Delay announcements for call centers with hyperexponential patience modeling
| Published date | 10 July 2017 |
| DOI | https://doi.org/10.1108/IMDS-07-2016-0254 |
| Pages | 1037-1057 |
| Date | 10 July 2017 |
| Author | Miao Yu,Jun Gong,Jiafu Tang,Fanwen Kong |
| Subject Matter | Information & knowledge management,Information systems,Data management systems,Knowledge management,Knowledge sharing,Management science & operations,Supply chain management,Supply chain information systems,Logistics,Quality management/systems |
Delay announcements for call
centers with hyperexponential
patience modeling
Miao Yu
School of Management, Shenyang Jianzhu University, Shenyang City, China
Jun Gong
College of Information Science and Engineering, Northeastern University,
Shenyang City, China
Jiafu Tang
Northeastern University, Shenyang City, China, and
Fanwen Kong
School of Management, Shenyang Jianzhu University, Shenyang City, China
Abstract
Purpose –The purpose of this paper is to provide delay announcements for call centers with
hyperexponential patience modeling. The paper aims to employ a state-dependent Markovian approximation
for informing arriving customers about anticipated delay in a real call center.
Design/methodology/approach –Motivated by real call center data, the patience distribution is modeled
by the hyperexponential distribution and is analyzed by its realistic significance, with and without delay
information. Appropriate M/M/s/r +H
2
queueing model is structured, including a voice response system that
is employed in practice, and a state-dependent Markovian approximation is applied for computing
abandonment. Based on this approximation, a method is proposed for estimating virtual delays, and it is
investigated about the problem of announcing virtual delays to customers upon their arrival.
Findings –There are two parts of findings from the results obtained from the case study and a numerical
study of simulation comparisons. First, using an H
2
distribution for the abandonment distribution is driven
by an empirical study which shows its good fit to real-life call center data. Second, simulation experiments
indicate that the model and approximation are reasonable, and the state-dependent Markovian approximation
works very well for call centers with larger pooling. It is concluded that our approach can be applied in a voice
response system of real call centers.
Originality/value –Many results pertain to announcing delay information, customer reactions and links to
estimating hyperexponential distribution based on real data that have not been established in previous
studies; however, this paper analytically characterizes these performance measures for delay announcements.
Keywords Predicting and announcing delays, Hyperexponential distribution, Impatient customers,
Markovian approximation, State-dependent analysis
Paper type Research paper
1. Introduction
Recent developments in technology and business environments have significantly increased
the need for service systems. A well-designed service system can generate reduced costs
and improved customer satisfaction. Numerous researchers and practitioners exert a
substantial amount of effort in the service sector. In this paper, we address a well-known
type of service system, namely, call centers. Call centers have limited resources and
experience significant demand, which frequently creates long wait times for customers;
thus, many important challenges need to be overcome. One of these challenges is
determining the best approach for modeling a customer’s patience; the majority of
customers are not infinitely patient and are only willing to wait for service within a limited
Industrial Management & Data
Systems
Vol. 117 No. 6, 2017
pp. 1037-1057
© Emerald PublishingLimited
0263-5577
DOI 10.1108/IMDS-07-2016-0254
Received 1 July 2016
Revised 23 September 2016
Accepted 6 October 2016
The current issue and full text archive of this journal is available on Emerald Insight at:
www.emeraldinsight.com/0263-5577.htm
This project is supported by the National Nature Science Foundation under Grant No. 71271052.
1037
Delay
announcements
for call centers
amount of time. Another challenge is alleviating congestion, for example, many call centers
have recently experimented with informing arriving customers about anticipated delays
(Brown et al., 2005). In this paper, we aim to confront these challenges by contributing to the
optimal design and management of real call centers.
First, we propose modeling customers’patience using a hyperexponential distribution,
which is motivated by real call center data. According to an analysis of this type of system, a
hyperexponential distribution is a very accurate representation of a real call center. In this
paper, we focus on a paper of special interest by Whitt (2005). Because analyzing this type of
queuing system with M/M/s/r +H
2
is difficult, we employ the state-dependent Markovian
approximation by Whitt (2005) to derive standard service level performance measures in the
M/M/s/r +H
2
queueing model. This approach will be a stepping stone for predicting delays
for arriving customers.
Second, our goal is to analyze announcing delays in the call center with a
hyperexponential distribution. Information about anticipated delays is very important in
call centers with invisible queues. A delay information system captures the customer
psychology that is associated with uncertain wait times. Customers have no means of
anticipating queue lengths, which causes a substantial amount of uncertainty in delay
timing. A maxim in the psychology of waiting is that “uncertain waits feel longer than
known finite waits”(Maister, 1985); uncertain wait times have been correlated with lower
levels of satisfaction (Taylor, 1994). Therefore, delay information can serve a distinct role in
increasing customer patience by reducing the uncertainty of the wait time in a queue.
In this paper, we propose new real-time anticipated delay that effectively modulates
customer reactions. Announcing delay information to customers via the effect on
customers can modulate these customer reactions. When we inform a customer about her
or his anticipated delay, she or he will soon decide to leave immediately because she or he
estimates that the delay is too long or will begin waiting in the queue. Customers
who enter the queue have a sufficient amount of patience to wait for the service upon
receiving delay information, whereas other customers may leave after waiting for a
specific amount of time. In this paper, customer reactions to delay information are directly
considered, and their response is modeled as blocking in a voice prompt system or as
abandoning in a queue.
In a call center configuration, we develop a method to estimate virtual delays of new
arrivals and provide information that is relevant to a specific customer at a specific time.
We focus on estimating the waiting time given the system state at the time of estimation.
Because we are exploring a stochastic system, we are unable to predict exact waiting times,
which motivates us to develop a method to estimate their distribution. In the context of the
prediction of delay and the announcement of delays, the analysis becomes more difficult
because we have to consider the description of the system, the announcements given to each
waiting customer in the queue and subsequent customer reactions. This model, which
employs a hyperexponential distribution, is formulated to be relevant in practice.
The incorporation of delay information in modeling has significant value for system ease of
implementation in real call centers.
The remainder of this paper is organized as follows: In Section 2, we review related
literature. In Section 3, we conduct a statistical analysis of customer abandonments using
real call center data. Based on this analysis, we obtain customer behavior for this type of
system and demonstrate that customer patience can be modeled by the hyperexponential
distribution. In Section 4, we develop a framework for an M/M/s/r+H
2
queueing system for a
call center without delay information and introduce the state-dependent Markovian
approximation for the abandonments in the model. In Section 5, a model with delay
information is formulated and analyzed based on the real call center and the framework of
an M/M/s/r+H
2
queueing system. In Section 6, we present the simulation results to
1038
IMDS
117,6
To continue reading
Request your trial