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

Review on the Research for Separated Continuous Linear Programming: With Applications on Service Operations

We give a review on the research for a class of optimization model—separated continuous linear programming (SCLP). SCLP takes several similar forms and can be used to find the dynamic control of a multiclass fluid network. We review the duality theory and solution methods for it. We also present application examples of SCLP on service operations

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

Enabling flexibility through strategic management of complex engineering systems

”Flexibility is a highly desired attribute of many systems operating in changing or uncertain conditions. It is a common theme in complex systems to identify where flexibility is generated within a system and how to model the processes needed to maintain and sustain flexibility. The key research question that is addressed is: how do we create a new definition of workforce flexibility within a human-technology-artificial intelligence environment? Workforce flexibility is the management of organizational labor capacities and capabilities in operational environments using a broad and diffuse set of tools and approaches to mitigate system imbalances caused by uncertainties or changes. We establish a baseline reference for managers to use in choosing flexibility methods for specific applications and we determine the scope and effectiveness of these traditional flexibility methods. The unique contributions of this research are: a) a new definition of workforce flexibility for a human-technology work environment versus traditional definitions; b) using a system of systems (SoS) approach to create and sustain that flexibility; and c) applying a coordinating strategy for optimal workforce flexibility within the human- technology framework. This dissertation research fills the gap of how we can model flexibility using SoS engineering to show where flexibility emerges and what strategies a manager can use to manage flexibility within this technology construct”--Abstract, page iii

Распознавание точек привязки трехмерных объектов по стереоизображению в системах технического зрения

В процессе реконструкции формы трехмерного тела по стереоизображению возникает задача распознавания точек привязки на поверхности объекта. Эти точки используются в алгоритме триангуляции, когда формируется описание модели объекта. Один из способов уточнения координат точек привязки – анализ карты диспаритета для выделенного сегмента стереоизображения. Предлагаемый метод распознавания основан на использовании марковской сети для описания карты диспаритета, преобразовании графа этой сети путём анализа распределения яркостей пикселей изображения. Возможность выбора приоритетного направления смещения при обходе графа карты диспаритета обеспечивает эффективность работы алгоритма, основанного на описанном метод

Stationary waiting time distribution in G/M/n/r with random renovation policy

Consideration is given to G/M/n/r FCFS queue with random renovation policy. This policy implies that a customer upon service completion with probability q(l) removes l customers from the queue and then leaves the system. The choice of customers to be removed from the queue is done in a random fashion. Customer from the queue are served in FCFS order. For this system in a series of papers there were obtained stationary characteristics related to the number of customers in the system. Here we obtain several expressions for the stationary time-related characteristics and specifically dwell on the stationary waiting time distribution, which is obtained in terms of the transforms

Формирование профессиональных компетенций юриста

В статье рассматривается проблема формирования профессиональных компетенций юриста в рамках дисциплины «Профессиональные навыки юриста» в условиях игрового состязательного судебного процесса, различные формы организации учебной деятельности студентов, которые способствуют приобретению студентами новых знаний, закреплению коммуникативных умений и навыков публичных выступлений