Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments traditional operational models are of great value--and at the same time fundamentally limited--in their ability to characterize system performance.We review the state of research on telephone call centers. We begin with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations. We then outline important problems that have not been addressed and identify promising directions for future research.

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Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects

We study the performance of a statistical multiplexer whose inputs consist of a superposition of packetized voice sources and data. The performance analysis predicts voice packet delay distributions, which usually have a stringent requirement, as well as data packet delay distributions. The superposition is approximated by a correlated Markov modulated Poisson process (MMPP), which is chosen such that several of its statistical characteristics identically match those of the superposition. Matrix analytic methods are then used to evaluate system performance measures. In particular, we obtain moments of voice and data delay distributions and queue length distributions. We also obtain Laplace-Stieitjes transforms of the voice and data packet delay distributions, which are numerically inverted to evaluate tails of delay distributions. It is shown how the matrix analytic methodology can incorporate practical system considerations such as finite buffers and a class of overload control mechanisms discussed in the literature. Comparisons with simulation show the methods to be accurate. The numerical results for the tails of the voice packet delay distribution show the dramatic effect of traffic variability and correlations on performance.

A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance

In many stochastic models, particularly in queueing theory, Poisson arrivals both observe (see) a stochastic process and interact with it. In particular cases and/or under restrictive assumptions it has been shown that the fraction of arrivals that see the process in some state is equal to the fraction of time the process is in that state. In this paper, we present a proof of this result under one basic assumption: the process being observed cannot anticipate the future jumps of the Poisson process.

https://www.jstor.org/stable/pdfplus/170165.pdf

Poisson Arrivals See Time Averages

Queueing systems in which the server works on primary and secondary (vacation) customers arise in many computer, communication, production and other stochastic systems. These systems can frequently be modeled as queueing systems with vacations. In this survey, we give an overview of some general decomposition results and the methodology used to obtain these results for two vacation models. We also show how other related models can be solved in terms of the results for these basic models. We attempt to provide a methodological overview with the objective of illustrating how the seemingly diverse mix of problems is closely related in structure and can be understood in a common framework.

Queueing systems with vacations—a survey

(1987). Applied Probability and Queues. Journal of the Operational Research Society: Vol. 38, No. 11, pp. 1095-1096.

https://link.springer.com/content/pdf/10.1057%2Fjors.1987.184.pdf

Applied Probability and Queues

This paper considers tandem queues for which the order of performing service tasks can be changed, the service times being independent of this order. It determines the optimal order of service when either the service times of different tasks are nonoverlapping or, for two queues in tandem, the service time of one task is constant. For the optimal ordering, the waiting time of every customer is stochastically smaller than for any other.

The Optimal Order of Service in Tandem Queues

Conditions are determined under which a the sum of forecasts of sales in market segments is preferred to a forecast of the whole market and b a forecast of an individual market segment is preferred to a forecast obtained through proration of a forecast of the whole market. The comparisons in a and b are also applied to the problem of forecasting for several time periods into the future.

Aggregation and Proration in Forecasting

A large sample theory for birth and death queuing processes which are ergodic and metrically transitive is applied to make inferences about arrival and service rates. Likelihood ratio tests and maximum likelihood estimators are derived for simple models. Composite hypotheses, for example that the arrival rate does not vary with the number in the system, are considered. A numerical example illustrating these results, based on data generated by simulating a known model, is presented, which includes the testing of both true and false composite hypotheses.

Problems of Statistical Inference for Birth and Death Queuing Models

This paper considers tandem queues in which a given customer has equal service times at each station. The case M/M/1 → M/1 is considered in detail and the expected waiting time in the case where any given customer has independent service times at the two stations is compared with the expected waiting time in the case where any given customer has equal service times at the two stations. This comparison is based on theoretical results as well as on simulation. Tandem queues with blocking (zero queue capacity between the stations) are also considered and the waiting time and system capacity in the case where any given customer has independent service times are compared with the waiting time and system capacity in the case where any given customer has equal service times.

Ronald W. Wolff

Papers

Poisson Arrivals See Time Averages

The Optimal Order of Service in Tandem Queues

Aggregation and Proration in Forecasting

Problems of Statistical Inference for Birth and Death Queuing Models

A Comparison Between Tandem Queues with Dependent and Independent Service Times