Queueing Models for Service Systems with Dependencies

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One of the main drivers of complexity in a service system is the dependence between different random variables describing the system. For example, the queue lengths at different time points and the waiting times of different items (jobs, customers) in queue are strongly dependent. To reduce dependence-related complexities, it is customary to assume that the system primitives (such as the arrival processes, service times, patience of different customers, etc.) are independent from one another as well as from the systems dynamics and state. However, in many settings, dependencies across different primitive processes, or between a primitive process and the state of the system, should clearly hold. For example, it stands to reason, and has been shown empirically in call centers, hospitals and restaurants, that the service requirement of a customer may depend on that customer's patience or on the time that customer spends waiting in queue. A natural question to ask is then: To what extent do these types of dependencies impact the performance, control and optimal design of a service system? In this thesis, I aim to answer this question for fundamental queueing models.I start by considering two relevant dependence structures in large service systems: In the first, customers' patience depends on their individual service requirement; in the second, the service requirement of each customer depends on that customer's delay in queue. Since either dependence structure renders exact analysis intractable, I employ a fluid approach to approximate the mean-field behavior of the stochastic queueing systems, which illustrates a first-order impact of both dependencies on the system's performance. Using a stationary analysis, I demonstrate a fundamental difference between the two dependencies in their stationary behavior for the corresponding fluid models. Despite this difference, surprisingly, a unified model can be developed to describe the two dependencies simultaneously, which is further used to characterize the relation between the two dependencies using the concept of equivalence class. Such relation yields important insights to the empirical identification of the dependence, which is otherwise very difficult given that any dataset of service systems is censored due to customer abandonment.To manifest the role of pricing in efficiently exploiting the underlying system structure, I consider another type of dependence in service systems in which a customer's value for service depends on that customer's service requirement. In a queueing-game framework, I analyze the impact of such dependence on the service provider's revenue performance. I show that a positive dependence between the service value and the service requirement may hurt the provider's revenue if customers are charged the same price. In response to the positive dependence, I propose a novel service-based pricing scheme which prices a customer's service based on that customer's realized service time. I demonstrate that the positive dependence could be exploited under service-based pricing to generate more revenue compared to the case of no dependence."]

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  • 09/30/2019
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