WP_ContactCenterPlanningMethodologies_whitepaper_laser

Contact Center Planning Calculations and Methodologies A Comparison of Erlang-C and Simulation Modeling

Ric Kosiba, Ph.D. Vice President Interactive Intelligence, Inc.

Bayu Wicaksono Manager, Operations Research Interactive Intelligence, Inc.

© 2014 Interactive Intelligence, Inc. 2 Contact Center Planning Calculations and Methodologies

Contents Introduction ......................................................................................................................................... 3 Methodology ........................................................................................................................................ 4 Service Prediction Comparison ............................................................................................................ 5 Staffing Requirement Comparison ....................................................................................................... 9 Summary and Operational Implications ............................................................................................ 12 Appendix A: Auto Insurance Call Type Charts .................................................................................... 13

Service Performance Comparisons .............................................................................................. 13 Staffing Requirements FTE Comparisons .................................................................................... 14

Appendix B: Retail Call Type Charts ................................................................................................... 15 Service Performance Comparisons .............................................................................................. 15 Staffing Requirements FTE Comparisons .................................................................................... 16

Appendix C: Preferred Service Call Type Charts ................................................................................. 17 Service Performance Comparisons .............................................................................................. 17 Staffing Requirements FTE Comparisons .................................................................................... 18

Appendix D: Credit Card Call Type Charts .......................................................................................... 19 Service Performance Comparisons .............................................................................................. 19 Staffing Requirements FTE Comparisons .................................................................................... 20

Appendix E: Member Services Call Type Charts ................................................................................. 21 Service Performance Comparisons .............................................................................................. 21 Staffing Requirements FTE Comparisons .................................................................................... 22

Appendix F: Loans Call Type Charts ................................................................................................... 23 Service Performance Comparisons .............................................................................................. 23 Staffing Requirement FTE Comparisons ...................................................................................... 24

Authors ............................................................................................................................................... 25

Copyright © 2014 Interactive Intelligence, Inc. All rights reserved. Brand, product, and service names referred to in this document are the trademarks or registered trademarks of their respective companies.

Interactive Intelligence, Inc. 7601 Interactive Way Indianapolis, Indiana 46278 Telephone (800) 267-1364 www.ININ.com

Publish date 10/14

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Introduction Contact centers are a major US industry, employing approximately 2.1 million phone

agents. They are sophisticated operations, using state-of-the-art contact routing, contact

monitoring, and agent staffing systems. These operations are expensive, and contact

center agent costs often represent one of the top costs for many companies. Correct

staffing for contact centers is important and well-studied. Surprisingly, there is little

documentation available on the accuracy of the standard staffing algorithms. This paper

focuses on the relative accuracy of two workforce staffing calculations and methodologies

most often used in the contact center industry.

The traditional contact center planning algorithm has been the Erlang-C calculation.

Developed by Agner Erlang in 1917, telephone companies used it to determine the

number of operators needed in early switchboard operations. It is compact, easy to use,

and easy to code in software or embed into spreadsheets. In fact, its ease of use is

responsible for its incredible adoption rate. For many years, it was the only option

available for developing agent schedules or contact center budgets, because alternative

methods were too demanding for the computers of the day. Improvements to the original

formula have been made over the years to overcome Erlang-C’s most significant

weakness: It does not account for caller abandonment and assumes that callers wait

indefinitely in the ACD queue. These improvements did not completely address the caller

abandonment issue due to simplifying assumptions on the distribution of caller patience.

Despite the limitations, it is still widely used today in workforce management or planning

systems and in contact center planning spreadsheets.

The Erlang-C formula solves two specific and interrelated problems:

1. How many agents does the operation require in order to handle calls within a

specific timeframe?

2. What service will the operation deliver given a specific staffing headcount?

Correct answers to these questions are critical in planning for and running an efficient and

effective contact center operation.

Is the Erlang-C equation accurate enough to answer these questions? This paper

demonstrates the range of the Erlang-C equation’s accuracy using a survey of real-world

call center data and compares it to newer simulation models that have begun to make

headway in determining staffing for contact centers.


Methodology Multiple contact centers supplied historical ACD performance data to help determine a

model’s service prediction accuracy. This data provides known values for the number of

calls, agent work hours, call handle times, and service levels for specific 60-minute

intervals. The differences between a model’s predictions and actual results are plotted

and summarized at the daily and weekly level. The results for an Erlang-C equation and a

discrete-event simulation model are compared.

A reverse analysis is also performed. Actual service levels are used as a model’s service

level goal, and the number of staff required to achieve this service is then determined.

The differences between the actual staffing (the number of ACD work hours) and a

model’s prediction of the number of staff required is plotted and summarized at the daily

and weekly level. These differences are extrapolated to determine wages wasted due to

model error.

Empirical data gathered from call centers includes retail, banking, and financial service

companies. The sample of call types within these operations varies in size from an average

of three FTE (fulltime equivalent agents) per hour to an average of 228 FTE per hour. The

samples vary from 3 weeks to 6 months due to data availability. The call types evaluated

are presented in Table 1.

Industry Call Type Size (Avg. Staff in FTE Hrs.)

Insurance Auto Insurance 228

Retail Retail 95

Banking Preferred Service 44

Banking Credit Card Service 15

Banking Member Services 6

Finance Loans 3

Table 1: Sample Call Types Evaluated

Simulation models for each of the call types were created, taking into account customer

patience profiles, historical average service level threshold, delays, and staffing

inefficiencies (e.g. idle times, scheduling inefficiencies etc.). These parameters are

optimized in order to get the best steady-state simulation models given the available data.


Service Prediction Comparison After the simulation models were created, a back-casting exercise was performed to

quantify model error by comparing predicted to actual performance across the historical

date ranges. Table 2 summarizes the average daily error rates for each call type.

Call Type Avg. Error Sim Avg. Error Erlang-C Avg. Abn. Rate (%) Avg. SL (%)

Loans 0.01% 21.34% 9.11% 76.45%

Member Services 0.04% 21.60% 7.48% 84.70%

Preferred Services 0.15% 23.51% 2.76% 73.55%

Retail 0.17% 2.18% 1.43% 93.79%

Credit Card -0.11% 9.46% 7.01% 56.03%

Auto Insurance -0.01% -3.93% 1.16% 87.20%

Average 0.04% 12.36% 4.83% 78.62%

Table 2: Daily Level Summary of Avg. Service Level, Actual Avg. Service Level, and Actual Abandonment Rate.

The results indicate that predicted Erlang-C service level inaccuracies increase with large

abandonment rates. This makes sense because Erlang-C assumes that no customers will

get impatient and abandon regardless of wait time (i.e. customers have infinite patience).

In contrast, the simulation prediction accuracy does not vary significantly with

abandonment. This is expected because the simulation models take customer patience

profiles into account.

Furthermore, Erlang-C results tend to underestimate performance, as actual results are

better than predictions. Again, this is most significant with higher abandonment rates.

This could occur when the contact center is severely understaffed relative to its goal. In

contrast, average error rates for the simulation models are less than one percent and tend

to converge to zero. Properly modeled, simulations tend to balance over and under

prediction across the evaluated time horizon.

The Erlang-C prediction is most accurate when the number of agents is large, and

utilization is low due to low to no abandonment – also indicated by very high service levels

(see Retail and Auto Insurance data in Table 2).


Figure 1 shows actual performance vs. predicted performance of simulation and Erlang-C

for daily service levels of the Preferred Services call type.

Figure 1: Daily service level summary of Preferred Service Call Type

Even though the average error summary presented in Table 2 is a good indicator of the

average accuracy and overall average bias of both prediction methods. It is also important

to show the magnitude of the prediction error.

Table 3 summarizes the absolute error for each call type across the evaluated date range

summarized at the daily level. Absolute error is defined as the absolute value of the

service level predictions minus actual service levels. Custom simulation modeling

significantly outperforms the Erlang-C calculation as measured by the absolute error of

both prediction methods.

Call Type Simulation Service Level Prediction Erlang-C Service Level Prediction

Avg. Abs. Error Std. Dev. Abs. Error Avg. Abs. Error Std. Dev. Abs. Error Loans 2.75% 1.53% 21.34% 10.25% Member Services 3.04% 2.68% 22.12% 10.38% Preferred Services 4.11% 3.01% 23.51% 7.62%

Retail 5.21% 6.50% 4.76% 7.42% Credit Card 1.42% 1.44% 9.47% 5.58% Auto Insurance 5.89% 6.02% 6.08% 4.78%

Average 3.74% 3.53% 14.55% 7.67% Table 3: Summary of the absolute error for each call type across the evaluated date range summarized at the daily level

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Preferred Service: Service Level Comparison Simulation vs. Erlang-C vs. Actual (Daily Summary)

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In a series of predictions, absolute error measures the difference from the correct value,

while standard deviation measures the range in which the prediction will most likely

occur, or how spread-out the predictions are. Average absolute error is a measure of

overall accuracy. The closer to zero, the more accurate the prediction, while standard

deviation is a measure of precision (Figure 2).

Figure 2: Accuracy vs. precision (taken from http://climatica.org.uk/climate-science-information/uncertainty)

Looking at the Loans call type in Table 3, any given prediction of the simulated service

level would most likely be 2.75% off the actual value. Additionally, the prediction is a bit

spread out. Not only would it be 2.75% away from the actual value, but chances are the

prediction could be as inaccurate as ±4.28% (2.75% + 1.53%) away from the actual value,

or as accurate as within ±1.22% (2.75% - 1.53%) from the actual value.

For long-term planning purposes, it is a best and common industry practice to summarize

the accuracy and precision to the weekly level, as hiring and staffing decisions are made at

this level of detail.

Call Type

Simulation Service Level Prediction

Erlang-C Service Level Prediction

Avg. Err Avg. Abs. Err

Std. Dev. Abs. Err

Avg. Err Avg. Abs. Err

Std. Dev. Abs. Err

Loans 0.59% 0.78% 0.65% 22.42% 22.42% 4.61% Member Services 0.24% 1.19% 1.20% 25.97% 25.97% 5.56% Preferred Services -1.27% 2.21% 1.75% 24.11% 24.11% 4.67% Retail 0.86% 2.66% 1.39% 3.36% 4.03% 4.85% Credit Card 0.31% 1.01% 1.08% 9.99% 9.99% 3.41% Auto Insurance 1.20% 2.45% 2.27% -3.46% 3.46% 1.59%

Average 0.32% 1.72% 1.39% 13.73% 15.00% 4.12% Table 4: Weekly Level Summary of Avg. and Std. Dev. of Error and Absolute Error of Service Level by Call Type

At the weekly level, the advantage of simulation over Erlang-C is more apparent with even

less variability (Table 4). This is not observed in the Erlang-C results. Properly developed

simulation models minimize variability over less granular time intervals due to their

steady-state assumptions. This is why the simulated predictions produce better results

compared to Erlang-C.

http://climatica.org.uk/climate-science-information/uncertainty


Figure 3 illustrates the differences between weekly service levels of actual performance

compared to simulation and Erlang-C predictions. For more visual comparisons of each of

the call types between historical actuals vs. simulation and Erlang-C, please refer to the

appendices at the end of this document.

Figure 3: Weekly Service Level Summary Comparison for Preferred Service Call Type

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Preferred Service: Service Level Comparison Simulation vs. Erlang-C vs. Actuals (Weekly Summary)



Staffing Requirement Comparison The modeling technique used to predict service performance, whether simulation or

Erlang, is most often used to determine the number of available contact center agents

required to meet a specific servicing standard. To compare staffing prediction accuracy

between Erlang-C and simulation models, a similar validation exercise is developed.

Using the same models as the previous analyses, a reverse calculation is performed to

determine the accuracy of staffing requirement predictions given a service level goal. In

both cases, it is assumed that the historical service level is the same as the servicing goal

the planner would set.

The average prediction error percentage listed in Table 5 is the relative error from the

actual staffing value, calculated as (𝐴𝑐𝑡𝑢𝑎𝑙−𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑜𝑛)

𝐴𝑐𝑡𝑢𝑎𝑙∗ 100%. The actual average daily

staff value (in hours) is also listed for a frame of reference.

Call Type Avg. Sim Req. Error % Avg. Erlang Req. Error % Avg. Daily Staff (Hrs)

Loans 2.26% -42.36% 35.24

Member Services -1.86% -20.54% 60.95

Preferred Services -1.79% -16.84% 1,054.73

Retail 2.01% 8.81% 1,335.10

Credit Card 0.93% -11.44% 309.29

Auto Insurance 3.14% 9.81% 5,043.52

Average 0.78% -12.09% 1,306.47

Table 5: Daily Summary of Average Relative Error of the Staff Requirement Prediction (in Hours) by Call Type

Similar to our previous service level predictions, the relative error for the simulated

staffing requirement is relatively low, averaging within 1% to 3% of historic staffing. In

contrast, the Erlang-C-developed requirement is often too high, especially where abandon

rates are high (Loans, Member Services, and Credit Card in Table 5). This corresponds

directly to Erlang-C’s under-prediction of service level.

The average absolute error and standard deviation is calculated and summarized in Table 6.

Table 6: Daily Summary of Average and Std. Dev. of Absolute Error of the Staff Requirement Prediction by Call Type

Call Type

Simulation Requirement Erlang-C Requirement Avg. Daily Staff

(Hrs) Avg. Abs. Rel. Err (%)

Std. Dev. Abs. Rel. Error (%)

Avg. Abs. Rel. Error (%)

Std. Dev. Abs. Rel. Error (%)

Loans 4.01% 3.60% 42.36% 14.22% 35.24

Member Services

4.90% 5.75% 20.54% 28.25% 60.95

Preferred Services

3.06% 4.47% 16.84% 12.07% 1,054.73

Retail 5.35% 4.93% 9.26% 5.14% 1,335.10

Credit Card 2.81% 2.76% 11.44% 8.22% 309.29

Auto Insurance 4.59% 5.78% 10.34% 6.57% 5,043.52

Average 4.12% 4.55% 18.46% 12.41% 1,119.83


Again, simulation modeling holds an advantage with accuracy and precision within ±5%

per day. Prediction variability is also lower compared to Erlang-C. Almost all of Erlang-C’s

predictions are consistently overstaffing by more than 10% from the actual historical

staffing (the exception being Retail). Predictions are also less precise with a spread of

more than 5%. Figure 4 charts the comparison for the Credit Card call type.

Figure 4: Daily Staffing Requirement Comparison for Credit Card Call Type

As with service performance in the previous analysis, a weekly summary (Table 7) is also

created. As most long-term staffing decisions are developed with a week-over-week view,

this is the appropriate level of detail to evaluate algorithms for strategic capacity planning.

Call Type

Simulation Requirement Erlang-C Requirement

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Staff (Hrs.)

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Avg. Abs. Rel. Err (%)

Stdev. Abs. Rel.

Error (%)

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Error (%)

Stdev. Abs. Rel. Error (%)

Loans 1.04% 2.29% 1.53% -42.72% 42.72% 7.30% 158.59

Member Services

-1.61% 2.15% 3.20% -14.32% 14.32% 5.55% 319.98

Preferred Services

-0.83% 1.34% 1.21% -12.73% 12.73% 2.93% 6,873.92

Retail 3.36% 4.03% 4.85% 9.98% 9.98% 5.26% 8,307.51

Credit Card

0.04% 2.20% 2.92% -11.75% 11.75% 5.79% 1,615.20

Auto Insurance

2.66% 2.89% 2.87% 10.43% 10.43% 3.73% 32,362.59

Average 0.78% 2.48% 2.76% -10.19% 16.99% 5.09% 7,091.11 Table 7: Weekly Summary Error Statistics of the Weekly Staff Requirement Prediction by Call Type

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Credit Card: Staffing Requirement Comparison Simulation vs. Erlang-C vs. Actuals (Daily Summary)

Actual Staff Simulation Requirement Erlang-C Requirement


In Table 7, it can be seen that with a weekly outlook both the relative and absolute error

of the simulation prediction is significantly reduced. This is due to the steady-state

behavior of the simulation modeling, as has been discussed in the previous section.

Erlang-C results do not improve when evaluating weekly results as they retain roughly the

same level of error in both daily vs. weekly models. A comparison of weekly staffing

requirements for the Credit Card call type is shown in Figure 5.

Figure 5: Weekly Staffing Requirements for Credit Card Call Type

Overall, it can be concluded that staffing requirements generated by simulation are more

accurate and precise than those generated by Erlang-C. A further analysis of the errors in

the prediction of staffing requirements indicate additional advantages of simulation

modeling over Erlang-C, as shown in Table 8.

Predictive Methodology Staffing Error > 5% per 𝑪𝒖𝒔𝒕𝒐𝒎𝒆𝒓 𝑫𝒂𝒚⁄ Staffing Error > 5% per 𝑪𝒖𝒔𝒕𝒐𝒎𝒆𝒓 𝑾𝒌⁄

Simulation 4.65% 1.49%

Erlang-C 18.22% 17.31% Table 8: Summary of Missed Staffing Requirement Prediction by more than 5% per day and week

In Table 8, the staffing requirement generated by simulation modeling has an error of

more than 5% a mere 4.65% of the time at the daily level, and only around 1.5% of the

time at the weekly level. Erlang-C generated requirements are off by more than 5%

more than 17% of the time both at the daily and weekly levels, indicating accuracy and

precision problems.

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Summary and Operational Implications Based on this comparative analysis, the following summary observations are arrived at:

The Erlang-C model, on average, is pessimistically biased when measuring service

performance (actual results are better than predicted), but may become

optimistically biased when utilization is high and arrival rates are uncertain.

Erlang-C error does not improve when models are evaluated weekly, rather

than daily.

Simulation modeling, by contrast, shows a slight optimistic bias when measuring

service performance, but not at the expense of its accuracy. It is also precise as

evidenced by the low variability around the mean. Simulation prediction of service

performance becomes more accurate and precise as the level of granularity

changes from daily to weekly.

The Erlang-C model is most accurate when the number of agents is large and

utilization is low due to the "no abandonment" assumption. In any other situation,

it tends to overstaff significantly. Empirical evidence suggests by more than 10%

on average, relative to the historical staffing. Simulation is accurate with any

contact center size.

Erlang-C measurement error is high when the contact center exhibits higher levels

of abandonment. Simulation does not show this shortcoming as abandonment

behavior can be derived from the customer patience profile.

That the Erlang-C method overstaffs contact centers is not surprising. Erlang-C equations

have long been suspected of requiring too many agents or under-predicting service. The

magnitude of the error is surprising, however. Extrapolating this small example, contact

centers relying on Erlang-C methods may be managing their operations with as much as

16% too many agents. Waste is easy to hide, and the overstaffed contact center often

loses more than the obvious extra agent costs, they lose their edge.

A subtler result from this study is that the Erlang-C method produces error rates that are

not consistent. Sometimes overstaffing by a lot and sometimes by just a bit. If service

consistency is important for your operation, this poses a problem.

Simulation models need to be customized in order to be accurate. Every call center is

different. Different distributions of call arrivals, handle times, customer patience,

efficiency, and staffing must all be represented in an accurate simulation model. For every

call type, a new and different simulation model may be necessary to produce accurate

results. Charts like those developed for this paper, demonstrating the accuracy of the

models, are required to verify any simulation system. Without these validation charts, the

models should be assumed inaccurate.

The most obvious implication of this empirical study is that Erlang-C errors result in

significant and wasteful costs for most organizations using it. Erlang-C is not usable for

accurate what-if analyses, and it will ensure service delivery that is inconsistent. Discrete-

event simulation models exist that address these substantial, and often hidden, costs.


Appendix A: Auto Insurance Call Type Charts

Service Performance Comparisons

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Staffing Requirements FTE Comparisons

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Appendix B: Retail Call Type Charts


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Appendix C: Preferred Service Call Type Charts


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Appendix D: Credit Card Call Type Charts


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Credit Card: Service Level Comparison Simulation vs. Erlang-C vs. Actuals (Daily Summary)


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Appendix E: Member Services Call Type Charts


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Appendix F: Loans Call Type Charts


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Staffing Requirement FTE Comparisons

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Authors Ric Kosiba is an expert in the field of call center management and

modeling, call center strategy development, and the optimization

of large-scale operational processes. He received a Ph. D in

Operations Research and Engineering from Purdue University and

an M.S.C.E. and B.S.C.E. from Purdue’s School of Civil Engineering.

He also has obtained a patent on the application of optimal

collection strategies to delinquent portfolios in addition to a patent

on the application of simulation and analytics to contact center planning.

At the start of his career, Ric served as Manager of Customer Service Analytics for USAir’s

Operations Research Division, and as Operations Management Senior Analyst with

Northwest Airlines. Later, he moved into Customer Support at First USA, where he served

as Vice President of Operations Research and guided all facets of the company’s call

center process improvement, including collections strategy modeling and detailed staff

plan development and call center budgeting. Ric then held a position as the Director of

Management Science at Partners First, where his responsibilities included the detailed

modeling of portfolio risks, in addition to predictive and prescriptive marketing and

operations engineering.

Ric ultimately founded Bay Bridge Decisions, which later joined Interactive Intelligence,

and now serves as Interactive’s Vice President in the strategic planning market. He

continues to write for numerous contact center publications and speaks at highly

acclaimed technical and contact center forums on a frequent basis.

Contact him at: [email protected] or 410.224.9883.

Bayu Wicaksono is the Manager of Operations Research

Department at Interactive Intelligence. He has been responsible for

developing the algorithms and analytic for Interaction Decisions

(formerly CenterBridge) for 10+ years, and has in-depth knowledge

of contact center analytic and strategic

planning/modeling/forecasting. He graduated both Bachelor's and

Master's in Industrial Engineering with focus on Operations

Research from Purdue University.

Bayu holds several patents relating to predictive and prescriptive simulation modeling and

analytic to contact center planning. His passion is continuous learning and process

improvement, programming, cloud-based solutions architecture, analytic algorithms, as

well as library deployment and integration. He also loves to talk about math, programming

and process improvements, and can be reached at [email protected] or

410.224.7620.

mailto:[email protected]

mailto:[email protected]

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