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Abstract

This dissertation studies the performance analysis and control of a queueing system when customers make their own routing decision (which queue to join) and abandonment decision (when to abandon the queue). In particular, there are two problems studied. ,The first part of the dissertation studies a multiclass queueing system with endogenous abandonments where the congestion affects customers' abandonment behavior and vice versa. This model captures this interaction by developing two closely related models: an abandonment model and a queueing model. In the abandonment model, customers take the virtual waiting time distribution as given. Class k customers receive a reward r_k from service and incur a cost c_k per period of waiting. Customers are forward looking and make wait or abandon decisions dynamically to maximize their expected discounted utilities. The queueing model takes the customers' abandonment time distribution as an input and studies the resulting virtual waiting time distribution. Because the multiclass queueing system is not amenable to exact analysis, we resort to an approximate analysis in the conventional heavy traffic limit (under the hazard rate scaling). Leveraging the so-called state-space collapse property, we provide a characterization of the system performance. Combining the results for the two models, we show that there exists a unique equilibrium in which the customers' abandonment time and the virtual waiting time for the various classes are consistent in the two models. Moreover, building on the closed-form results of Baccelli and Hebuterne [22] for the M/M/1+G queue, we prove the existence and uniqueness of the equilibrium in that special case via an exact analysis. Lastly, we provide computational schemes to calculate the equilibrium numerically for both the single- and multi-class queueing systems. ,The second part of the dissertation studies how to manage the callback option effectively to mitigate congestion due to temporary surges in the arrivals to a call center. The call arrival process can be an arbitrary point process, allowing uncertainty and temporary surges in the arrival rate, provided that the system is stable. However, particular attention will be paid to the Poisson process with the Cox-Ingresoll-Ross (CIR) process as its stochastic intensity both in our model development and numerical results because of its practical importance, although our theoretical results hold for any arbitrary point process. When a customer arrives, the call center manager reviews the system state and decides whether to keep him in the online queue or to offer the callback option. For each customer in the online queue, she incurs a waiting cost of h per time unit. Similarly, whenever she routes a customer to an offline queue (for a callback later), she incurs a one-time penalty of p.,Initially, we allow complete foresight policies that look into the entire future. We first study the case where all customers are willing to accept a callback offer. A simple lookahead policy that looks into the future for the next p/h time units is pathwise optimal among the complete foresight policies. Next, we consider the setting where some customers may reject the callback offer. We show that a modified lookahead policy that looks into the future arrivals and service completion times for the next p/h time units and uses the current number of customers in the system who previously rejected a callback offer (but does not look into the accept/reject decisions of future customers) is pathwise optimal among the complete foresight policies. Building on the insights gleaned from the optimal lookahead policies, we also propose a non-anticipating policy, referred to as the line policy, to decide when to offer the callback option. Lastly, we conduct a simulation study using a dataset from a US bank call center which shows that the line policy has excellent performance.

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