Feedback control ideas for call center staffing

European Control Conference 2009 • Budapest, Hungary, August 23–26, 2009Call centers are nowadays a widespread solution to deal with customer support and as platform for different kind of business. Call center staffing is crucial to provide adequate service levels at acceptable costs. The task is usually accomplished using heuristics with the help of a human experts or with some static offline optimization based on operations research. Simulators based on queue theory are in some cases also used. The aim of the paper is to show that call center staffing can be posed as a feedback control problem with the advantage of getting a higher level of automation, and a wealth of results from control theory that can help to obtain the best possible staffing. In the paper the authors briefly describe the working procedures of call centers and how the staffing is usually made. They propose a feedback controller that it is used with a call center simulator. The results show that good call center staffing can be obtained even with a not very sophisticated controller

Fluid Approximation of a Call Center Model with Redials and Reconnects

In many call centers, callers may call multiple times. Some of the calls are re-attempts after abandonments (redials), and some are re-attempts after connected calls (reconnects). The combination of redials and reconnects has not been considered when making staffing decisions, while ignoring them will inevitably lead to under- or overestimation of call volumes, which results in improper and hence costly staffing decisions. Motivated by this, in this paper we study call centers where customers can abandon, and abandoned customers may redial, and when a customer finishes his conversation with an agent, he may reconnect. We use a fluid model to derive first order approximations for the number of customers in the redial and reconnect orbits in the heavy traffic. We show that the fluid limit of such a model is the unique solution to a system of three differential equations. Furthermore, we use the fluid limit to calculate the expected total arrival rate, which is then given as an input to the Erlang A model for the purpose of calculating service levels and abandonment rates. The performance of such a procedure is validated in the case of single intervals as well as multiple intervals with changing parameters

Establishing agent staffing levels in queueing systems with cross-trained and specialized agents

The determination of the right number of servers in a multi-server queueing system is one of the most important problems in applied queueing theory. The problem becomes more complex in a system that consists of both cross-trained and specialized servers. Such queueing systems are readily found in the call centres (also called contact centres) of financial institutions, telemarketing companies and other organizations that provide services to customers in multiple languages. They are also found in computer network systems where some servers are dedicated and others are flexible enough to handle various clients' requests. Over-staffing of these systems causes increased labour costs for the underutilized pool of agents on duty, while under-staffing results in reduced revenue from lost customers and an increase in queue times. The efficient design and analysis of these systems helps management in making better staffing decisions. This thesis aims to develop models for establishing agent staffing levels in organizations with cross-trained and specialized staff with a view to minimizing cost and maintaining a desirable customer satisfaction. The work investigates the effect of various traffic loads on the number of agents required and the cost. It also considers how using specialized agents, flexible agents and a combination of both categories of agents affects the system. It uses a contact centre that has agents with monolingual, bilingual and trilingual (English, French and Spanish) capabilities to do the study

Scheduling a multi class queue with many exponential servers: asymptotic optimality in heavy traffic

We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, linear or nonlinear, of appropriately normalized performance measures. As a special case, the cost per unit time can be a function of the number of customers waiting to be served in each class, the number actually being served, the abandonment rate, the delay experienced by customers, the number of idling servers, as well as certain combinations thereof. We study the system in an asymptotic heavy-traffic regime where the number of servers n and the offered load r are simultaneously scaled up and carefully balanced: n\approx r+\beta \sqrtr for some scalar \beta. This yields an operation that enjoys the benefits of both heavy traffic (high server utilization) and light traffic (high service levels.

Coping with Time-Varying Demand When Setting Staffing Requirements for a Service System

We review queueing-theory methods for setting staffing requirements in service systems where customer demand varies in a predictable pattern over the day. Analyzing these systems is not straightforward, because standard queueing theory focuses on the long-run steady-state 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-offered-load 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