Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective

A call center is a service network in which agents provide telephone-based services. Customers that seek these services are delayed in tele-queues. This paper summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer abandonment behavior and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. We then survey how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations. Key Words: call centers, queueing theory, lognormal distribution, inhomogeneous Poisson process, censored data, human patience, prediction of Poisson rates, Khintchine-Pollaczek formula, service times, arrival rate, abandonment rate, multiserver queues.

A Simulation of the ECSS Help Desk with the Erlang A Model

During steady states, the Level 1 help desk might expect about 500 to 600 calls per month. That is about 0.39 to 0.46 calls per user per month, which represents the workload once ECSS is established and most of the users have already received training for the system. The optimal level for this workload is about 12 agents to operate the entire 24 hour period. At this level, the Level 1 help desk would minimize the amount of customers that renege from the system to about 15 to 22 percent and still maintain acceptable utilization percentages of about 52% to 59% while keeping the average wait time under a minute. The Level 2 help desk will experience similar environments like the Level 1 help desk. The major differences are that the Level 2 help desk would see lower call volumes since only about 40% of Level 1 calls are passed on the Level 2; and that the Level 2 help desk will have a longer average service rate. The simulation shows that the optimal staffing level is about 12. The simulation shows average wait times about 1 to 2.6 minutes, utilization from 47% to 60%, and 12% to 33% of customers that would renege

Parameter Tolerance in Capacity Planning Models

In capacity planning for a service operation, analytical models based on queueing theory allow the user to quickly estimate the capacity required and to easily experiment with different system designs or configurations, for a given set of input parameters. An input parameter of the model could be inaccurate or may not be known beyond a good guess. In order to determine if the analysis results (and hence the system design) are robust to parameter estimation errors, sensitivity analysis can be performed. We study an alternative approach that involves specifying a tolerance range of a system performance measure and calculating a feasible region of the uncertain parameters for which the performance measure will be within the tolerance range. We illustrate this approach using basic exponential queueing models as well as a model of an order fulfillment operation in a distribution center

Bayesian control of the number of servers in a GI/M/c queueing system

In this paper we consider the problem of designing a GI/M/c queueing system. Given arrival and service data, our objective is to choose the optimal number of servers so as to minimize an expected cost function which depends on quantities, such as the number of customers in the queue. A semiparametric approach based on Erlang mixture distributions is used to model the general interarrival time distribution. Given the sample data, Bayesian Markov Chain Monte Carlo methods are used to estimate the system parameters and the predictive distributions of the usual performance measures. We can then use these estimates to minimize the steady-state expected total cost rate as a function of the control parameter c. We provide a numerical example based on real data obtained from a bank in Madrid

Modelling and Optimisation of GSM and UMTS Radio Access Networks

The size and complexity of mobile communication networks have increased in the last years making network management a very complicated task. GSM/EDGE Radio Access Network (GERAN) systems are in a mature state now. Thus, non-optimal performance does not come from typical network start-up problems, but, more likely, from the mismatching between traffic, network or propagation models used for network planning, and their real counterparts. Such differences cause network congestion problems both in signalling and data channels. With the aim of maximising the financial benefits on their mature networks, operators do not solve anymore congestion problems by adding new radio resources, as they usually did. Alternatively, two main strategies can be adopted, a) a better assignment of radio resources through a re-planning approach, and/or b) the automatic configuration (optimisation, in a wide sense) of network parameters. Both techniques aim to adapt the network to the actual traffic and propagation conditions. Moreover, a new heterogenous scenario, where several services and Radio Access Technologies (RATs) coexist in the same area, is now common, causing new unbalanced traffic scenarios and congestion problems. In this thesis, several optimisation and modelling methods are proposed to solve congestion problems in data and signalling channels for single- and multi-RAT scenarios

Holistic assessment of call centre performance

In modern call centres 60–70% of the operational costs come in the form of the human agents who take the calls. Ensuring that the call centre operates at lowest cost and maximum efficiency involves a trade‐off of the cost of agents against lost revenue and increased customer dissatisfaction due to lost calls. Modelling the performance characteristics of a call centre in terms of the agent queue alone misses key performance influencers, specifically the interaction between channel availability at the media gateway and the time a call is queued. A blocking probability at the media gateway, as low as 0.45%, has a significant impact on the degree of queuing observed and therefore the cost and performance of the call centre. Our analysis also shows how abandonment impacts queuing delay. However, the call centre manager has less control over this than the level of contention at the media gateway. Our commercial assessment provides an evaluation of the balance between abandonment and contention, and shows that the difference in cost between the best and worst strategy is £130K per annum, however this must be balanced against a possible additional £2.98 m exposure in lost calls if abandonment alone is used

A tool for model-checking Markov chains

Markov chains are widely used in the context of the performance and reliability modeling of various systems. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both discrete [34, 10] and continuous time settings [7, 12]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker EÎMC2, where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore, we report on successful applications of the tool to some examples, highlighting lessons learned during the development and application of EÎMC2