Journal ArticleDOI
Hazard Rate Scaling of the Abandonment Distribution for the GI/M/n + GI Queue in Heavy Traffic
Josh Reed,Tolga Tezcan +1 more
TLDR
This work obtains a heavy traffic limit for the GI/M/n + GI queue, which includes the entire patience time distribution, and shows that for various performance measures, its approximations tend to outperform those commonly used in practice.Abstract:
We obtain a heavy traffic limit for the GI/M/n + GI queue, which includes the entire patience time distribution. Our main approach is to scale the hazard rate function of the patience time distribution in such a way that our resulting diffusion approximation contains the entire hazard rate function. We then show through numerical studies that for various performance measures, our approximations tend to outperform those commonly used in practice. The robustness of our results is also demonstrated by applying them to solving constraint satisfaction problems arising in the context of telephone call centers.read more
Citations
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Book ChapterDOI
Convergence of probability measures
TL;DR: Weakconvergence methods in metric spaces were studied in this article, with applications sufficient to show their power and utility, and the results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables.
Journal ArticleDOI
Asymptotic analysis of queueing systems with reneging: A survey of results for FIFO, single class models
TL;DR: A focus is on finding situations in which simple performance measure approximations can be developed in the conventional heavy traffic and Halfin–Whitt limit regimes and the overloaded regime in which there is a single server as well as the overloaded many-server regime.
Journal ArticleDOI
Joint Panel Sizing and Appointment Scheduling in Outpatient Care
Christos Zacharias,Mor Armony +1 more
TL;DR: This work addresses the joint problem of determining the panel size of a medical practice and the number of offered appointment slots per day, so that patients do not face long backlogs and the clinic is not overcrowded.
Journal ArticleDOI
Data-stories about (im)patient customers in tele-queues
Avishai Mandelbaum,Sergey Zeltyn +1 more
TL;DR: In this paper, abandonment of customers, while queueing for service, is the operational manifestation of customer patience, perhaps impatience, or (im)patience for short, and is the focus of the present paper.
Journal ArticleDOI
A study of the effect of the loss function on Bayes Estimate, posterior risk and hazard function for Lindley distribution
TL;DR: In this article, mathematical properties of Lindley distribution via Bayesian approach are derived under different loss functions, such as: Bayes Estimators, posterior risks and failure rate function for simulation scheme.
References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Book
Markov Processes: Characterization and Convergence
TL;DR: In this paper, the authors present a flowchart of generator and Markov Processes, and show that the flowchart can be viewed as a branching process of a generator.
Book ChapterDOI
Convergence of probability measures
TL;DR: Weakconvergence methods in metric spaces were studied in this article, with applications sufficient to show their power and utility, and the results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables.
Journal ArticleDOI
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
TL;DR: This work begins with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations, which identifies important problems that have not been addressed and identifies promising directions for future research.
Journal ArticleDOI
Heavy-Traffic Limits for Queues with Many Exponential Servers
Shlomo Halfin,Ward Whitt +1 more
TL;DR: In this article, two different kinds of heavy-traffic limit theorems have been proved for s-server queues: the first involves a sequence of queueing systems having a fixed number of servers with an associated sequence of traffic intensities that converges to the critical value of one from below.