Call Center Experience Optimization: A Case for a Virtual Predictive Queue

The evolution of the call center into contact centers and the growth of their use in providing customer-facing service by many companies has brought considerable capabilities in maintaining customer relationships but it also has brought challenges in providing quality service when call volumes are high. Limited in their ability to provide service at all times to all customers, companies are forced to balance the costs associated with hiring more customer service representatives and the quality of service provided by a fewer number. A primary challenge when there are not enough customer service representatives to engage the volume of callers in a timely manner is the significant wait times that can be experienced by many customers. Normally, callers are handled in accordance with a first-come, first-served policy with exceptions being skill-based routing to those customer service representatives with specialized skills. A proposed call center infrastructure framework called a Virtual Predictive Queue (VPQ) can allow some customers to benefit from a shorter call queue wait time. This proposed system can be implemented within a call center’s Automatic Call Distribution (ACD) device associated with computer telephony integration (CTI) and theoretically will not violate a first-come, first served policy

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

Modelling and Analysis of Resource Management Schemes in Wireless Networks. Analytical Models and Performance Evaluation of Handoff Schemes and Resource Re-Allocation in Homogeneous and Heterogeneous Wireless Cellular Networks.

Over recent years, wireless communication systems have been experiencing a dramatic and continuous growth in the number of subscribers, thus placing extra demands on system capacity. At the same time, keeping Quality of Service (QoS) at an acceptable level is a critical concern and a challenge to the wireless network designer. In this sense, performance analysis must be the first step in designing or improving a network. Thus, powerful mathematical tools for analysing most of the performance metrics in the network are required. A good modelling and analysis of the wireless cellular networks will lead to a high level of QoS. In this thesis, different analytical models of various handoff schemes and resource re-allocation in homogeneous and heterogeneous wireless cellular networks are developed and investigated. The sustained increase in users and the request for advanced services are some of the key motivations for considering the designing of Hierarchical Cellular Networks (HCN). In this type of system, calls can be blocked in a microcell flow over to an overlay macrocell. Microcells in the HCN can be replaced by WLANs as this can provide high bandwidth and its users have limited mobility features. Efficient sharing of resources between wireless cellular networks and WLANs will improve the capacity as well as QoS metrics. This thesis first presents an analytical model for priority handoff mechanisms, where new calls and handoff calls are captured by two different traffic arrival processes, respectively. Using this analytical model, the optimised number of channels assigned to II handover calls, with the aim of minimising the drop probability under given network scenarios, has been investigated. Also, an analytical model of a network containing two cells has been developed to measure the different performance parameters for each of the cells in the network, as well as altogether as one network system. Secondly, a new solution is proposed to manage the bandwidth and re-allocate it in a proper way to maintain the QoS for all types of calls. Thirdly, performance models for microcells and macrocells in hierarchical cellular networks have been developed by using a combination of different handoff schemes. Finally, the microcell in HCN is replaced by WLANs and a prioritised vertical handoff scheme in an integrated UMTS/WLAN network has been developed. Simulation experiments have been conducted to validate the accuracy of these analytical models. The models have then been used to investigate the performance of the networks under different scenarios

Call centres with balking and abandonment: from queueing to queueing network models

The research on call centres has attracted many researchers from different disciplines recently. In this thesis, we focus on call centre modelling, analysis and design. In terms of modelling, traditionally call centres have been modelled as single-node queueing systems. Based on the Semiopen Queueing Network (SOQN) model proposed by Srinivasan et al. [42], we propose and study SOQN models with balking and abandonment (both exponential and general patience time distributions). In addition, we study the corresponding single-node queueing systems and obtain new results. For each model, we study the queue length distribution, waiting time distribution and the related performance measures. To facilitate the computation, we express the performance measures in terms of special functions. In terms of call centre design, we develop a design algorithm to determine the minimal number of CSRs (S) and trunk lines (N) to satisfy a given set of service level constraints. The explicit expressions for performance measures obtained allow for theoretical analysis of the performance measures. For example we prove monotonicity and convexity properties of performance measures for the M/M/S/N and M/M/S/N + M models. We also study the comparison of different patience time distributions for the M/M/S/N+G model. We provide numerical examples for each model and discuss numerical results such as monotonicity properties of performance measures. In particular, we illustrate the efficacy of our design algorithm for various models including patient, balking and abandonment models. The impact of model parameters on the design of call centres is also discussed based on the numerical examples. The results are computed using Matlab, where special functions are available

Stability Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia

Performance analysis of cellular networks.

Thesis (Ph.D.)-University of Natal, Durban, 2000.Performance analysis in cellular networks is the determination of customer orientated grade-of-service parameters, such as call blocking and dropping probabilities, using the methods of stochastic theory. This stochastic theory analysis is built on certain assumptions regarding the arrival and service processes of user-offered calls in a network. In the past, cellular networks were analysed using the classical assumptions, Poisson call arrivals and negative exponential channel holding times, borrowed from earlier fixed network analysis. However, cellular networks are markedly different from fixed networks, in that, they afford the user a unique opportunity: the ability to communicate while on the move. User mobility and various other cellular network characteristics, such as customer-billing, cell· layout and hand·off mechanisms, generally invalidate the use of Poisson arrivals and negative exponential holding times. Recent measurements on live networks substantiate this view. Consequently, over the past few years, there has been a noticeable shift towards using more generalised arrival and service distributions in the performance analysis of cellular networks. However, two shortcomings with the resulting models are that they suffer from state space explosion and / or they represent hand off traffic as a state dependent mean arrival rate (thus ignoring the higher moments of the hand-off arrival process). This thesis's contribution to cellular network analysis is a moment-based approach that avoids full state space description but ensures that the hand-off arrival process is modelled beyond the first moment. The thesis considers a performance analysis model that is based on Poisson new call arrivals, generalised hand-off call arrivals and a variety of channel holding times. The thesis shows that the performance analysis of a cellular network may be loosely decomposed into three parts, a generic cell traffic characterising model, a generic cell traffic blocking model and a quality of service evaluation model. The cell traffic characterising model is employed to determine the mean and variance of hand-off traffic offered by a cell to its neighbour. The cell traffic-blocking model is used to detennine the blocking experienced by the various traffic streams offered to each cell. The quality of service evaluation part is essentially afued-point iteration of the cell traffic characterising and cell traffic blocking parts to determine customer orientated grade-of-service parameters such as blocking and dropping probabilities. The thesis also presents detailed mathematical models for user mobility modelling. Finally, the thesis provides extensive results to validate the proposed analysis and to illustrate the accuracy of the proposed analysis when compared to existing methods