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This work considers a many-server queueing system in which impatient customers with i.i.d., generally distributed service times and i.i.d., generally distributed patience times enter service in the order of arrival and abandon the queue if the time before possible entry into service exceeds the patience time. The dynamics of the system is represented in… (More)

A many-server queueing system is considered in which customers arrive according to a renewal process, and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables. Customers enter service in the order of arrival and are assumed to abandon the queue if the waiting time in queue… (More)

We consider the Skorokhod problem in a time-varying interval. We prove existence and uniqueness for the solution. We also express the solution in terms of an explicit formula. Moving boundaries may generate singularities when they touch. We establish two sets of sufficient conditions on the moving boundaries that guarantee that the variation of the local… (More)

For a general class of stochastic differential equations with reflection that admit a Markov weak solution and satisfy a certain L continuity condition, p > 1, it is shown that the associated reflected diffusion can be decomposed as the sum of a local martingale and a continuous, adapted process of zero p-variation. In particular, when p = 2, this implies… (More)

Given a domain G, a reflection vector field d(·) on ∂G, the boundary of G, and drift and dispersion coefficients b(·) and σ(·), let L be the usual second-order elliptic operator associated with b(·) and σ(·). Under mild assumptions on the coefficients and reflection vector field, it is shown that when the associated submartingale problem is well posed, a… (More)

- Weining Kang, Guodong Pang
- 2017

Four different fluid model formulations have been recently developed for Gt/GI/N+ GI queues, including a two-parameter fluid model in Whitt (2006) by tracking elapsed service and patience times of each customer, a measure-valued fluid model in Kang and Ramanan (2010) and its extension in Zuñiga (2014) by tracking elapsed service and patience times of each… (More)

- Weining Kang
- Oper. Res. Lett.
- 2014

In this paper, we establish a new (direct) proof for existence and uniqueness of the fluid model for Gt/GI/N + GI queues proposed recently by Kang and Ramanan under mild conditions on the arrival, service and patience time distributions. In particular, the existence of the fluid model is established directly from the fluidmodel itself. Thenmain technique… (More)

- Weining Kang
- Queueing Syst.
- 2015

- Weining Kang, Hongyuan Lu, Guodong Pang
- SIGMETRICS Performance Evaluation Review
- 2013

We consider many-server queues with delayed feedback where the service (patience) times of new customers and feedback customers are differentiated, and new and feedback customers are served under the first-come-first-serve (FCFS) discipline in the service station. The arrival process, service, patience and delay times are all general and mutually… (More)

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