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The paper analyzes the mathematical models of call centers that take into account repeated calls and the specific features and key aspects of modeling call centers as retrial queues. Queuing systems M/ M/ c/0/ L/ H j, M/ M/ c/0/// E2, and M/ M/ c/0/ L// E2 are considered as models of call centers. Numerical results for the performance indices of these systems are given. [ABSTRACT FROM AUTHOR]

Algorithms for approximate evaluation of the characteristics of microcellular wireless networks with queues of new and handover calls are developed. It is assumed that unlike calls may leave the queue if their waiting time is greater than some threshold value. Results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

The term “mass service theory” introduced by A.Ya. Khinchin implies that the probability theory is applied to the studies of diverse problems of servicing which often are related to formation of queues. The problems of design and calculation of the communication networks and their elements are pivotal here. In the shop language of the communication community this domain of knowledge is called the teletraffic theory. The first publication of A.K. Erlang whose centenary is celebrated this year was devoted namely to this theory. It is not occasional that this jubilee is observed. Today the mankind has the worldwide communication network offering fabulous possibilities in information transmission, storage, and processing. Creation of such a network would not be possible without wide use of the teletraffic theory. [ABSTRACT FROM AUTHOR]

This paper models a call center as a Markovian queue with multiple servers, where customer balking, impatience, and retrials are modeled explicitly. The resulting queue is analyzed both in a stationary and non-stationary setting. For the stationary setting a fluid approximation is proposed, which overcomes the computational burden of the continuous time markov chain analysis, and which is shown to provide an accurate representation of the system for large call centers with high system load. An insensitivity property of the retrial rate to key system parameters is established. The fluid approximation is shown to work equally well for the non-stationary setting with time varying arrival rates. Using the fluid approximation, the paper explores the retrial phenomenon for a real call center. The model is used to estimate the real arrival rates based on demand data where retrials cannot be distinguished from first time calls. This is a common problem encountered in call centers. Through numerical examples, it is shown that disregarding the retrial phenomenon in call centers can lead to huge distortions in subsequent forecasting and staffing analysis. [ABSTRACT FROM AUTHOR]

Our research is motivated by a phenomenon that has been observed in telephone call center data: a clear linear relation between the probability to abandon and average waiting time. Such a relation is theoretically justifiable when customers' patience is memoryless, but it lacks an explanation in general. We thus analyze its robustness within the framework of the M/M/n+G queue, which gives rise to further theory and empirically-driven experiments. In the theoretical part of the paper, we establish order relations for performance measures of the M/M/n+G queues, and some light-traffic results. In particular, we prove that, with λ, u, n and average patience time fixed, deterministic patience minimizes the probability to abandon and maximizes the average wait in queue. In the experimental part, we describe the behavior of M/M/n+G performance measures for different patience distributions. The findings are then related to our theoretical results and some observed real-data phenomena. In particular, clear non-linear relations (convex, concave and mixed) emerge between the probability to abandon and average wait. However, when restricted over low to moderate abandonment rates, approximate linearity prevails, as observed in practice. [ABSTRACT FROM AUTHOR]

This paper describes a decomposition algorithm to estimate the performance of a call center with two types of customers and two server categories. In this system specialized servers can process only one customer type, while flexible servers handle both types. The algorithm divides the system’s state space into regions, and simple approximate models find the conditional system performance within each region. While the procedure described here is tailored for a system with a priority queue discipline and two customer classes, it can be adapted for systems with FCFS queue disciplines and for systems with more than two customer types. Performance measures generated by the procedure are sufficiently accurate for many service system design decisions, such as setting telephone call center staffing levels and long-term capacity planning. The procedure is also extremely fast, and its computational requirements do not grow with system congestion. Numerical tests demonstrate that its running time is significantly lower than traditional numerical methods for generating approximations. As an example of its use, we employ the procedure to demonstrate the benefits of server flexibility in a particular telephone call center. [ABSTRACT FROM AUTHOR]

Many call centers provide service for customers of different classes with differently qualified groups of agents. Since call arrivals and call handling times are random in inbound call centers, we investigate queueing models for their performance analysis. This paper describes a Markov queueing model with two customer classes and three groups of specialized or flexible agents. The mean call handling time may depend on the respective customer class as well as on the agent group serving this call. The customers are assumed to be impatient. We consider skills-based routing with priority-based rules and derive both steady-state probabilities and performance measures. We present some numerical experiments and show the impact of different mean processing times. The influence of the allocation of the agents into the three groups is analyzed for different levels of patience. [ABSTRACT FROM AUTHOR]

Temporary overload situations in queues can be approximated by fluid queues. We strengthen earlier results on the comparison of multi-server tandem systems with their fluid limits. At the same time we give conditions under which economies of scale hold. We apply the results to call centers. [ABSTRACT FROM AUTHOR]

The classical Erlang and Engset loss models have been used extensively in the traffic engineering of traditional telephone exchanges. More recently, these models have been generalized to the so-called loss networks, which provide models for resource-sharing in multi-service telecommunication networks. In this paper, we introduce a new generalized class of models, queueing-loss networks, which captures both queueing and loss aspects of a system. The queueing-loss network model is a natural extension of queueing networks and loss networks that have the product-form solution. We discuss applications of the model and analyze a particular example of a simple queueing-loss network. [ABSTRACT FROM AUTHOR]

Points out that the primary objective of this special issue is to present recent operations research-related research contributions to Call Center Management and to examine promising directions of future research. Decomposition algorithm to estimate performance measures for a call center; Impact of retrials of impatient customers on call center planning; Impact of the patience distribution on delay and abandonment.