CALL CENTERS (CENTRES) - Faculty of Industrial Engineering and ...

systems is not straightforward, because standard queueing theory focuses on the long-run steadystate
behavior of stationary models. We show how to adapt stationary queueing models for use
in nonstationary environments so that time-dependent performance is captured and staffing
requirements can be set. Relatively little modification of straightforward stationary analysis applies
in systems where service times are short and the targeted quality of service is high. When
service times are moderate and the targeted quality of service is still high, time-lag refinements
can improve traditional stationary independent period-by-period and peak-hour approximations.
Time-varying infinite-server models help develop refinements, because closed-form expressions
exist for their time-dependent behavior. More difficult cases with very long service times and
other complicated features, such as end-of-day effects, can often be treated by a modified-offeredload
approximation, which is based on an associated infinite-server model. Numerical algorithms
and deterministic fluid models are useful when the system is overloaded for an extensive period of
time. Our discussion focuses on telephone call centers, but applications to police patrol, banking
and hospital emergency rooms are also mentioned.
Keywords: Staffing, Call centers, Time-varying demand, Queues with time-varying arrival rate,
Nonstationary queueing models, Police patrol, Banking, Hospital emergency rooms
162. Khudyakov, Polina. Designing a call center with an IVR (Interactive Voice Response). M.Sc.
thesis, Technion—Israel Institute of Technology, Haifa, Israel, 2006.
Abstract. A call center is a popular term for a service operation that handles telephone calls of
customers. A call center typically consists of agents that handle incoming calls, telephone trunk
lines, an Interactive Voice Response (IVR) unit, and a switch that routes calls to agents.
The subject of this thesis is a Markovian model for a call center with an IVR. We calculate
operational performance measures, such as the probability for a busy signal and average wait for
an agent. The calculations of these measures are cumbersome and they lack insight. We thus
approximate the measures in an asymptotic regime known as QED (Quality Efficiency Regime),
which is suitable for moderate to large call centers. The approximations are both insightful and
easy to calculate (for up to 1000’s of agents). They yield, as special cases, known approximations
for the Erlang-B, Erlang-C and M/M/S/N queue.
Finally, we develop an algorithm for optimal staffing and trunk level. The algorithm is then
used to analyze ways for reducing the operational costs of a call center, to understand the effect
of a call center’s size on its service level, and to investigate the effect of changes in system parameters
on performance—for example, increasing IVR functionality (which would reasonably
imply fewer but longer agent calls).
163. Mandelbaum, A. and S. Zeltyn. Staffing many-server queues with impatient customers: Constraint
satisfaction in call centers. Working paper, Technion—Israel Institute of Technology,
Haifa, Israel, 2006. Available at
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Abstract. Motivated by call center practice, we study asymptotically optimal staffing of manyserver
queues with abandonment. A call center is modelled as an M/M/n+G queue, which is
characterized by Poisson arrivals, exponential service times, n servers and Generally distributed
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