosen as best representing the inter-arrival pattern for all of them. The mean inter-arrival time is given in the table below:
counters Self-service Drop-in box
Mean inter-arrival time 1.2166 min 3.61666 min 3.3 min distribution resembles exponential
Processing time and efficiency
Case Summaries
Processing times
N 48
Mean 1:10
Median 0:52
Minimum 0:07
Maximum 4:04
Range 3:57
Std. Deviation 0:58
Differences in efficiency:
Although we assumed above that both work at the same rate it appeared that counter 2 has been more efficient taking 26 enquires and solving them in just 21 minutes while counter 1 worked 35 minutes solving only 22 enquires (see attached tables). In order to differentiate between the 2 we have calculated the average processing time for the two counters.
Counter 1: 35/22 = 1.59 minutes
Counter 2: 21/26 = 0.87 minutes
We will assume these times resemble a Poisson distribution as with the total processing time. Similarly we have calculated average processing time for the self servicing machines and the drop-in box. The values are shown below:
counters Self-service Drop-in box 1 2 1 2
0.25 min
Mean Processing time 1.56 min 0.833 min 0.917 min 0.583 min distribution Poisson We have also modified efficiency levels for the two counters in order to account for periods of time when these were left unattended.
Queuing:
Case Summaries (queueing time) Case Summaries (number in queue)
Queuing time
N 48
Mean 0:42
Median 0:14
Minimum 0:04
Maximum 2:52
Range 2:48
Std. Deviation 0:48 No. in queue
N 48
Mean 0.7500
Median 0.0000
Minimum 0.00
Maximum 5.00
Range 5.00
Std. Deviation 0.93399
Queuing times are important when we compare the simul8 model with the actual real data. The queuing times have been calculated by deducting the time a customer joins a counter from the time it joins a queue. Brief summaries on the queuing figures are shown in the two tables above.
The queuing time histogram and box and whisker plots give us a better understanding of the actual queuing time distribution and outliers. It is important to understand queuing figures because they can affect in a great measure the level of customer satisfaction.
The queuing times above represent the figures for the main counter. At the drop in box and self-servicing machines there has been a maximum queue of 1 which occurred because of an unexpected "re-start" of one of the two computers.
The validity of the Model
After entering the parameters into simul8 we ran the model in order to check its validity against our real data. The comparison was quite successful. Below we will compare the simulation results with the results obtained in our own data collection.
It should be mentioned before we start the comparison that the data collection has been set in Simul8 to take place for 60 minutes with a lead time of 3 minutes.
measurement Real data simulation
Total number of arrivals 77 79
Main counter arrivals 48 48
Average queue 0.75 people 0.62 people
Enquires counter 1 45.8% of total 46%
Enquires counter 2 54.2% of total 54%
Counter 1 working 58% of time 60.95% of time
Counter 2 working 36% of time 52.65% of time
Average queuing time 0:42 min 0:47 min
Maximum queuing time 2:52 min 3.37 min
Maximum queue 3 people 3 people
Self issue
Number of non zero queuing times 1 2
Maximum queuing time 0:13 min 0.14 minutes arrivals 15 15
Self-issue counter 1 13 13
Idle 78% of time 69.03%
Self-issue counter 2 2 2
Idle 96% (shut down 50%) 97%
Drop in box arrivals 14 16
As seen in our table (above), the predicted figures resemble fairly good our real data and therefore we can assume our simulation is viable.
The only places where differences are noticeable are the maximum queuing time which has an error of about half a minute (2:52 min compared to the simulated 3.37 minutes). This might be explained by the modifications in efficiency which we made in order to reflect the fact that counters were closing from time to time because of the operator tacking another job (for example sorting returned books) or simply by tacking a break. However one of the two counters were permanently staffed at all time and we do not know whether the simulation considered this fact or not.
Efficiency for counter 1 has been set to 85% because there were times when the counter was closed. In the same way efficiency of the other working units have been altered in order to better reflect the reality. (i.e. self servicing machine 2 experienced software problems and it was out of order for most of the time)
Another adjustment we made to our simulation in order to best fit the real data was to set the inter-arrival and processing time in terms of our own designed distributions instead of using the classical built-in Exponential
distribution.
Below there is an example of the distribution of inter-arrival times at the main counter which we designed from our own data analysis. The same procedure has been applied generally to some inter-arrival times and processing times.
In order to best understand how well our simulation works and compares to the real data we have attached both our simul8 model and our raw data collection excel file on the provided floppy disk.
Scenarios and conclusions
The next step after we decided that our model compares well with the real data is to analyse what are its advantages and weaknesses and how can we improve it. One way to do this is to test different scenarios and find out whether the system is able to cope with fluctuation in demand, staff levels or breakdowns of the self-issuing machines.
For example let's see What if demand doubles during exams time?
One way of adjusting the simulation to the new condition (doubling the number of users) is by simply duplicating the entry points. See below
Running the scenario proves that average queue size would increase to 6.6 people and average queuing time would increase from the current 0.47 to 7.35 minutes while the maximum queue size would increase to a staggering 22 people and only
However the system can adjust by opening an extra counter which we found out is reserved for busy conditions only. Adding the extra counter in simul8 and printing another set of results would indeed reduce the queuing time to a more acceptable average of 2.81 minutes and a maximum of 5 people in queue.
New counter has been added and the new results can be predicted within seconds by pressing Results Summaries:
Similarly if we want to find out what happened if we leave only one counter and direct all other queries to the self issuing machines which appear to be under used at the moment the model is easily adaptable.
In this case the results of our simulation predict a slight increase in queuing time from 0.47 to 0.59 while the maximum queuing size would go up from 3 in normal conditions to 4. However this still considers the case that self-service machine 2 is most of the time out of order.
If machine 2 was repaired it would mean that the system could cope well to normal Tuesday night demand conditions even if one of the 2 staff were missing.
Conclusion
As we have seen the simulation of a simple real life system can be quite a laborious project requiring data collection, data analysis, a good conceptual model and nevertheless a good platform to run the simulation on. Of course Uncertainty will always be an issue with real-life systems, but the development of simulations can be very helpful in the decision making process by providing estimates and forecasts for the future. We are confident that our model is a good simulation of the Loughborough University Library long-loan service desk and could be used to predict the behaviour of the system in various circumstances enabling its further optimization.
Our findings and proposals are outlined below
Increase the use of self-issuing machines because they are under-used and to release pressure from the main counters.
Machine 2 needs looking at since it's not always in working order
Opening a flexible-counter is an effective way of dealing with sudden increases in demand
Keep 95% of queuing time under 2 minutes at the main counter (currently it's 96%)
Reference
L. Oakshott, 1997, Business Modelling & Simulation
Library website accessed from http://www.lboro.ac.uk/library/objectives.html
Pilkington Library Main Issuing Desk
Abstract: This paper investigates the activity of the main issuing desk at the 3rd floor of Pilkington Library during weekdays between 5 and 6pm. The aim is to find ways of minimizing queuing times and respond to flexibility in demand. Two sets of data have been analysed and transposed into a simulation study using the Simul8 software package. The results of the simulation are presented in support of our optimization proposals.
Introduction
With more than 370,000 books issued last year, serving almost 15,000 users which made up to 600,000 enquires, the Pilkington Library is definitely one of the busiest place on campus especially when it gets near the examination period.
One …show more content…
of the library objective is:
"To support and facilitate the research, learning, teaching and administrative activities of the University, by organising, maintaining and providing access to appropriate literature and information resources in such a way as to provide optimum benefit for Library users." (Loughborough Library)
Of course, the library is a complex facility providing a range of services which far exceeds our simulation capabilities requiring the support of over 80 staff and use of specialised computer packages to track all items, users, requests and staff resources ensuring the functionality of the whole system.
The scope of our research therefore will be limited to the long-loan counter at the 3rd floor of the library which is the main contact point between the users and the library circulation system. Our aim is consistent with the library's own objective of optimizing the service for the benefit of its users. One way of doing this is by finding ways to minimize queuing times and respond to flexibility in demand.
Data Collection
In order to gain a better understanding of how the issuing desk operate we ran 2 sessions of data collection (1 hour each). We decided to collect the data on Monday and Tuesday between 5pm and 6pm. During these sessions we looked at how the system operates starting with a sketch of our conceptual model and analysing whether the scope of our project should include any other information. For example beside the main counter there is a drop-in box for returns only and there are another 2 self-service issuing machines. We decided to include these into our research since they can be often used to supplement or substitute the main counter duties. Regarding short-loan items we decided not to include them since they are organised as a self-contained system.
Since users (especially students) DO NOT come to the library in a orderly deterministic fashion there is a high level of uncertainty and the system presents a stochastic behaviour. To accommodate this problem we decided to use a diary of significant events in which we recorded the following information:
Initial length of each queue
Time when somebody joins a queue (main, self-service, drop-in box)
Time when somebody joins counter (which counter)
Time when somebody leaves counter (which counter)
We used the following tables:
N Joins queue
(main) Joins counter 1 Joins counter 2 Joins counter 3 Leaves counter
N Joins queue
(self service) Joins counter 1 Joins counter 2 Leaves counter
N Joins queue
(drop-in box) Starts unloading Leaves
* tables are provided in appendix A
The Conceptual Model
Once our data collection was over we had to develop our computer model in order to simulate the real system. According to Oakshott, 1997 "a conceptual model of a system should be developed before specifying the computer model. The conceptual model will specify the interactions between the different components of a system". Oakshott recommends the use of activity cycle diagrams in which all components of the system are assumed to have a life cycle, and the purpose of the diagram is "to show how the different life cycles combine to create the system."
Before composing the simulation model, we made some assumptions about the library system. These were as follows:
If a person had an enquiry, they would use a counter if it was available and staffed.
Once a person had finished their enquiry or action, they would move away from the counter, drop-in box or machine so it was free again.
Enquiries would be able to be solved by the member of staff behind the counter.
Both self-issue machines were in working order
Drop-in box is not full
People will queue in an orderly fashion
We believe our conceptual model gives a good representation of the library system that we observed. It takes into account the assumptions we made and therefore we took this forward as a basis for the Simul8 model.
Below is a screenshot of the model which was created. Starting from the left hand side, the first 3 icons are work entry points. They represent the entrance to the queuing systems for the counters, self-issue systems and drop-in boxes respectively. These work entry points are then joined to storage areas which represent the queues for each of the different points of service. From the first storage area there are two arrows connecting to two work centres, representing counter 1 and counter 2 at the main enquiry desk. From the second storage area there are also two arrows connecting to two work centres, and these represent the two self-issue machines. The third storage area has one arrow leading from it to the work centres representing the drop-in box. Finally each of the work centres is connected to a work exit point representing the exit from each point of service.
Analysis of the data
In order to configure the Simul8 model in such a way as to best reflect the reality we needed to find out the inter-arrival times, processing times and queuing times for each stage of the process and how these values are distributed. Below we will try to briefly analyse each of these sets of data.
Inter-arrival times have been calculated by subtracting the time between two arrivals. The results for the main counter are summarised below
Case Summaries (inter-arrival times)
N 48
Mean 1:13 min
Median 0:44 min
Minimum 0:02 min maximum 5:23 min
Range 5:21 min
Std. Deviation 1:17 min
The two diagrams above give us an idea on the distribution of the inter-arrival times. It is noticeable that the values tail off reflecting an exponential pattern.
Similar values have been calculated for the drop-in box and the self servicing machines. The exponential distribution has been chosen as best representing the inter-arrival pattern for all of them. The mean inter-arrival time is given in the table below:
counters Self-service Drop-in box
Mean inter-arrival time 1.2166 min 3.61666 min 3.3 min distribution resembles exponential
Processing time and efficiency
Case Summaries
Processing times
N 48
Mean 1:10
Median 0:52
Minimum 0:07
Maximum 4:04
Range 3:57
Std. Deviation 0:58
Differences in efficiency:
Although we assumed above that both work at the same rate it appeared that counter 2 has been more efficient taking 26 enquires and solving them in just 21 minutes while counter 1 worked 35 minutes solving only 22 enquires (see attached tables). In order to differentiate between the 2 we have calculated the average processing time for the two counters.
Counter 1: 35/22 = 1.59 minutes
Counter 2: 21/26 = 0.87 minutes
We will assume these times resemble a Poisson distribution as with the total processing time. Similarly we have calculated average processing time for the self servicing machines and the drop-in box. The values are shown below:
counters Self-service Drop-in box 1 2 1 2
0.25 min
Mean Processing time 1.56 min 0.833 min 0.917 min 0.583 min distribution Poisson We have also modified efficiency levels for the two counters in order to account for periods of time when these were left unattended.
Queuing:
Case Summaries (queueing time) Case Summaries (number in queue)
Queuing time
N 48
Mean 0:42
Median 0:14
Minimum 0:04
Maximum 2:52
Range 2:48
Std. Deviation 0:48 No. in queue
N 48
Mean 0.7500
Median 0.0000
Minimum 0.00
Maximum 5.00
Range 5.00
Std. Deviation 0.93399
Queuing times are important when we compare the simul8 model with the actual real data. The queuing times have been calculated by deducting the time a customer joins a counter from the time it joins a queue. Brief summaries on the queuing figures are shown in the two tables above.
The queuing time histogram and box and whisker plots give us a better understanding of the actual queuing time distribution and outliers. It is important to understand queuing figures because they can affect in a great measure the level of customer satisfaction.
The queuing times above represent the figures for the main counter. At the drop in box and self-servicing machines there has been a maximum queue of 1 which occurred because of an unexpected "re-start" of one of the two computers.
The validity of the Model
After entering the parameters into simul8 we ran the model in order to check its validity against our real data. The comparison was quite successful. Below we will compare the simulation results with the results obtained in our own data collection.
It should be mentioned before we start the comparison that the data collection has been set in Simul8 to take place for 60 minutes with a lead time of 3 minutes.
measurement Real data simulation
Total number of arrivals 77 79
Main counter arrivals 48 48
Average queue 0.75 people 0.62 people
Enquires counter 1 45.8% of total 46%
Enquires counter 2 54.2% of total 54%
Counter 1 working 58% of time 60.95% of time
Counter 2 working 36% of time 52.65% of time
Average queuing time 0:42 min 0:47 min
Maximum queuing time 2:52 min 3.37 min
Maximum queue 3 people 3 people
Self issue
Number of non zero queuing times 1 2
Maximum queuing time 0:13 min 0.14 minutes arrivals 15 15
Self-issue counter 1 13 13
Idle 78% of time 69.03%
Self-issue counter 2 2 2
Idle 96% (shut down 50%) 97%
Drop in box arrivals 14 16
As seen in our table (above), the predicted figures resemble fairly good our real data and therefore we can assume our simulation is viable.
The only places where differences are noticeable are the maximum queuing time which has an error of about half a minute (2:52 min compared to the simulated 3.37 minutes). This might be explained by the modifications in efficiency which we made in order to reflect the fact that counters were closing from time to time because of the operator tacking another job (for example sorting returned books) or simply by tacking a break. However one of the two counters were permanently staffed at all time and we do not know whether the simulation considered this fact or not.
Efficiency for counter 1 has been set to 85% because there were times when the counter was closed. In the same way efficiency of the other working units have been altered in order to better reflect the reality. (i.e. self servicing machine 2 experienced software problems and it was out of order for most of the time)
Another adjustment we made to our simulation in order to best fit the real data was to set the inter-arrival and processing time in terms of our own designed distributions instead of using the classical built-in Exponential
distribution.
Below there is an example of the distribution of inter-arrival times at the main counter which we designed from our own data analysis. The same procedure has been applied generally to some inter-arrival times and processing times.
In order to best understand how well our simulation works and compares to the real data we have attached both our simul8 model and our raw data collection excel file on the provided floppy disk.
Scenarios and conclusions
The next step after we decided that our model compares well with the real data is to analyse what are its advantages and weaknesses and how can we improve it. One way to do this is to test different scenarios and find out whether the system is able to cope with fluctuation in demand, staff levels or breakdowns of the self-issuing machines.
For example let's see What if demand doubles during exams time?
One way of adjusting the simulation to the new condition (doubling the number of users) is by simply duplicating the entry points. See below
Running the scenario proves that average queue size would increase to 6.6 people and average queuing time would increase from the current 0.47 to 7.35 minutes while the maximum queue size would increase to a staggering 22 people and only
However the system can adjust by opening an extra counter which we found out is reserved for busy conditions only. Adding the extra counter in simul8 and printing another set of results would indeed reduce the queuing time to a more acceptable average of 2.81 minutes and a maximum of 5 people in queue.
New counter has been added and the new results can be predicted within seconds by pressing Results Summaries:
Similarly if we want to find out what happened if we leave only one counter and direct all other queries to the self issuing machines which appear to be under used at the moment the model is easily adaptable.
In this case the results of our simulation predict a slight increase in queuing time from 0.47 to 0.59 while the maximum queuing size would go up from 3 in normal conditions to 4. However this still considers the case that self-service machine 2 is most of the time out of order.
If machine 2 was repaired it would mean that the system could cope well to normal Tuesday night demand conditions even if one of the 2 staff were missing.
Conclusion
As we have seen the simulation of a simple real life system can be quite a laborious project requiring data collection, data analysis, a good conceptual model and nevertheless a good platform to run the simulation on. Of course Uncertainty will always be an issue with real-life systems, but the development of simulations can be very helpful in the decision making process by providing estimates and forecasts for the future. We are confident that our model is a good simulation of the Loughborough University Library long-loan service desk and could be used to predict the behaviour of the system in various circumstances enabling its further optimization.
Our findings and proposals are outlined below
Increase the use of self-issuing machines because they are under-used and to release pressure from the main counters.
Machine 2 needs looking at since it's not always in working order
Opening a flexible-counter is an effective way of dealing with sudden increases in demand
Keep 95% of queuing time under 2 minutes at the main counter (currently it's 96%)
Reference
L. Oakshott, 1997, Business Modelling & Simulation
Library website accessed from http://www.lboro.ac.uk/library/objectives.html