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Table of Contents
Service Quality and Customer Abandonment: a System
Dynamics approach to Call Center Management.
Massimiliano Caramia
Istituto per le Applicazioni del Calcolo “M. Picone”
caramia@iac.rm.cnr.it
Stefano Armenia, Riccardo Onori
DISP - Faculty of Engineering - “Tor Vergata” University, Rome
armenia@disp.uniroma2.it - onori@disp.uniroma2.it
Valerio Giannunzio
Faculty of Engineering - “Tor Vergata” University, Rome
v.giannunzio@virgilio. it
Abstract
The ability to profitably manage the level of resources in a service system can be considered a
strategic skill in all those organizations, including no-profit ones and Public Administrations, that
aim at providing an added value service to customers as well as balancing the level of service (in
terms of quality) with costs. In this paper we will focus on a typical service system inside of which,
in every moment, management struggles in order to reach that balance, because of the extremely
dynamic behavior of the entire system: a Call Center. Our aim is to show that an efficient
management of the customers abandonment and the quality of service offered to customers, can
positively impact on a correct resource leveling in the system, which may otherwise be found by
means of typical Operations Research or Queuing Theory methods. In particular, we want to show
that this can be more easily inferred and understood by resorting to simulation. After introducing
some preliminary aspects by means of Queuing Theory (Erlang’s formula), we’ll first study the
problem of customer abandonment (balking and reneging) by simulating a Call Center simple
model by means of a process-oriented discrete-time simulation tool (Arena), and then explore a
more complex model taking into account customer satisfaction an the quality of the service offered
approaching the modelling process of the system by means of System Dynamics. Results show that
the level of resources can be further reduced, and that the customer (often thought as an entity
external to the system) plays instead an important role on the performance of the whole system,
both operationally and economically.
1. Introduction
Since the beginning of the so called civilized society, man has always had to deal with queues, e.g.
in order to receive food, for entering into buildings, or generally in processing customers orders in a
shop. As customers, we are usually quite disappointed with long waiting times, but also managers
of the establishments at which we wait do not like us to wait for too long, since it may cost them a
lot in terms of business, money, customer fidelity, and so on.
The evolution in the ways of doing business is today greatly based on the fast growing awareness
that managing the relationships with customers has become one of the key factors which can lead a
modern organization to success. That is why organizations need to understand that correctly
managing their Service Systems may in the long run reveal itself as one of their best competitive
advantages.
In this work we will describe how to take into account customer satisfaction in order to describe
queue abandonment and how a qualitative service can reduce a system resources usage, thus
improving those results which could have been drawn with a typical mathematical approach,
Queuing Theory (QT) or Operations Research (OR). In particular, we will show some of the issues
which the management of a Call Center must traditionally confront with, and we will try to explain
how simulation tools and System Dynamics (SD) may be used to better analyze the performance of
a generic Service System and its management policies.
Specifically, in the first part we will try to put in evidence how a strategic issue like resource
management in a Service System like a Call Center may suffer from critical aspects, e.g. customer
abandonment or quality of the service offered, and how simulation tools may help to overcome
some of the problems encountered in the analysis. We will start with an introductory scenario, with
hard data, and with an analysis drawn according to Erlang’s formulas. Then we will see how
simulation with an Event Driven Simulation (EDS) software like Arena fits better in some
situations where mathematical analysis may become too difficult because of the complexity of the
system, and we will give an example based on the same scenario. Simulation results will also be
provided. We will see how System Dynamics may help to show more evidently the strict
relationship between Service Level and Quality of Service, Customer Satisfaction and Agent
Burnout, as well as how these are connected to staffing issues or to workload forecasting and
handling. In particular, we will show how a SD model can improve the performance of a Call
Center by comparing with the results obtained by Erlang’s formulas and with Arena.
2. Where simulation fits in the analysis of a Service System
Whilst queuing theory can be used to analyze simple service systems, more complex service
systems are typically analyzed using simulation. In fact it turns out that it is not possible to develop
analytical models for service systems because of the characteristics of the input or the service
policy, the complexity of the system itself, the nature of the queue discipline or combination of the
above. For example, a multi-station multi-server system with some recycling, where service times
are normally distributed and a complex priority system is in effect, it becomes almost impossible to
model analytically (Hillier, Lieberman, 1990). Furthermore, if one were interested in the transient
behavior of a service system or if the probability distributions were to vary with time according to
various relationships between dynamic parts of the system, it might not be possible to develop
analytical solutions or efficient numerical schemes.
More in detail, there are three major reasons that justify the use of simulation tools in a Service
Center analysis:
1. Uncertainty: arrival times are highly unpredictable and arrivals tend to come up in bunches,
making it very difficult to properly assess system resources without the right tool.
Simulation is designed, as one of its core values, to handle uncertainty;
2. Complexity of the Service System structure: other tools like spreadsheets do not allow to
put in due evidence the many interactions and interdependencies occurring in the system;
3. Dynamic environment: most service centers are today going through dramatic changes in
technology and work flow processes.
Some very general applications of simulation in a service system may be to perform evaluations
and/or comparisons between policies or strategies as well as also between simulation and other
analytic tools, to predict outcomes, optimize solutions, analyze functional relationships and perform
sensitivity analysis. No matter what type of analysis is carried out, the latter generally begins with a
series of “what-if” questions like, for instance, what would be the impact on a Call Center’s
efficiency and effectiveness if more staff is added or a Voice Response Unit (VRU) is installed,
calls are rerouted to another center after a certain hour in the day, demand increases/decreases, calls
are rerouted on a skill-based basis, several Call Centers are consolidated into a single one (Anton-
Bapat, 1999).
We can generally group simulation applications to Call Center Management into short-term
(Service Level setting, forecast analysis, allocating staff, budget analysis, customer affectivity
analysis, agent scheduling, impact of new technologies, call-flow pattern analysis, introduction of
new products/services, productivity analysis, turnover analysis) and long-term planning horizons
(adding a new CC, consolidation, CC assessment and benchmarking, becoming a virtual Call
Center, adding electronic access, outsourcing, integration, multifunctional Call Center).
Some of these issues could have never been analyzed using traditional methods, while other get
better and more consistent results when analyzed through simulation. In the past, many poor
decisions about procedural change were probably taken in such a light mood that the disruption they
provoked went unnoticed until after the companies had already paid a high price in term of lost
customers and tarnished reputation. No customer-conscious company can afford to take such risks
anymore in this competitive age.
2.1 Setting the context: the call center
Recall from the queuing theory that in essence all service systems can be broken down into
individual sub-systems consisting of entities queuing for some activity (as shown below).
Queue
-@ je | Activity —
To analyze these sub-systems we need information relating to six basic characteristics: the arrival
process (how customers arrive, how arrivals are distributed in time and whether the population is
finite or infinite), the service mechanism (base resources, service time distribution, number of
available servers, whether they are in parallel or in series, whether pre-emption is allowed, etc...),
queue discipline (FIFO, LIFO, etc...) and characteristics (is there any balking or reneging?), system
capacity, number of service channels and number of service stages (Gross-Harris, 1998).
A quick look inside a typical Call Center (denoted throughout the paper as CC) reveals complex
interactions between several “resources” and “entities”, where the former are the operators
answering the phone and the latter take the form of calls or, rather, customers calling the CC in
order to receive a certain service. These calls, usually classified by call types, then navigate through
the various CC structures; this means that while traversing through the CC, calls occupy trunk lines,
wait in one or several queues, abandon queues and are redirected through interactive voice response
(IVR) systems until they reach their destination, an agent or some predetermined self-service
feature. Once the call is handled, or the customer has received service, it then leaves the call center.
During all of these transactions, another critical resource is consumed, time.
By referring to the queuing theory, a call center can be sketched as a parallel-server birth-death
(Kleinrock, 1975) model, also known as a M/M(G)/c/K service system, based on:
an exponential or Poisson call arrival process (M)
an exponential or general service time distribution (M or G)
a finite number of parallel servers (c)
a finite system capacity (K, in our case the capacity of the queue)
pits Fe
Notwithstanding these general concepts, we could model the arrival process by imposing that calls
do not arrive simultaneously, but one by one and with a given expected inter-arrival time (“birth
process”). We know that calls tend to bunch up especially in certain moments of the day, but we are
not too wrong in our limitation, especially because calls enter the queue according to a certain
discipline and thus any two (or more) of them cannot occupy a queue slot at the same time. It is also
necessary to know the reaction of the customer upon entering the system. A customer may decide to
stay in line no matter how long he has to wait or may decide not to enter the system. If he/she
decides not to enter the queue upon arrival, he is said to have balked. In a CC, a customer calling
may not have any idea of how long the queue is until he really is in the line (and in the latter case,
only if he receives information about expected waiting times), thus we cannot talk about balking but
we can model the fact that the customer may find a busy line because of trunks already full to their
limit. On the other hand, a customer waiting may decide to leave the queue (that is reneging, also
known as abandonment) either because he has been waiting for too long or because he received
information on how long the waiting time is in that particular moment. If we model this aspect only
by taking into account that customers may all the time retain the prerogative to renege if their
estimate of the total wait is intolerable, we may run the risk to underestimate (or overestimate,
depending on the situation) abandons (refer to the queuing theory for the aspect of queues with
impatience; Gross-Harris, 1998). This is one of the main reasons (even if not the most important, as
we will see later on) that would account for the use of simulation in such a context.
Moreover, we assume that calls get service according to the FIFO discipline and as soon as there is
a free agent. This brings us directly to the issue of the service process. We can divide it in two
phases: the first, during which customer and agent talk and the customer gets service (thus talk time
equaling service time by the customer point of view), the second, during which the agent is required
to make a sort of after call work, in order to store all the information he did not have the time to
write down during the conversation or to perform those actions requested by the customer. The
expected mean service time, by the service process side, is then given by the sum between talk time
and after call work (in such a context, this is the so called “death rate’’). This means that every time
an agent gets free again, he picks up a call, thus getting busy, and becomes free again only after a
certain time.
Another important issue is about the finite system capacity, which in our case may be simplified by
assuming a finite queue. From the CC point of view, this translates in finite number of trunks, each
with a finite number of call slots available, even if we will further simplify the situation by
assuming that the system has only a single service channel and a single stage of service. The chance
that customers might want to call back if they were not satisfied with the service they received
should carefully be accounted for, as well as callback probability in the chance that a customer finds
a busy line or after having abandoned.
2.2 The advantages and disadvantages of simulating a Call Center
In such a dynamic and volatile environment as a service system, the intrinsic value of simulation
resides in that it may allow a top senior manager, or just an analyst or advisor, to take better
decisions than those eventually derived from traditional analytical approaches, as well as virtually
cutting any risk associated to an improper or useless business strategy. The objective of the CC
manager or analyst is twofold: first, to achieve a high service level (SL), i.e., to get the caller to an
agent in the shortest amount of time, and second, to provide the caller with the appropriate
information in the most efficient manner (measured in terms of call talk time and handle time). The
net objective is to minimize the time spent by the caller in the CC while providing the best possible
service. Ultimately, these issues generally come down to a trade off of better customer service
versus the expense of providing more service capability, that is determining the increase in
investment of service for a corresponding decrease in customer delay (and sometimes also in costs
due to a tool-free service; Cleveland-Mayben, 1997-1999). These primary measures and objectives
usually reflect the performance of a CC, and balancing these objectives can be a challenging task
for call center analysts. Furthermore, there exists a great deal of sensitivity in the cause and effect of
the performance parameters involved (Anton-Bapat, 1999). For example, a small adjustment in call
routing may have a significant debilitating change on customer, or a minor reduction in trunk-line
capacity may cause too many “busies” and raise the potential for lost customers (which, in turn,
according to the well known Customer Based View, may in the long run lower the revenues and
profits of the company). Moreover, also very important, an incorrect staffing may cause long
waiting times, frustrated customers and exasperated agents. Such circular relationships must
carefully be defined and analyzed in order to achieve peak performance for the call center.
A disadvantage in simulating a Service System is that it is sometimes difficult to find optimal
solutions, unlike linear programming where, for example, we may have different algorithms that
will automatically find an optimal solution. One way to attempt to optimize using simulation is to
make changes to the model (by setting its parameters) and run the simulation computer program to
see if an improvement has been achieved or not, and repeat. This process can consume large
amounts of computer time. Nowadays there are fortunately some simulation packages which also
support some optimization tools. In our paper, we didn’t resource to any optimization since it goes
beyond the basic scope of this article. In the last paragraph we will also address this issue among
those to be further explored in future works.
Instead, the advantages of using simulation, as opposed to analytical methods, are that it can more
easily deal with time-dependent behavior; that the mathematics of queuing theory is hard and only
valid for certain statistical distributions - whereas the mathematics of simulation is easy and can
cope with any statistical distribution; that in some situations it is virtually impossible to build the
equations that queuing theory demands (e.g. for features like queue switching, queue dependent
work rates) and, finally, that simulation is much easier for managers to grasp and understand than
queuing theory or difficult analytical methods.
2.3 Modeling a Service System like the Call Center with System Dynamics
By means of a systemic approach (i.e., System Dynamics) to the analysis of those phenomena
present in any service system, it is possible to consider in the model also those soft variables which
in other modeling methods would only be accounted for as external factors, and not as strictly
correlated with the behavior of the so called internal system’s variables. By simulating a SD model
of the system, in which such “soft” factors have been included (as for example the so called Agent’s
Burnout) it is possible to see how the overall behavior may dramatically change as well as also the
requested resource level. And in the particular context of our study, we will show how this is
particularly true when accounting in the model for service quality, operator burnout and customers
motivations, as well as for other causal relationships (Sterman J., 2000).
In order to develop our model, we only partially referred to existing System Dynamics literature on
similar models. Other authors (Oliva, 1996), in fact, report SD modeling of waiting line based
systems which only in part have helped us in understanding the absolutely peculiar dynamics of a
telephone service system, mostly because they deal very specific issues in fields like the Health
System (Gonzales Busto-Garcia,1999; Van Aeckere-Smith,1999; Emergency Room Dynamics
Model, HPS Inc. 2002), the restaurant business (Fung 1999 and Fung 2001) and others (see also the
well known Hanover Insurance model). Even if we haven’t found clear evidence of previous
specific literature on CC modeling with SD, we have however found many interesting issues on this
topic in the queuing theory (Gross-Harris 1998, Kleinrock 1975, Naor 1969) as well as in the OR
(Hillier-Lieberman 1990) and of course specific CC Management literature (Cleveland-Mayben
1999, Anton-Bapat 2000). We have thus sketched our own maps of the most evident causal
relationships in such an environment and then drawn our SD model by also keeping well into
account the typical processes in a system based on waiting lines (call flows and agent flows).
3. Call Center structure and dynamics
In this paragraph we will illustrate some of the issues connected to the analysis of particular
problems in a typical CC. More in detail, we will analyze the impact of Abandonment and Quality
on Staffing and Service Level. Towards an improved understanding of the issues we are going to
deal with, we will develop some simple cause/effect diagrams in order to elicit and show the
various systemic structures that drive the behaviors of a CC system.
This is a function
of staffing
This doesn’t get
on trunks
Delay Agent Load
C Y \
Incoming , Ring | DelayAnnouncement | Music ; Talk | Work
Call T I l T l
\ )
Trunk Load
\ )
Caller’s “Load”
Figure 1: A view of a call flow inside the call center.
3.1 Some definitions
Let us introduce some of the acronyms and definitions used during the following pages (Cleveland-
Mayben 1999, AA.VV. 2000):
Service Level (SL): X % of calls answered in Y seconds.
Average Speed of Answer (ASA): (from Little’s formulas of the queuing theory: Wg, the expected
waiting time in queue), also called Average Delay or Waiting Time (when seen from a customer
point of view). It represents the average delay of all calls in a queue and can be calculated by
dividing the total delay by the number of calls in a queue. It is the average waiting time of a
customer in a queue.
Average Handling Time (AHT): it is the sum of the Average Talk Time (ATT) and the average
After Call Work time (ACW). Also called “Agent Load” (from Little’s formulas of the queuing
theory: 1, the expected mean service time).
Agent Occupancy (OCC): it is the percentage of time that agents (also referred as TSR) spend in
AHT with respect to the total time of their shift in schedule (from Little’s formulas of the queuing
theory: p=A/(u*c), the expected measure of traffic congestion for c-server queues). The inverse of
OCC, represents the time agents are available and waiting to handle calls.
Telephone Service Representative (TSR): the generic human server who answers the phone. Also
called operator, rep, agent.
Trunk: also called a line, a telephone circuit linking two switching systems.
Trunk Load (TKLD): it includes all aspects of the transaction other than the ACW. Can be viewed
as ATT +ASA. Trunk load carries the delay (ASA). It is measured in erlangs (hours of trunk
traffic), that is: (ASA+ATT)in sees * N°_of_Callscin 1 hour)
In general, a call flow inside a CC follows the scheme represented in Figure 1 (Cleveland Mayben
1999)). A customer dials the CC number and if he/she gets a “busy”, depending on some factors
affecting his degree of tolerance (his actual mood, motivation, the availability of substitutes, and so
on) he decides whether to retry or not. Once he gets connected, in most of the situations, he then
enters into a waiting line, characterized from ASA. Once again, with reference to the so called
“seven factors affecting callers tolerance” (which include: service level of the CC, the time being in
a queue and the possibility of “perceiving” its length, customers degree of motivation, availability
of substitutes, competition’s service level, level of expectations, time available to wait, who’s
paying for the call, human behavior; Cleveland-Mayben 1999) the customer may then decide to
hold on and stay in the queue or to hang up (“abandon” the queue). Once at last a customer reaches
an agent, the call gets handled. Handling a call requires time (AHT), in terms both of talk time
between agent and customer and of wrap-up work time. From an agent point of view, the process
does not stop after having handled a call. Instead it goes on in circle, because as soon as an agent
becomes free again, he suddenly picks up the next waiting call.
3.2 Basic Call Center dynamics: a classical analytical method
In this paragraph we will make some general considerations on usual CC management practices as
well as describe a classical analytical method, both in order to put the basis for understanding which
ones are the high leverage points to act upon with the aim of improving the system’s performance.
We will put in evidence some limitations of the classical methods, thus setting the context for an
approach with system dynamics.
The key to achieving Service Level objectives, ultimately comes down to having the right people in
the right places at the right times and doing the right job (which means quality!). Base staffing and
trunking calculations cannot be separated from a reasonably accurate forecast of call loads, which in
the following, we will assume as being the best possible one. Note that, in the example shown in
this paragraph, trunking should be calculated in conjunction with staffing because staffing impacts
delay (or ASA), which, in turn, affects the load that trunks must then carry (see Figure 1). In fact, as
also can be seen from the definitions in the previous paragraph, as a rule of thumb, the more staff
handling a given call load, the less delay the callers will experience, and therefore it directly
impacts how many trunks are required. There is no way to know base trunking needs without
knowing how many agents will be handling the forecasted call load. Moreover, in general, there is
no staff-to-trunk ratio or formulas that can be universally applied. In fact, if SL is low, the trunks
will have to carry more delay and, consequently, more trunks would be needed. Staff and trunks are
a classic example of the need to look at “the big picture”, especially when speaking about the issue
of integrating their related budgets.
Still, many CC managers calculate base staffing by using some ratios or formulas; even though
these methods may sound logical, they are dead wrong, since they do not relate the outcome of
staffing to the desired SL. That is mostly because the desired “targets” are moving. For example,
staff productivity (calls that a group of agents can handle) is not a constant factor, rather it is
continuously fluctuating because it is heavily influenced by vacillating call loads and SL objective.
The biggest problem of these operative approaches is that they are quite simplistic, because they
ignore one of the most important driving laws in incoming call centers: calls bunch up.
As seen in Paragraph 2.1, the whole CC service process may be simply summarized, without taking
into account complicate interrelationships between the different parts of the system, only by a few
key factors and equations. First, the arrival process can be modeled with a Poisson process based on
a given inter arrival constant, A; second the service process can be modeled either with an
exponential or a general distribution with a mean value of 1/u=AHT, third, the system capacity is
given by the product of the number of trunks and the number of calls that each trunk can hold;
fourth, the system has c operators, that manage customer calls according to a FIFO discipline. The
queue has a single channel and the service has a single stage. This kind of models were studied in
particular by Erlang, in 1917, and the original physical situation which motivated him to devise
analytical formulas was of course the telephone network. Later on, Erlang’s original formulas were
adapted to staffing calculations as Erlang C and to trunking purposes as Erlang B. In particular,
Erlang C was so formulated:
A = total traffic (in erlangs)
where: N = number of active servers
P(>0) = probability of delay greater
than 0
This formula calculates predicted waiting times (ASA) based on the number of reps, the number of
customers waiting to be served and the average amount of time it takes to serve each customer; it
can also predict the resources required to keep waiting times within targeted limits, and that is why
it is useful for staffing.
But, as with any mathematical formula, Erlang C has built-in assumptions that do not perfectly
reflect real circumstances. One problem is that by assuming that all incoming calls are anyway
staying in queue, it means that customers will wait until they get an answer, i.e. they will never
abandon. Moreover, as said, it assumes that there is an infinite trunking and system capacity, thus
that nobody will ever get a busy signal. The result is that Erlang C may overestimate the staff really
needed. Erlang C is not of exclusive use in the telecommunications world; it can be used to
determine resources in any situation where people might wait in a queue for service, and thus there
are tables to make it easier to use and more accessible than the formula itself. Of course there are
also computer programs.
In the following example, we show Erlang C results based on the use of an Erlang C program
provided by ICMI (AA.VV. 2000). It basically requires four variables as input: Average Talk Time
(ATT), Average After Call Work (ACW), number of calls (the projected volume for the time unit -
say, typically, half an hour - we are analyzing), Service Level objective in seconds (i.e., 90 calls in
20 seconds, the input 20). Once the numbers are fed as an input to the program, the output provides
a wealth of information and insight into the dynamics of a CC.
TSRs | P(0) (%) | ASA | DLYDLY | Q1 | Q2 | SL(%) | OCC (%) | TKLD
30 83 209 252 29 | 35 24 97 54.0
31 65 75 115 10 | 16 45 94 35.4
32 51 38 74 5 | 10 61 91 30.2
33 39 21 55 3 8 73 88 28.0
34 29 13 43 2 6 82 86 26.8
35 22 8 36 1 5 88 83 26.1
36 16 5 31 1 4 92 81 25.7
37 11 3 27 0 4 95 79 25.4
38 8 2 24 0 3 97 77 25.3
39 6 U 21 0 3 98 75 25.2
40 4 1 19 0 3 99 73 25.1
41 3 if 18 0 2 99 71 25.1
42 2 0 16 0 2 100 69 25.0
Table 1: Erlang C for Incoming Call Centers.
In Table | we reported values for the following factors and variables:
TSRs: number of reps required on the phone
P(0): probability of delay greater than 0 secs
ASA: Avg. delay of “all” calls
SL: X% of calls answered in Y seconds
DLYDLY: Avg. delay of delayed calls
Ql: Avg. number of calls in queue at any time, even when there is no queue
Q2: Avg. number of calls in queue when all reps are busy or when there is a queue
occ: Percentage of agent occupancy: the pct. of time agents will be spending while
handling calls
TKLD: hours (erlangs) of trunk traffic. The actual traffic carried by trunks in a half-hour will
be, in each row, half of what is given
Note that in our application of Erlang C, we assumed the following parameters, which are typical
values in a CC environment:
Average Talk Time in seconds: 180
Calls per half hour: 250
Average after call work in seconds: 30
Service Level in seconds: 20
The first interesting column to focus our attention on in Table 1, SL (Service Level), represents the
percentage of calls to be answered in a given number of seconds. If, for example, your objective is
80/20 (which means 80 percent of calls answered in 20 seconds), keeping going down the column,
we pass from 73% to 82%. Since the program is calculating staff required, some rounding is
involved (people are obviously integer numbers), and since 82% meets our 80/20 standard, then that
is the row we will concentrate on. Each column provides insight and information into the chosen
service level.
With a concluding remark on analytic methods, we can say that Erlang C is fairly accurate for good
service levels, while for bad ones it cannot truly show how bad they really are. As pointed out in the
previous paragraphs, it has however some disadvantages: for instance, it assumes no abandoned
calls or busy signals as well as “steady state” arrival (traffic does not increase or decrease beyond
random fluctuation within the considered time period). It also assumes a fixed number of staff
handling calls throughout the time period and that all agents within a group can handle the calls
presented to the group, thus neglecting peaked traffic or the need for skill-based routing, different
groups of agents or complex network interflow. There is where computer simulation enters the
game.
3.3 The impact of customer abandonment: a simulation with Arena
Arena Call Center can be used in conjunction with standard Arena constructs (a widely-used,
general purpose simulation tool) to generate models of specific CC architectures. Building a model
entails developing flowchart-style scripts that depict the current and proposed call routing process.
For that purpose we use the process illustrated at a higher level in previous sections. The model
generates streams of arriving calls that are held by the Call Center. As soon as they enter the CC,
calls are assigned to a trunk line and routed through the center to agents who will eventually serve
them.
There are other complicating factors that are built into the model. Calls can be blocked if trunks are
busy, or if a certain limit, based on the ratio of calls in progress to the number of agents available, is
exceeded. Once a call is blocked, it may contact back, depending on a specified distribution.
Moreover, abandons may occur when the caller terminates the contact before reaching an agent. For
each call, abandonment is modeled by a distribution for the amount of time a customer will wait
(ASA) prior to abandoning the CC. For each call, a value is generated from this distribution to
determine how long a customer will wait before abandoning, if not yet connected with an agent.
Once a call abandons the CC, it may as well contact back.
Data were collected from a subset of 30 runs per each value of the main leverage parameter, with a
“warm up” (transitory) period of 900 seconds. We show the results in the following table:
TSRs | ASA (sec) | Handled | Abandoned | SL(%) | OCC (%)
30 29 210 45 42 97
31 26 223 26 56 94
32 19 233 18 68 91
33 12 241 6 81 89
34 8 243 4 88 86
35) 6 243 2 90 82
36 4 247 1 92 81
Table 2: Simulation Data obtained with Arena 7.0 ®
In Table 2 we reported values for the following factors and variables:
TSRs: number of reps required on the phone
ASA: Avg. delay of “all” calls
Handled: Total calls handled
Abandoned: Total calls abandoned
SL: X% of calls answered in Y seconds
occ: Percentage of agent occupancy: the pct. of time agents will be spending while
handling calls
Note that in our simulations, we assumed the following parameters:
Average Talk Time in seconds: 180
Calls per half hour: 250
Average after call work in seconds: 30
Service Level in seconds: 20
Simulation Time: 2700
Warm Up period: 900
Note how taking into account queue abandonment has allowed us to reach our target Service Level
with only 33 agents instead of 34. Also ASA improves, even if occupancy gets a little bit higher,
but this depends on one of the so called five “immutable laws” in incoming CC (see next chapter),
that is: for a given service level, larger agent groups are more efficient than smaller groups. With 34
agents, we see how the situation dramatically improves. Whether choosing to have 33 or 34 agents
could then seem obvious if agent’s burnout (depending on high occupancy) is not taken into
account.
Burnout, errors and rework, and the effort for a qualitative service are some of the issues we will
focus on in the next paragraph in order to extend our understanding not only of the processes acting
in a CC but also of other existing relationships between physical processes and “soft” variables like
agent stress or burnout and customer satisfaction.
3.4 A system dynamics approach: the impact of Quality and Service Level
Let us start from the five fundamental principles that govern a call center and characterize its
dynamics (Cleveland-Mayben 1999):
1. For a given call load, when service level goes up, agent occupancy goes down (mostly
because the call load is evenly distributed among them)
2. By keeping improving the Service Level, a point of diminishing returns will be reached
(limit to the growth)
3. Given a SL, larger agent groups are more efficient than smaller ones (agents show a higher
occupancy percentage)
4. All other things being equal, pooled groups are more efficient than specialized ones (handle
more calls with same number of agents, same call load with fewer agents, same call load
with same number of agents at a higher SL)
5. Given a call load, if staff is increased, then ASA will decrease and trunk load will go down
Moreover, we have found evidence, also in the literature (Busacca-Valdani 1999, Sterman et al.
1997), that the quality of the service offered depends both on factors connected with the effort and
commitment of the management towards a qualitative service, as well as also with customer
expectations and satisfaction (e.g. calls handled qualitatively by agents), and on variables which are
typical of a call center structure, i.e. Service Level (SL), Average Handling Time (AHT), Average
Speed of Answer (ASA), free line, and so on.
In particular, we can say that an effort of the management towards making agents handle calls in a
qualitative way may be viewed as a tendency to skill agents so that they can meet customer
expectations, thus improving the customer satisfaction index. In fact, reducing errors and rework
has been seen to have a positive impact on service level, morale, customer satisfaction and, last but
not least, costs. Typically, customers expect a CC to be accessible, to be treated courteously, to
promptly do what they ask, not to deal with poorly trained agents, to be responsive to what they
need and want, to do it right the first time, to be socially responsive and ethical, and so on. As said
before, a call is defined as “qualitative” when: the customer is satisfied with the received service
and of his/her experience in the CC, the TSR captures all needed/useful information, all data entry
in the ACW phase is correctly done, the TSR provided correct response and the caller received clear
and correct information in a time not perceived as too long, the caller does not get transferred
around the CC or does not get rushed, the customer has confidence that his call was effective, the
caller does not feel necessary to verify, check-up, repeat or even call back, the TSR is satisfied of
how he just handled the call, the caller did not get any busies or was not placed on hold for too long,
and, in the end, the CC mission is accomplished. In the end, the equation that puts in strict
relationship quality effort and highly skilled or experienced agents seems not to be too far from
reality.
‘Agents Vs.
AV.
Errors & ™ ;
ey Quality Handling
Figure 2: Positive (+) Feedback loop between Quality and Service Level.
We can thus draw a first qualitative causal map which consists of a main positive feedback loop
between Quality and Service Level. This means that if SL is improved (because of a better quality
in service), OCC generally decreases and then also staff burnout goes down. Thus, agents do not
need to frequently take breather, have a higher schedule adherence and can then manage call
handling more qualitatively (fewer errors). On the other hand, when SL deteriorates, also Quality
(perceived and effective) gets worse, thus starting a dangerous degenerative snowball effect, which
may put the performance of the entire structure at stake.
In the first part of Figure 2, we want to show how a quality service positively influences both
customer satisfaction and agent satisfaction (pride in their job), thus acting also positively on
service level. This of course also brings to the result of increasing profits for the company, since
increasing customer satisfaction means also increasing customer fidelity and, in the long run,
revenues, thus having a positive return on higher investments in quality.
In particular, when quality goes down, customer complaints drive up average talk time, thus
disrupting AHT and increasing network costs. Moreover, as AHT goes up, the number of reps
becomes insufficient to handle the call load at a desired Service Level. This, in turn, increases agent
OCC, deteriorates SL and lowers customer satisfaction, thus increasing rework, which negatively
act back on quality, lowering it further and so on. However, it must be noted that as AHT grows,
also average delay (ASA) goes up. This causes abandons to grow larger and the queue to shorten.
This effect acts in a balancing way (negative loop) on the entire structure of the system (thus
showing the presence of a “Limits to the Growth” archetype).
In light of what has just been explained, and developing further the causal loop devised in Figure 2,
we can finally draw the causal loop diagram of Figure 3, where:
- Call Load: this one has been considered as an exogenous variable since we’re modeling our
system on a very short time window. Thus, it would be meaningless to model the call load as
an endogenous variable (a sort of beginning population to serve). Its value is based on real
forecasts.
- Staff Size and Effort in Quality: decision leverages. We have already said about the need to
consider, at this stage, the latter as a policy leverage. As long as instead the Staff Size is
concerned, once again, we have considered it as an exogenous variable since the simulation
runs over such a short amount of time which would make it almost impossible to appreciate
any change in the level of staff (if we simulated the performance of a call center over an entire
day, it would then make sense to analyze, for example, schedule adherence. In that case, the
staff size should be modeled as endogenous).
- B1: Balancing Loop.
- R1, R2, R3: Reinforcing Loops.
LON,
Abandons
cupanc! AHT.
~, a
Burnout
Effort in
Quality
- ps s Pa
Service Level
Rework
Customer R3 .
+ Satisfaction Quali
+
Figure 3: Causal Loop Diagram of a Call Center system model.
Looking at the balancing loop (B1), we see that if gueue_length increases, then ASA increases: in
fact, a new customer arriving at the back of the queue would have to wait, on average, more than if
the queue would have been shorter. This in turn drives up Abandons (in particular, a customer may
abandon also in dependence of the customers tolerance factors, cited in Paragraph 3.1, but these are
not depicted in the CLD of Figure 3) which of course tend to reduce the length of the queue.
The first positive loop (R1) shows instead how gueue_length drives up the agents occupancy, then
causing them stress. This in turn causes more errors_and_rework, thus negatively influencing the
quality of the service offered. If quality decreases and there is not any effort in order to prevent
quality deterioration, then the necessary time to handle a call (AHT) becomes longer: this is due
because of operators stress. Of course, if AHT goes up, then on average an operator sets free in
more time. This means that, on average, fewer customers are drawn from the queue into service: so
queue_length increases (even with the assumption that the number of working agents remains
constant over the whole simulation runtime).
The second reinforcing loop (R2) mostly consists of the same elements of R1, but focuses on the
influence of Service_Level (SL) over Quality (meant as the quality of service). In fact, if
queue_length decreases, this in general drives up SL. With a certain delay, a good SL is known to
have a positive effect on the opinion that customers have of the organization, thus driving up their
satisfaction. A someway satisfied customer, tends to believe more favorably that the operator he
was on the phone with has understood his/her needs, and then does not make him waste time on
useless conversations. This can be seen as to drive down the errors_and_rework factor, thus
allowing the CC to offer a better service.
The third snowball effect loop (R3) takes into account the immediate effect that a qualitative call
may have on the conversation and thus on customer satisfaction. In our model, the quality effort
tends to drive down errors and rework, thus driving up the overall quality performance and in the
long run, customer satisfaction.
Note that the quality of service may be defined according to several indicators that identify how the
call has been managed all through the process. As said before, there are several aspect that may help
define a call as “qualitative”. For each of these aspects of quality, a custom key indicator may be
developed or identified. In this paper we want to show how acting on a high leverage point as
pushing on the quality of service, may help to improve a CC performance. We will then just use
such a parameter as an aggregate of key indicators which may for sure be developed in many ways.
3.5 The modeling process
The model has been implemented with Ithink 7.0° (Demo Version) and has been run on an Intel”
PC Processor Pentium IV, 2.0 GHz. The modeling process has taken into account the real process
that basically consists of two main flows: a customer flow and an agents flow.
The customer flow has been modeled by taking into account four main states for the incoming calls:
a call can, in fact, be: in the queue state (Queue Level), or being served (in the Service Center
Level) and then either abandon (Abandoned Level) or being handled (Handled Level). This is
shown in detail in Figure 4: the incoming traffic can enter the queue only if the capacity of the
system allows for it, and lost calls due to busies are calculated by taking into account the difference
between the whole amount of arrived calls and the sum of calls in queue, in service and handled and
abandoned calls. Note that the balancing loop B1 has been modeled here with the following
variables: Queue (a level), Queue length, ASA (the delay experienced by customers), Leakage
Fraction (which basically accounts for the people who abandon) and the outflow driven by
Abandons. Customers, who are not satisfied with the service received, have been modeled as an
inflow back from the service center level into the queue.
The agents co-flow has been modeled by considering the two possible states for any operator, which
can be either “Free” or “Working”. As soon as there is free agent, he picks up a call as long as there
is one waiting in the queue, thus flowing into the Working_Agents level, modeled here as a
conveyor. In fact, it takes a working agents a time which is equal to the stochastic variable
Handling_Time (sum of two exponential distributions: Ta/k_Time and After_Call_Work) in order to
set free again and flow back into the Free_Agents level (Figure 5).
In Figure 6 we can see how the constant Quality_Effort represents the policy of a qualitative
service, then directly influencing the amount of “errors” during a conversation. This in turn has an
effect on the level of reworked customers, thus driving the overall quality of the service
(Quality_Factor) and hence customer satisfaction.
Service Level (Figure 7) has been defined as the fraction (percentage) of handled calls that have
been answered into the service level objective (that is, in our case, 20 seconds). We have the
following equation:
Service Level = Calls answered in SL obj. | (Calls Answered + Calls Abandoned)
Note that with Customer Satisfaction (CS) we mean here the ability to delight customers; it is in
some way also connected to how customers perceive the quality of the offered service. We have
modeled it as dependant on two main key factors: Service Level and Quality Factor (representing
the percentage of correctly handled calls with respect to the overall call load experienced by the CC
in the considered time window). Since both variables may assume values in the range from 0 to 1
(percentage factors), also Customer Satisfaction, being modeled as their product, will assume values
in the same range.
cams tena ine ‘Seconds in time unit
“OK
Tank cemensin Free soets
, Queue Lenght
\ ‘Queue Dimension /
x i omeana
Ss Pa Queue f Service Center cat anes tans,
" ee -_——— ges | —J
Inbound traffic
7
a Xi Getting Rework
Se /
Errors Factor i. ‘,
= \ é
QO it a cate vd
ss | __=*fe—___f
. tas Gate
an ( F acanh \
“—S_" “Sa fy Customer Satistaction i
Delay Distribution aot
)- ~ Leakage fraction : :
Froe agents
aT : “
Figure 4: The Customers co-flow.
It is necessary to take into account also abandoned calls at the denominator because it is then
possible to have a better idea of the accessibility of the call center and because an increase in
abandonments gives a key measure also of the deterioration of the overall service level.
‘Occupancy
‘Queue Lenght
a Initial statt
working agents
OCC Fraction
Taking call
OCC Lenght
Free agams working agents
OCC Time
ready for next cal
Bumout
UNOCC Time
Handling time
After Call Work Critical Ocoupacy
Talk time
AHT
Figure 5: The Agents co-flow.
wo,
Errors Factoi
OCC Fraction
Calls Answered in SL
a
Service Level
Handled
SL objective
. Service leno ll ‘saihnea i
Lost Calls
Calls answering in SL
Abandoned
Customer Satisfacti
Quality Ractor
Rhworked Reworking
Handled Figure 7: Service Level
Getting Rework
Figure 6: Effect of Quality
Getting into details, the variable Leakage_Fraction is a graphical auxiliary that returns the
probability that a customer will abandon the queue. It has been modeled as a function of the fraction
ASA/Customer_Satisfaction and the graphical function was obtained by real data analysis and by
evaluating how the percentage of abandons was varying according to ASA and CS. As ASA
remains constant, it is possible to appreciate the influence of a worse CS on Abandonments. As
said, the graphical function has been sketched by referring to some real CC data: by analyzing it, we
noticed a correlation between ASA and abandoned calls, relatively to the total of incoming calls.
Interpolation of point data has the allowed us to sketch the above function. In order to model ASA,
we first noticed how such a factor is highly variable, even for a constant number of customers in the
waiting line: that is why it has been modeled with a normal distribution. In order to evaluate the o,
we observed a correlation between expected values of waiting times and queue length. This allowed
us to calculate the expected value of the waiting time for a call in the queue which has undergone an
Average _Handling_Time (AHT) of just one second: that is a percentage factor estimating the
average waiting time in the queue (AWT). In this way, the average value of ASA comes from the
product AWT*AHT*Queue_Lenght. Moreover, the Gaussian distribution has a variance set so that
99.7% of calls have an expected ASA belonging to the following interval:
[AWT*AHT*(Queue_Lenght-1); AWT*AHT*(Queue_Lenght+1)]
We also want to put here in evidence some other basic assumptions and simplifications adopted in
the modeling process. First, we have assumed that customers not satisfied with the service received,
directly go back into the queue, instead of being considered as a factor to be added to the incoming
traffic. This is a worst case situation in which all unsatisfied customers are able to get into the
queue. On the other hand we have completely neglected the situation for which those customer
getting a busy signal or those abandoning the queue may decide to call back. For good service
levels, this did not seem to alter considerably the obtained results (the percentage of reworked calls
was quite low), but the risk could be to overestimate the number of agents. Second, we have not
directly taken into account the seven customer tolerance factors in a separated way, but only
considered the most important ones for simplification purposes. Third, we have modeled the effect
of service quality on customer satisfaction as instantaneous, and not with a delay that could have cut
it out of the simulation time span. Though this approach may not seem very systemic, our intent
was to model the effect that a good offered service has on the customer calling and the immediate
feedback that the latter may put in the dialoguing process (i.e., as soon as the customer feels that the
service is not that good, he immediately start asking for more information or clarifications that
make the agent loose time and stress more). Fourth, we have neglected the effect of trunk load on
system capacity. An improvement of the model could also take well into account an optimization of
such technological resources (number of trunks, trunk load, and so on). Fifth, we haven’t optimized
the model. At this introductory level of this subject, we just wanted to show some basic behaviors
of a CC environment.
3.6 Simulations of the model and results
We have run two different sets of simulation according to the following policies:
1) Fixed Effort in Quality and variation of the leverage connected to the Initial Staff;
2) Fixing the Initial Staff value found in the first set of simulations, according to which the
objective Service Level has been met, we show how ASA improves by varying the effort in
Quality;
In both cases, basic data have been chosen in order to compare results with the previous method.
Data were collected from a subset of 30 runs per each value of the main leverage parameter, with a
“warm up” (transitory) period of 900 seconds. We show the results in the following tables:
TSRs | ASA (sec) | Handled | Abandoned | Reworked | SL (%) | OCC (%) | Avg. Queue
30 27 210 48 7 53 95 4
31 23 223 29 5 62 93 3
32 18 233 17 4 70 91 2
33 11 241 5 2 81 89 2
34 8 243 4 2 87 85 1
35) 6 243 3 1 90 82 1
36 4 247 1 1 93 81 1
Table 3: Simulation Data obtained with IThink 7.0 ® .- SET (1): Fixed Quality (0,85) — Variable Agents (TSRs)
In Table 3 and Table 4 we reported values for the following factors and variables:
TSRs: number of reps required on the phone
ASA: Avg. delay of “all” calls
Handled: Total calls handled
Abandoned: Total calls abandoned
Reworked: Total of calls reworked
Avg. Queue: N° of calls which on average form the Queue
SL: X% of calls answered in Y seconds
Qty Effort: effort in order to provide a qualitative service
occ: Percentage of agent occupancy: the pct. of time agents will be spending while
handling calls
Note that in our simulations, we assumed the following parameters:
Average Talk Time in seconds: 180
Calls per half hour: 250
Average after call work in seconds: 30
Service Level in seconds: 20
Simulation Time: 2700
Warm Up period: 900
Comparing results shown in Table 3 with those in Table 1, we can see how the situation sensibly
improves when the initial staff is composed of 34 agents. SL is now 87% (compared to 82% of the
Erlang’s method), OCC goes down to 85% (it was 86%) and most of all, ASA falls to 8 seconds
against a previous value of 13. Even more interesting, if we just wanted to meet our service level
objective of 80/20, we will only need 33 reps instead of 34, still with a better ASA and with an
occupancy slightly higher (89% versus 86%).
Comparing results shown in Table 3 with those in Table 2, we can see how, even if not in an
extraordinary way, the situation also improves when the initial staff is instead composed of 33
agents. We can see that, if both ASA and Abandons improve marginally, we also have here some
reworked calls which brings the total “served” calls up to 243 instead 241. In general, however, the
situation improves.
For the second set of simulations (Table 4), we fixed the value of 34 for the group of agents and
simulated the model with different values of the Quality Effort parameter. It is interesting to
observe how a deterioration of the service quality may bring to a deterioration of ASA due to a
higher agents Occupancy: this, in turn, does not allow us to meet our SL objective. Notice also how
the level of abandons and reworks increases, especially as we fall under the 0.5 critical quality
threshold.
Furthermore, the results returned by each simulation show how the higher values of Abandons and
Reworked calls, as well as the ones of Service Level and Occupancy, are a consequence of the
reinforcing feedback loops connected with a low quality of the service that bring the system to
uncontrollable behaviors; more in detail, during our simulations the number of runs that showed
such an atypical behavior is higher for low levels of Quality effort (9 out of 30 runs for a Qty Effort
level of 0.35) and lower for high quality (1 out of 30 runs for a Qty Effort of 0.85, and no one at all
in our 30 runs for a quality of 0.95).
Qty Effort | ASA (sec) | Handled | Abandoned | Reworked | SL (%) | OCC (%) | Avg. Queue
0,35 13 235 21 14 78 88 2
0,5 12 235 15 7 82 87 2
0,65 9 240 9 5 84 86 1
0,75 9 241 6 3 85 85 1.
0,85 8 243 4 2 86,9 85 1
0,95 7 247 3 1 86,9 85 1
Table 4: Simulation Data obtained with IThink 7.0 ® .- SET (2): Fixed N°of Agents (34) — Variable Quality
3.7 Conclusions and future work
In this paper we have shown how simulation may considerably help in the analysis and evaluation
of resources in a service system. In particular, we have seen the case of one of the most classic
service systems: the call center. We have applied different techniques to a very simple and basic CC
model, representing the main processes and aspects that drive its basic behaviors and dynamics.
We have also seen the typical limitations of a classical queuing theory approach and shown how
simulation may help overcome such limitations (though maybe introducing other and new ones).
The System Dynamics approach has allowed us to further improve our understanding of the
system’s behaviors as well as to appreciate the impact that a qualitative service may have on
Service Level and ASA (and on the management of resources).
Some of the simplifications described in Paragraph 3.4 are to be removed in future works, and other
aspects will be further developed. In particular, we plan to distinguish between a strategic level and
a tactical level of the model. According to the tactical point of view, we are looking forward to
extend our model by taking into account aspects like skill-based routing, call transfers, agent
groups, impacts of a VRU installation and the extension of the simulation period to one day. At a
strategic level, we want to explore aspects connected to the flow of human resources in the call
center, analyzing how their learning curve may influence the Average Handling Time and how a
qualitative service, described in terms of those quality effort indicators which we haven’t specified
at this stage, may in the long run influence both customer satisfaction and the economic result of the
organization which the call center refers to (cash flow, profits, return on investments, etc...). We
will also try to investigate issues related to the trade off between optimization of resources and costs
(i.e., trade off between agent costs or trunk load costs) as well as the simulation of Graph
Partitioning algorithms concerning the problem of skill-based agent routing.
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