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

Staffing and Scheduling to Differentiate Service in Many-Server Service Systems

This dissertation contributes to the study of a queueing system with a single pool of multiple homogeneous servers to which multiple classes of customers arrive in independent streams. The objective is to devise appropriate staffing and scheduling policies to achieve specified class-dependent service levels expressed in terms of tail probability of delays. Here staffing and scheduling are concerned with specifying a time-varying number of servers and assigning newly idle servers to a waiting customer from one of K classes, respectively. For this purpose, we propose new staffing-and-scheduling solutions under the critically-loaded and overloaded regimes. In both cases, the proposed solutions are both time dependent (coping with the time variability in the arrival pattern) and state dependent (capturing the stochastic variability in service and arrival times). We prove heavy-traffic limit theorems to substantiate the effectiveness of our proposed staffing and scheduling policies. We also conduct computer simulation experiments to provide engineering confirmation and practical insight

Many server queueing models with heterogeneous servers and parameter uncertainty with customer contact centre applications

In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the Halfin-Whitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates are i.i.d. random variables. We derive a diffusion approximation using a novel method. The diffusion has a random drift, and hence depending on the realisations of service rates, the system can be in Quality Driven (QD), Efficiency Driven (ED) or Quality-Efficiency-Driven (QED) regime. When the system is under QD or QED regime, the abandonments are negligible in the fluid limit, but when it is under ED regime, the probability of abandonment will converge to a non-zero value. We then analyse the optimal staffing levels to balance holding costs with staffing costs combining these three regimes. We also analyse how the variance of service rates influence abandonment rate. Next, we focus on the state space collapse (SSC) phenomenon. We prove that under some assumptions, the system process will collapse to a lower dimensional process without losing essential information. We first formulate a general method to prove SSC results inside pools for heavy traffic systems using the hydrodynamic limit idea. Then we work on the SSC in multi-class queueing networks under the Halfin-Whitt heavy traffic when service rates are i.i.d. random variables within pools. For such systems, exact analysis provides limited insight on the general properties. Alternatively, asymptotic analysis by diffusion approximation proves to be effective. Further, limit theorems, which state the diffusively scaled system process weakly converges to a diffusion process, are usually the central part in such asymptotic analysis. The SSC result is key to proving such a limit. We conclude by giving examples on how SSC is applied to the analysis of systems

Performance Analysis of a Multi-Class, Preemptive Priority Call Center with Time-Varying Arrivals

We model a call center as a an $M_{t}/M/n$, preemptive-resume priority queue with time-varying arrival rates and two priority classes of customers. The low priority customers have a dynamic priority where they become high priority if their waiting time exceeds a given service-level time. The performance of the call center is estimated by the mean number in the system and mean virtual waiting time for both classes of customers. We discuss some analytical methods of measuring the performance of call center models, such as Laplace transforms. We also propose a more-robust fluid approximations method to model a call center. The accuracy of the performance measures from the fluid approximation method depend on an asymptotic scheme developed by Halfin and Whitt. Here, the offered load and number of servers are scaled by the same factor, which maintains a constant system utilization. The fluid approximations provide estimates for the mean number in system and mean virtual waiting time. The approximations are solutions of a system of nonlinear differential equations. We analyze the accuracy of the fluid approximations through a comparison with a discrete-event simulation of a call center. We show that for a large enough scale factor, the estimates of the performance measures derived from the fluid approximations method are relatively close to those from the discrete-event simulation. Finally, we demonstrate that these approximations remain relatively close to the simulation estimates as the system state varies between under-loaded and over-loaded status

Multimedia

The nowadays ubiquitous and effortless digital data capture and processing capabilities offered by the majority of devices, lead to an unprecedented penetration of multimedia content in our everyday life. To make the most of this phenomenon, the rapidly increasing volume and usage of digitised content requires constant re-evaluation and adaptation of multimedia methodologies, in order to meet the relentless change of requirements from both the user and system perspectives. Advances in Multimedia provides readers with an overview of the ever-growing field of multimedia by bringing together various research studies and surveys from different subfields that point out such important aspects. Some of the main topics that this book deals with include: multimedia management in peer-to-peer structures & wireless networks, security characteristics in multimedia, semantic gap bridging for multimedia content and novel multimedia applications

Future of Wireless Data Communication

This thesis develops four scenarios, illustrating the future of wireless data communication

Methods in Modeling Wildlife Disease from Model Selection to Parameterization With Multi-Scale Data

The effects of emerging wildlife diseases are global and profound, resulting in loss of human life, economic and agricultural impacts, declines in wildlife populations, and ecological disturbance. The spread of wildlife diseases can be viewed as the result of two simultaneous processes: spatial spread of wildlife populations and disease spread through a population. For many diseases these processes happen at different timescales, which is reflected in available data. These data come in two flavors: high-frequency, high-resolution telemetry data (e.g. GPS collar) and low-frequency, low-resolution presence-absence disease data. The multi-scale nature of these data makes analysis of such systems challenging. Mathematical models serve as valuable tools for forecasting disease spread. To produce meaningful predictions a model must include appropriate mechanisms for both transmission and animal movement and be parameterized with data. Herein, a framework is developed for modeling wildlife disease spread. Model competition is used to select and parameterize appropriate transmission mechanisms given time-series prevalence data. For animal movement a parameterization method for a mechanistic, population-scale wildlife movement model is derived for use with individual telemetry data. Throughout, special attention is payed to computational complexity. Homogenization and other asymptotic methods are used to maintain feasibility of parameterization. In tandem, these two methods determine and parameterize the movement and transmission mechanisms that play a role in wildlife disease spread, taking into account the types of available data and inherent separation of scales between the two processes

Mean-Field Methods in Large Stochastic Networks

Analysis of large-scale communication networks (e.g. ad hoc wireless networks, cloud computing systems, server networks etc.) is of great practical interest. The massive size of such networks frequently makes direct analysis intractable. Asymptotic approximations using fluid and diffusion scaling limits provide useful methods for approaching such problems. In this dissertation, I study such approximations in two different settings. In the first, I consider a rate control problem for a weakly interacting particle system. I show that by considering an associated diffusion control problem, one can construct controls which are asymptotically optimal for the finite particle system control problem. In the second, I consider a class of load balancing mechanisms in a large cloud-storage network that uses a Maximum Distance Separable coding scheme to store a large set of files. Fluid and diffusion approximations are developed for this system and the long-time behavior of the network is studied.Doctor of Philosoph