We study systems with two classes of impatient customers who differ across the classes in their distribution of service times and patience times. The customers are served on a first-come, first served basis (FCFS) regardless of their class. Such systems are common in customer call centers, which often segment their arrivals into classes of callers whose requests differ in their complexity and criticality. We first consider an M /G/1 + M queue and then analyze the M /M /k + M case. Analyzing these systems using a queue length process proves intractable as it would require us to keep track of the class of each customer at each position in queue. Consequently, we introduce a virtual waiting time process where the service times of customers who will eventually abandon the system are not considered. We analyze this process to obtain performance measures such as the percentage of customers receiving service in each class, the expected waiting times of customers in each class, and the average number of customers waiting in queue. We use our characterization to perform a numerical analysis of the M /M /k + M system, and find several managerial implications of administering a FCFS system with multiple classes of impatient customers. Finally, we compare the performance a system based on data from a call center with the steady-state performance measures of a comparable M /M /k + M system. We find that the performance measures of the M /M /k + M system serve as good approximations of the system based on real data.Keywords Call centers · Impatient customers · Virtual queueing time process · M /M /k + M queue · M /G/1 + M queue PACS PACS code1 · PACS code2 · more Mathematics Subject Classification (2000) 60K25 · 68M20 · 90B22

Although call centers have recently invested in callback technology, the effects of this innovation on call center performance are not clearly understood. In this paper, we take a data-driven approach to quantify the operational impact of offering callbacks under a variety of callback policies. To achieve this goal, we formulate a structural model of the caller decision-making process under a callback option and impute their underlying preferences from data. Our model estimates shed light on caller preferences under a callback option. We find that callers experience three to six times less discomfort per unit of time while waiting for callbacks than while waiting in queue, suggesting that offering callbacks can increase service quality by channeling callers to an alternative service channel where they experience less discomfort while waiting. However, after controlling for expected waiting times, callers generally prefer waiting in a queue over accepting a callback and waiting offline. This suggests that managers of this call center may want to spend efforts in educating their customers on the benefits of the callback option. Using the callers’ imputed preferences, we are able to conduct counterfactual analyses of how various callback policies affect the performance of this call center. We find that in this call center, offering to hold the callers’ spot in line or to call back within a window (guaranteed timeframe) reduces average online waiting time (the average time callers wait on the phone) by up to 71% and improves service quality by decreasing callers’ average incurred waiting cost by up to 46%. Moreover, we find that offering callbacks as a demand postponement strategy during periods of temporary congestion reduces average online waiting time by up to 86%, increases service quality by up to 54%, and increases system throughput by up to 2.1%. This paper was accepted by Vishal Gaur, operations management.

To increase revenue or improve customer service, companies are increasingly personalizing their product or service offerings based on their customers' history of interactions. In this paper, we show how call centers can improve customer service by implementing personalized priority policies. Under personalized priority policies, managers use customer contact history to predict individual-level caller abandonment and redialing behavior and prioritize them based on these predictions to improve operational performance. We provide a framework for how companies can use individual-level customer history data to capture the idiosyncratic preferences and beliefs that impact caller abandonment and redialing behavior and quantify the improvements to operational performance of these policies by applying our framework using caller history data from a real-world call center. We achieve this by formulating a structural model that uses a Bayesian learning framework to capture how callers’ past waiting times and abandonment/redialing decisions affect their current abandonment and redialing behavior and use our data to impute the callers’ underlying primitives such as their rewards for service, waiting costs, and redialing costs. These primitives allow us to simulate caller behavior under a variety of personalized priority policies and hence, collect relevant operational performance measures. We find that, relative to the first-come, first-served policy, our proposed personalized priority policies have the potential to decrease average waiting times by up to 29% or increase system throughput by reducing the percentage of service requests lost to abandonment by up to 6.3%. This paper was accepted by Vishaul Gaur, operations management.

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