Service Systems with Outbound Work and Blending

Overview. The vast majority of the queueing literature on service systems is concerned with systems that process inbound work only, typically assumed to arrive in accordance with some stochastic arrival process. In particular, most of the contact-center literature deals with inbound call centers. However, many service systems, and the majority of large contact centers, handle outbound work in addition to their inbound work, and that outbound work typically requires a substantial proportion of the total service capacity. We propose new stochastic models to investigate and analyze large service systems with many agents that process these two types of jobs. Our focus is on contact centers that handle inbound and outbound calls simultaneously, a process referred to as blending in the contact-center literature. We aim to prove new many-server heavy-tra�c limits in order to approximate those systems, and demonstrate the operational advantages that blending o�ers to large-scale service systems. Those advantages are due to the exibility in execution times of outbound calls, in contrast to the inbound calls, which have to be replied within a short period. In turn, this exibility reduces the variability in the system, making stochastic uctuations relatively small. The goal of the proposed research is to study combined sta�ng and control problems in the blending settings. If successful, we will prove that it is possible to provide excellent service levels, in terms of waiting times for inbound work and throughput rate of outbound work, while achieving signi�cant savings in sta�ng costs when compared to systems that handle both types of calls in separate service pools. Intellectual Merit. The proposed research aims to provide novel limit theorems to approximate complex queueing systems that process outbound work and employs blending. We will consider (i) multi-dimensional settings (i.e., stochastic networks); (ii) non-stationary settings with time-varying arrival rates; and (iii) systems with uncertain arrival rates. E�ective routing and scheduling policies are proposed so as to achieve optimality in the many-server heavy-tra�c limiting regime when costs of abandonment (or dropped outbound calls) and pro�ts for successful outbound calls are considered. A challenging aspect of the systems we consider is that they comprise of processes that evolve in di�erent orders of size, and therefore operate in di�erent time scales. Those smaller-order processes require a re�ned analysis, which is relatively di�cult to carry out in heavy-tra�c asymptotic regimes that provide a macroscopic approximation that is oblivious to small-order uctuations. Broader Impact. The proposed research will contribute to the academic literature on stochastic queueing models, and in particular, to the relatively small literature on queueing systems with outbound work and blending, and will rigorously demonstrate the operational advantages of blending. Since most contact centers in practice process the two types of calls, and technology makes blending simple to implement, our results could potentially have a large impact on contact-center operations. In addition, despite the fact that the focus of this research is on contact-center operations, the results and methods extend to other queueing systems that process inbound work, but can also \create" work whenever this is desired, e.g., large healthcare units that have scheduled patients. Finally, we intend to involve graduate students in the project, and to integrate some of its �ndings