In Defense of the Broader Application of Virtual Queues

The broader application of virtual queues is proposed. A review of the current state of queuing theory is presented as well as an acknowledgment of the deficiencies in the practicality of queuing theory. It is suggested that the queuing process can be improved by implementing the option of pursuing a virtual line. Specifically, the potential utility of introducing virtual queues is discussed in the context of the FastPass system, highlighting the major features of the method as well as examining the disadvantages of the service. The implementation of a FastPass-style queuing process outside of theme parks is presented as a combination of two common, everyday queuing principles, namely the first-come, first-served and reservation systems. A case study analyzing the impact of applying the proposed queuing system to a customer call center is investigated in which clients have the option to receive a call-back time in place of waiting for a representative. Finally, a review of two primary obstacles to the complete application of the queuing model is conducted

Proactive Customer Service: Operational Benefits and Economic Frictions

Problem Definition: We study a service setting where the provider has information about some customers' future service needs and may initiate service for such customers proactively, if they agree to be flexible with respect to the timing of service delivery. Academic / Practical Relevance: Information about future customer service needs is becoming increasingly available through remote monitoring systems and data analytics. However, the literature has not systematically examined proactive service as a tool that can be used to better match demand to service supply when customers are strategic. Methodology: We combine i) queueing theory, and in particular a diffusion approximation developed specifically for this problem that allows us to derive analytic approximations for customer waiting times, with ii) game theory, which captures customer incentives to adopt proactive service. Results: We show that proactive service can reduce customer waiting times, even if only a relatively small proportion of customers agree to be flexible, the information lead time is limited, and the system makes occasional errors in providing proactive service - in fact we show that the system's ability to tolerate errors increases with (nominal) utilization. Nevertheless, we show that these benefits may fail to materialize in equilibrium because of economic frictions: customers will under-adopt proactive service (due to free-riding) and over-join the system (due to negative congestion-based externalities). We also show that the service provider can incentivize optimal customer behavior through appropriate pricing. Managerial Implications: Our results suggest that proactive service may offer substantial operational benefits, but caution that it may fail to fulfill its potential due to customer self-interested behavior

Stability of Service under Time-of-Use Pricing

We consider "time-of-use" pricing as a technique for matching supply and demand of temporal resources with the goal of maximizing social welfare. Relevant examples include energy, computing resources on a cloud computing platform, and charging stations for electric vehicles, among many others. A client/job in this setting has a window of time during which he needs service, and a particular value for obtaining it. We assume a stochastic model for demand, where each job materializes with some probability via an independent Bernoulli trial. Given a per-time-unit pricing of resources, any realized job will first try to get served by the cheapest available resource in its window and, failing that, will try to find service at the next cheapest available resource, and so on. Thus, the natural stochastic fluctuations in demand have the potential to lead to cascading overload events. Our main result shows that setting prices so as to optimally handle the {\em expected} demand works well: with high probability, when the actual demand is instantiated, the system is stable and the expected value of the jobs served is very close to that of the optimal offline algorithm.Comment: To appear in STOC'1

Essays on Service Information, Retrials and Global Supply Chain Sourcing

In many service settings, customers have to join the queue without being fully aware of the parameters of the service provider (for e.g., customers at check-out counters may not know the true service rate prior to joining). In such blind queues\u27\u27, customers typically make their decisions based on the limited information about the service provider\u27s operational parameters from past experiences, reviews, etc. In the first essay, we analyze a firm serving customers who make decisions under arbitrary beliefs about the service parameters. We show, while revealing the service information to customers improves revenues under certain customer beliefs, it may however destroy consumer welfare or social welfare. When consumers can self-organize the timing of service visits, they may avoid long queues and choose to retry later. In the second essay, we study an observable queue in which consumers make rational join, balk and (costly) retry decisions. Retrial attempts could be costly due to factors such as transportation costs, retrial hassle and visit fees. We characterize the equilibrium under such retrial behavior, and study its welfare effects. With the additional option to retry, consumer welfare could worsen compared to the welfare in a system without retrials. Surprisingly, self-interested consumers retry too little (in equilibrium compared to the socially optimal policy) when the retrial cost is low, and retry too much when the retrial cost is high. We also explore the impact of myopic consumers who may not have the flexibility to retry. In the third essay, we propose a comprehensive model framework for global sourcing location decision process. For decades, off-shoring of manufacturing to China and other low-cost countries was a no-brainer decision for many U.S. companies. In recent years, however, this trend is being challenged by some companies to re-shore manufacturing back to the U.S., or to near-shore manufacturing to Mexico. Our model framework incorporates perspectives over the entire life cycle of a product, i.e., product design, manufacturing and delivering, and after-sale service support, and we use it to test the validity of various competing theories on global sourcing. We also provide numerical examples to support our findings from the model

Stochastic approximation of symmetric Nash equilibria in queueing games

We suggest a novel stochastic-approximation algorithm to compute a symmetric Nash-equilibrium strategy in a general queueing game with a finite action space. The algorithm involves a single simulation of the queueing process with dynamic updating of the strategy at regeneration times. Under mild assumptions on the utility function and on the regenerative structure of the queueing process, the algorithm converges to a symmetric equilibrium strategy almost surely. This yields a powerful tool that can be used to approximate equilibrium strategies in a broad range of strategic queueing models in which direct analysis is impracticable

The effect of workload constraints in mathematical programming models for production planning

Linear and mixed integer programming models for production planning incorporate a model of the manufacturing system that is necessarily deterministic. Although these eterministic models are the current-state-of-art, it should be recognized that they are used in an environment that is inherently stochastic. This fact should be kept in mind, both when making modeling choices and when setting the parameters of the model. In this paper we study the relation between workload constraints that reflect the finite capacity of the manufacturing system, and the use of planned lead times. It is a common practice in rolling schedule based production planning to limit the periodic output to the average production rate. If lead times are not modeled explicitly, this also implies a restricition on the periodic releases to the average production rate. We demonstrate that this common practice results in inefficient use of the production capacity and show that the use of planned lead times leads to a better trade-off between efficiency and reliability. We analyze a stylized model of a manufacturing system with a single exponential server and two queues in series: an admission queue and a work-in-progress (WIP) queue. The admission queue represents the pool of unreleased orders that is virtually present in the state variables of the planning model. Periodically, jobs from the admission queue are released to the WIP queue such that the number of jobs in WIP and in service does not exceed the workload constraint. We present a simple formula for the maximum utilization rate of such a system, characterize the stationary queue-length distribution by its generating function, and give the distribution of the sojourn time of a job. We use the results to compare various settings of the workload constraint and the planned lead time

The effect of workload constraints in mathematical programming models for production planning

Linear and mixed integer programming models for production planning incorporate a model of the manufacturing system that is necessarily deterministic. Although these eterministic models are the current-state-of-art, it should be recognized that they are used in an environment that is inherently stochastic. This fact should be kept in mind, both when making modeling choices and when setting the parameters of the model. In this paper we study the relation between workload constraints that reflect the finite capacity of the manufacturing system, and the use of planned lead times. It is a common practice in rolling schedule based production planning to limit the periodic output to the average production rate. If lead times are not modeled explicitly, this also implies a restricition on the periodic releases to the average production rate. We demonstrate that this common practice results in inefficient use of the production capacity and show that the use of planned lead times leads to a better trade-off between efficiency and reliability. We analyze a stylized model of a manufacturing system with a single exponential server and two queues in series: an admission queue and a work-in-progress (WIP) queue. The admission queue represents the pool of unreleased orders that is virtually present in the state variables of the planning model. Periodically, jobs from the admission queue are released to the WIP queue such that the number of jobs in WIP and in service does not exceed the workload constraint. We present a simple formula for the maximum utilization rate of such a system, characterize the stationary queue-length distribution by its generating function, and give the distribution of the sojourn time of a job. We use the results to compare various settings of the workload constraint and the planned lead time