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.

The impact of reneging in processor sharing queues

We investigate an overloaded processor sharing queue with renewal arrivals and generally distributed service times. Impatient customers may abandon the queue, or renege, before completing service. The random time representing a customer’s patience has a general distribution and may be dependent on his initial service time requirement. We propose a scaling procedure that gives rise to a fluid model, with nontrivial yet tractable steady state behavior. This fluid model captures many essential features of the underlying stochastic model, and we use it to analyze the impact of impatience in processor sharing queues. We show that this impact can be substantial compared with FCFS, and we propose a simple admission control policy to overcome these negative impacts

Numerical Analysis of Finite Source Markov Retrial System with Non-Reliable Server, Collision, and Impatient Customers

A retrial queuing system with a single server is investigated in this paper. The server is subject to random breakdowns. The number of customers is finite and collision may take place. A collision occurs when a customer arrives to the busy server. In case of a collision both customers involved in the collision are sent back to the orbit. From the orbit the customers retry their requests after a random waiting time. The server can be down due to a failure. During the failed period the arriving customers are sent to the orbit, as well. The novelty of this analysis is the impatient behaviour of the customers. A customer waiting in the orbit may leave it after a random waiting time. The requests of these customers will not be served. All the random variables included in the model construction are assumed to be exponentially distributed and independent from each other. The impatient property makes the model more complex, so the derivation of a direct algorithmic solution (which was provided for the non-impatient case) is difficult. For numerical calculations the MOSEL-2 tool can be used. This tool solves the Kolmogorov system equations, and from the resulting steady-state probabilities various system characteristics and performance measures can be calculated, i.e. mean response time, mean waiting time in the orbit, utilization of the server, probability of the unserved impatient requests. Principally the effect of the impatient property is investigated in these results, which are presented graphically, as well

On the M/M/c/N Call Center Queue Modeling and Analysis

The M/M/c/c model is the most widely applied queueing model in the mathematical analysis of call centers. The M/M/c/c model is also referred to as the Erlang Loss System. The Erlang loss model does not take into consideration system attributes such as blocking and busy signals, balking and reneging, retrials and returns. Although, the Erlang loss model is analytically tractable, it is not easy to obtain insight from its results. The need to develop a more accurate call center model has necessitated the modification of the Erlang loss model. In this research, we model and analyze a call center using M/M/c/N the model. The goal of this paper is to extend existing results and prove new results with regards to the monotonicity and limiting behaviour of the M/M/c/N model with respect to the system capacity N

Controlling excessive waiting times in emergency departments: an extension of the ISA algorithm.

In an emergency department (ED), the demand for service is not constant over time. This cannot be accounted for by means of waiting lists or appointment systems, so capacity decisions are the most important tool to influence patient waiting times. Additional complexities result from the relatively small system size that characterizes an ED (i.e. a small number of physicians or nurses) and the presence of customer impatience. Assuming a single-stage multiserver M(t)/G/s(t) + G queueing system with general abandonment and service times and time-varying demand for service, we suggest a method inspired by the simulation-based Iterative Staffing Algorithm (ISA) proposed by Feldman and others (2008) as a method to set staffing levels throughout the day. The main advantage of our extension is that it enables the use of performance measures based on the probability of experiencing an excessive waiting time, instead of the common focus on delay probability as a performance metric.Emergency department; Personnel planning; Time-varying arrival rate;