@article{sun_liu_li_2024, title={Mail back or in-store dropoff? Optimal design of product-exchange policies in omnichannel retailing systems}, volume={125}, ISSN={["1873-5274"]}, DOI={10.1016/j.omega.2023.103024}, abstractNote={Online retailing has been booming over the past several years as people grow increasingly comfortable with it and accustomed to its ease and speed. A major drawback of online retailing is the lack of consumer-product interaction before a purchase is finalized, which often leads to consumer dissatisfaction due to mismatched expectation of the received product. In response, retailers usually promise that online orders may be returned or exchanged free of extra charges, which can be processed either online (e.g., by mail) or onsite i.e., in-store dropoff. In this work, we study the implications of both online and onsite exchange policies in the setting of a queueing model that offers omnichannel services. Taking into account customers’ behavioral responses to these policies, we aim to inform the retailer of the one that generates a higher system revenue. Our results reveal that the online exchange policy is a double-edged sword: On the one hand, it helps eliminate the inconvenience cost for exchange customers to revisit the store; on the other hand, it can trigger more feedback orders and render a higher system congestion level, which in turn, deters future customers from placing orders. Specifically, we discover that online exchange becomes an inferior policy relative to in-store exchange when the market size is large.}, journal={OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE}, author={Sun, Ke and Liu, Yunan and Li, Xiang}, year={2024}, month={Jun} }
 @article{chen_liu_hong_2023, title={An Online Learning Approach to Dynamic Pricing and Capacity Sizing in Service Systems}, ISSN={["0030-364X"]}, DOI={10.1287/opre.2020.612}, abstractNote={ Online Learning in Queueing Systems }, journal={OPERATIONS RESEARCH}, author={Chen, Xinyun and Liu, Yunan and Hong, Guiyu}, year={2023}, month={Jun} }
 @article{chen_liu_hong_2023, title={An Online Learning Approach to Dynamic Pricing and Capacity Sizing in Service Systems}, ISSN={["0030-364X"]}, DOI={10.1287/opre.2020.0612}, abstractNote={ Online Learning in Queueing Systems }, journal={OPERATIONS RESEARCH}, author={Chen, Xinyun and Liu, Yunan and Hong, Guiyu}, year={2023}, month={Jun} }
 @article{sun_liu_li_2023, title={Energy harvesting cognitive radio networks with strategic users: A two-class queueing model with retrials}, volume={199}, ISSN={["1873-703X"]}, DOI={10.1016/j.comcom.2022.12.017}, abstractNote={Motivated by the rapid growth in wireless communication systems, we develop a single-server queueing model with service retrials for the cognitive radio network (CRN). A key appeal of CRN is its flexible allocation scheme of limited spectrum for two user groups: (1) the licensed user, hereby referred to as primary user (PU), and (2) unlicensed users, referred to as secondary users (SUs). The PU take priority over SUs: when a PU arrives and observes a busy server currently occupied by an SU, it will take over the server by preempting the SU out of service. SUs are strategic and delay sensitive: they decide immediately upon arrivals on whether to join the CRN or to balk, based on the anticipated expected utility (service reward minus delay cost). In case the server is unavailable, SUs temporarily join an orbit queue where they wait for future accesses to service. Another realistic feature of our model is that, after successfully serving a user (PU or SU), the server becomes unavailable and undergoes an energy harvesting phase of a random time. We characterize the equilibrium system performance in the following three steps: First, we obtain the equilibrium joining behavior for utility-maximizing SUs; second, we derive the optimal joining strategy from the perspective of a social planner; and finally, we enforce that users adopt the socially optimal strategy by imposing an admission fee. We also investigate the impact of the energy harvesting time on users?? equilibrium strategies and report numerical experiments to provide qualitative and quantitative insights of our results.}, journal={COMPUTER COMMUNICATIONS}, author={Sun, Ke and Liu, Yunan and Li, Kaili}, year={2023}, month={Feb}, pages={98–112} }
 @article{xie_lu_wang_su_liu_xu_2023, title={Improving Workers' Musculoskeletal Health During Human-Robot Collaboration Through Reinforcement Learning}, volume={5}, ISSN={["1547-8181"]}, url={https://doi.org/10.1177/00187208231177574}, DOI={10.1177/00187208231177574}, abstractNote={Objective This study aims to improve workers’ postures and thus reduce the risk of musculoskeletal disorders in human-robot collaboration by developing a novel model-free reinforcement learning method. }, journal={HUMAN FACTORS}, author={Xie, Ziyang and Lu, Lu and Wang, Hanwen and Su, Bingyi and Liu, Yunan and Xu, Xu}, year={2023}, month={May} }
 @article{sun_liu_2023, title={Optimal interventions of infectious disease}, ISSN={["1520-6750"]}, DOI={10.1002/nav.22114}, abstractNote={Abstract}, journal={NAVAL RESEARCH LOGISTICS}, author={Sun, Xu and Liu, Yunan}, year={2023}, month={Apr} }
 @article{nambiar_mayorga_liu_2023, title={Routing and staffing in emergency departments: A multiclass queueing model with workload dependent service times}, volume={13}, ISSN={["2472-5587"]}, DOI={10.1080/24725579.2022.2100522}, abstractNote={Abstract Efficient patient flow through an emergency department is a critical factor that contributes to a hospital’s performance, which influences overall patient health outcomes. In this work, we model a multiclass multiserver queueing system where patients of varying acuity receive care from one of several wards, each ward is attended by several nurses who work as a team. Supported by empirical evidence that a patient’s time-in-ward is a function of the nurse-patient ratio in that ward, we incorporate state-dependent service times into our model. Our objective is to reduce patient time in system and to control nurse workload by jointly optimizing patient routing and nurse allocation decisions. Due to the computational challenges in formulating and solving the queueing model representation, we study a corresponding deterministic fluid model which serves as a first-order approximation of the multiclass queueing model. Next, we formulate and solve an optimization model using the first-order control equations and input the results into a discrete-event simulation to estimate performance measures, such as patient length-of-stay and ward workload. Finally, we present a case study using retrospective data from a real hospital which highlights the importance of accounting for nurse workload and service behavior in developing routing and staffing policies.}, number={1}, journal={IISE TRANSACTIONS ON HEALTHCARE SYSTEMS ENGINEERING}, author={Nambiar, Siddhartha and Mayorga, Maria E. and Liu, Yunan}, year={2023}, month={Jan}, pages={46–61} }
 @article{sun_liu_li_2022, title={Make waiting not to seem like waiting: Capacity management of waiting-area entertainment}, volume={50}, ISSN={["1872-7468"]}, DOI={10.1016/j.orl.2022.10.015}, abstractNote={To operationalize the psychological principle that “occupied time feels shorter than unoccupied time”, it is common for service providers to offer entertainment options in the waiting areas. Typical examples that put in practice this mechanism include amusement parks, car dealers, airports, hospitals, restaurants, etc. In this paper, we study a queueing system where the server provides entertainment services to waiting customers. Assuming customers are strategic and delay-sensitive, we formulate a game-theoretical model and study customers' equilibrium behavior in response to this mechanism. Because offering waiting-area entertainment incurs extra operational costs, we discuss whether and when this option will benefit the service provider and obtain the optimal entertainment capacity that maximizes the system's profit. Our analysis reveals that this option is appealing if and only if the market size is intermediate and that the optimal capacity of the entertainment is a unimodal function in the market size. Our insights continue to remain valid when the service fee becomes endogenous.}, number={6}, journal={OPERATIONS RESEARCH LETTERS}, author={Sun, Ke and Liu, Yunan and Li, Xiang}, year={2022}, month={Nov}, pages={745–752} }
 @article{wang_liu_fang_2022, title={Pay to activate service in vacation queues}, ISSN={["1937-5956"]}, DOI={10.1111/poms.13705}, abstractNote={ We study a vacation queueing model where an arriving customer, upon finding the server to be on vacation, is offered an opportunity to pay a fee to instantaneously end the server's vacation, which is referred to as pay‐to‐activate‐service (PTAS). If no one utilizes PTAS, the service will automatically resume when the system's workload reaches a critical level. We investigate customers' equilibrium strategies: (i) joining or balking and (ii) if joining, accepting PTAS or rejecting PTAS, in response to such a mechanism; we show that customers' equilibrium strategies exhibit both avoid‐the‐crowd (ATC) and follow‐the‐crowd (FTC) types of behavior. Our results indicate that the adoption of PTAS is efficient in improving the system performance (e.g., revenue and throughput) when the demand volume is intermediate. We also discover that, upon selecting the appropriate queue‐length information disclosure policy, the service provider has to trade off between collecting a higher revenue through PTAS and improving the system throughput, because revealing the queue‐length information will impact the aforementioned two performance metrics in opposing directions. Finally, we compare our new setting to other common mechanisms including regular vacation queues and pay‐for‐priority queues. }, journal={PRODUCTION AND OPERATIONS MANAGEMENT}, author={Wang, Zhongbin and Liu, Yunan and Fang, Lei}, year={2022}, month={Mar} }
 @article{li_liu_wan_huang_2021, title={A discrete-event simulation model for the Bitcoin blockchain network with strategic miners and mining pool managers}, volume={134}, ISSN={["1873-765X"]}, DOI={10.1016/j.cor.2021.105365}, abstractNote={As the first and most famous cryptocurrency-based blockchain technology, Bitcoin has attracted tremendous attention from both academic and industrial communities in the past decade. A Bitcoin network is comprised of two interactive parties: individual miners and mining pool managers, each of which strives to maximize its own utility. In particular, individual miners choose which mining pool to join and decide on how much mining power to commit under limited constraints on the mining budget and mining power capacity; managers of mining pools determine how to allocate the mining reward and how to adjust the membership fee. In this work we investigate the miners’ and mining pool managers’ decisions in repeated Bitcoin mining competitions by building a Monte-Carlo discrete-event simulation model. Our simulation model (i) captures the behavior of these two parties and how their decisions affect each other, and (ii) characterizes the system-level dynamics of the blockchain in terms of the mining difficulty level and total mining power. In addition, we study the sensitivity of system performance metrics with respect to various control parameters. Our analysis may provide useful guidelines to mining activity participants in the Bitcoin network.}, journal={COMPUTERS & OPERATIONS RESEARCH}, author={Li, Kejun and Liu, Yunan and Wan, Hong and Huang, Yining}, year={2021}, month={Oct} }
 @article{li_zhang_liu_2021, title={A little bit flexibility on headway distribution is enough: Data-driven optimization of subway regenerative energy}, volume={554}, ISSN={["1872-6291"]}, DOI={10.1016/j.ins.2020.12.030}, abstractNote={As an emerging energy-efficient management approach, the essential idea of subway regenerative energy optimization is to maximize the absorption of energy generated from train deceleration by adjusting train schedules. In the extant literature, performance evaluation and optimization rely on synthetic data (e.g., computer simulations) and train energy-efficient operation (EEO) strategy. However, when compared to real automatic train operation (ATO) data, the above-mentioned method exhibits significant errors. In this work, we develop a new optimization method driven by real ATO data for maximizing subway regenerative energy based on the following three steps: first, we provide a high-frequency ATO data-driven method for simulating the amount of regenerative energy absorption; second, we propose a concept of uniformity to measure the homogeneous degree of headway distribution; third, we formulate a headway optimization model to maximize the regenerative energy absorption under uniformity constraint. To handle the high complexity of the ATO data-driven objective function (e.g., non-monotonicity, non-convexity, multi-modality), we propose an improved genetic algorithm with multiple crossover and mutation operators to search for near-optimal solutions, in which an adaptive operator selection mechanism with reduction process on ATO data is considered for speeding up the regenerative energy simulation and optimization. The effectiveness of the proposed method is confirmed by using the real ATO data of Beijing Subway Changping line. Our numerical study reveals that, benchmarked with the uniform headway distribution (the policy that is presently in use), our proposed approach achieves a relative improvement of 7.75% at off-peak hours and 42.44% at peak hours for the regenerative energy absorption; and we show that such a significant performance improvement is obtained by allowing a small level of scheduling flexibility (less than 6% relaxation on uniformity level).}, journal={INFORMATION SCIENCES}, author={Li, Xiang and Zhang, Bowen and Liu, Yunan}, year={2021}, month={Apr}, pages={276–296} }
 @article{yang_huang_liu_2021, title={Mind your own customers and ignore the others: Asymptotic optimality of a local policy in multi-class queueing systems with customer feedback}, ISSN={["2472-5862"]}, DOI={10.1080/24725854.2021.1952358}, abstractNote={Abstract This work contributes to the investigation of optimal routing and scheduling policies in multi-class multi-server queueing systems with customer feedback. We propose a new policy, dubbed local policy that requires access to only local queue information. Our new local policy specifies how an idle server chooses the next customer by using the queue length information of not all queues, but only those this server is eligible to serve. To gain useful insights and mathematical tractability, we consider a simple W model with customer feedback, and we establish limit theorems to show that our local policy is asymptotically optimal among all policies that may use the global system information, with the objective of minimizing the cumulative queueing costs measured by convex functions of the queue lengths. Numerical experiments provide convincing engineering confirmations of the effectiveness of our local policy for both W model and a more general non-W model.}, journal={IISE TRANSACTIONS}, author={Yang, Jiankui and Huang, Junfei and Liu, Yunan}, year={2021}, month={Jul} }
 @article{liu_sun_hovey_2021, title={Scheduling to Differentiate Service in a Multiclass Service System}, ISSN={["0030-364X"]}, DOI={10.1287/opre.2020.2075}, abstractNote={ Dynamic Scheduling to Differentiate Delay-Based Service Levels in Multiclass Service Systems }, journal={OPERATIONS RESEARCH}, author={Liu, Yunan and Sun, Xu and Hovey, Kyle}, year={2021}, month={Mar} }
 @article{sun_liu_2021, title={Staffing many-server queues with autoregressive inputs}, volume={68}, ISSN={["1520-6750"]}, DOI={10.1002/nav.21960}, abstractNote={Abstract}, number={3}, journal={NAVAL RESEARCH LOGISTICS}, author={Sun, Xu and Liu, Yunan}, year={2021}, month={Apr}, pages={312–326} }
 @article{li_liu_wan_zhang_2020, title={CAPTURING MINER AND MINING POOL DECISIONS IN A BITCOIN BLOCKCHAIN NETWORK: A TWO-LAYER SIMULATION MODEL}, ISSN={["0891-7736"]}, DOI={10.1109/WSC48552.2020.9383980}, abstractNote={Motivated by the growing interests in Bitcoin blockchain technology, we build a Monte-Carlo simulation model to study the miners’ and mining pool managers’ decisions in the Bitcoin blockchain network. Our simulation model aims to capture the dynamics of participants of these two different parties and how their decisions collectively affect the system dynamics. Given the limited amount of monetary budget and mining power capacity, individual miners decide on which mining pools to join and determine how much hashing power to invest. Mining pool managers need to determine how to appropriately allocate the mining reward and how to adjust the membership fee. In addition to the aforementioned miner and pool behavior, we also characterize the system-level dynamics of the blockchain in terms of mining difficulty level and total hashing power.}, journal={2020 WINTER SIMULATION CONFERENCE (WSC)}, author={Li, Kejun and Liu, Yunan and Wan, Hong and Zhang, Ling}, year={2020}, pages={3152–3163} }
 @article{wang_wang_liu_2020, title={Reducing Delay in Retrial Queues by Simultaneously Differentiating Service and Retrial Rates}, volume={68}, ISSN={["0030-364X"]}, DOI={10.1287/opre.2019.1933}, abstractNote={ Customer retrials commonly occur in many service systems, such as healthcare, call centers, mobile networks, computer systems, and inventory systems. However, because of their complex nature, retrial queues are often more difficult to analyze than queues without retrials. In “Reducing Delay in Retrial Queues by Simultaneously Differentiating Service and Retrial Rates”, J. Wang, Z. Wang, and Y. Liu develop a service grade differentiation policy for queueing models with customer retrials. They show that the average waiting time can be reduced through strategically allocating the rates of service and retrial times without needing additional service capacity. Counter to the intuition that higher service variability usually yields a larger delay, the authors show that the benefits of this simultaneous service-and-retrial differentiation (SSRD) policy outweigh the impact of the increased service variability. To validate the effectiveness of the new SSRD policy, the authors provide (i) conditions under which SSRD is more beneficial, (ii) closed-form expressions of the optimal policy, (iii) asymptotic reduction of customer delays when the system is in heavy traffic, and (iv) insightful observations/discussions and numerical results. }, number={6}, journal={OPERATIONS RESEARCH}, author={Wang, Jinting and Wang, Zhongbin and Liu, Yunan}, year={2020}, pages={1648–1667} }
 @article{cao_he_huang_liu_2020, title={To Pool or Not to Pool: Queueing Design for Large-Scale Service Systems}, ISSN={["0030-364X"]}, DOI={10.1287/opre.2019.1976}, abstractNote={ In large-scale service systems, it is a common practice to organize customers with similar service requirements into a single queue served by a group of servers. This pooled queue structure is deemed highly efficient because the servers’ idleness will be minimized. In “To Pool or Not to Pool: Queueing Design for Large-Scale Service Systems,” Cao, He, Huang, and Liu demonstrate that the dedicated queue structure, under which each server has her own queue, could be more advantageous for improving the system’s service level. Moreover, the servers’ additional idleness induced by the dedicated queue structure will be negligible when the system scale is large. By solving a staffing problem, this study also intends to help service system designers answer the following question: To achieve a specified service-level objective in a more efficient manner, should the servers have a common queue or separate queues? }, journal={OPERATIONS RESEARCH}, author={Cao, Ping and He, Shuangchi and Huang, Junfei and Liu, Yunan}, year={2020}, month={Dec} }
 @article{liu_kuhl_liu_wilson_2019, title={Modeling and Simulation of Nonstationary Non-Poisson Arrival Processes}, volume={31}, ISSN={["1526-5528"]}, DOI={10.1287/ijoc.2018.0828}, abstractNote={ We develop CIATA, a combined inversion-and-thinning approach for modeling a nonstationary non-Poisson process (NNPP), where the target arrival process is described by a given rate function and its associated mean-value function together with a given asymptotic variance-to-mean (dispersion) ratio. CIATA is based on the following: (i) a piecewise-constant majorizing rate function that closely approximates the given rate function from above; (ii) the associated piecewise-linear majorizing mean-value function; and (iii) an equilibrium renewal process (ERP) whose noninitial interrenewal times have mean 1 and variance equal to the given dispersion ratio. Transforming the ERP by the inverse of the majorizing mean-value function yields a majorizing NNPP whose arrival epochs are then thinned to deliver an NNPP having the specified properties. CIATA-Ph is a simulation algorithm that implements this approach based on an ERP whose noninitial interrenewal times have a phase-type distribution. Supporting theorems establish that CIATA-Ph can generate an NNPP having the desired mean-value function and asymptotic dispersion ratio. Extensive simulation experiments substantiated the effectiveness of CIATA-Ph with various rate functions and dispersion ratios. In all cases, we found approximate convergence of the dispersion ratio to its asymptotic value beyond a relatively short warm-up period. }, number={2}, journal={INFORMS JOURNAL ON COMPUTING}, author={Liu, Ran and Kuhl, Michael E. and Liu, Yunan and Wilson, James R.}, year={2019}, pages={347–366} }
 @article{guo_liu_pei_2018, title={Functional law of the iterated logarithm for multi-server queues with batch arrivals and customer feedback}, volume={264}, ISSN={["1572-9338"]}, DOI={10.1007/s10479-017-2529-9}, number={1-2}, journal={ANNALS OF OPERATIONS RESEARCH}, author={Guo, Yongjiang and Liu, Yunan and Pei, Renhu}, year={2018}, month={May}, pages={157–191} }
 @article{aras_chen_liu_2018, title={Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment}, volume={89}, DOI={10.1007/s11134-018-9575-0}, number={1-2}, journal={Queueing Systems}, author={Aras, A. K. and Chen, X. Y. and Liu, Y. A.}, year={2018}, pages={81–125} }
 @article{liu_2018, title={Staffing to Stabilize the Tail Probability of Delay in Service Systems with Time-Varying Demand}, volume={66}, ISSN={["0030-364X"]}, DOI={10.1287/opre.2017.1678}, abstractNote={ Analytic formulas are developed to set the time-dependent number of servers to stabilize the tail probability of customer waiting times for the Gt/GI/st + GI queueing model, which has a nonstationary non-Poisson arrival process (the Gt), nonexponential service times (the first GI), and allows customer abandonment according to a nonexponential patience distribution (the +GI). Specifically, for any delay target w > 0 and probability target α ∈ (0, 1), we determine appropriate staffing levels (the st) so that the time-varying probability that the waiting time exceeds a maximum acceptable value w is stabilized at α at all times. In addition, effective approximating formulas are provided for other important performance functions such as the probabilities of delay and abandonment, and the means of delay and queue length. Many-server heavy-traffic limit theorems in the efficiency-driven regime are developed to show that (i) the proposed staffing function achieves the goal asymptotically as the scale increases, and (ii) the proposed approximating formulas for other performance measures are asymptotically accurate as the scale increases. Extensive simulations show that both the staffing functions and the performance approximations are effective, even for smaller systems having an average of three servers. }, number={2}, journal={OPERATIONS RESEARCH}, author={Liu, Yunan}, year={2018}, pages={514–534} }
 @article{kim_hodgson_king_liu_kay_2017, title={Allocation heuristics for high-altitude long- endurance UAV image intelligence platforms}, volume={22}, number={3}, journal={Military Operations Research}, author={Kim, G. and Hodgson, T. J. and King, R. E. and Liu, Y. N. and Kay, M. G.}, year={2017}, pages={5–19} }
 @article{liu_whitt_2017, title={Stabilizing performance in a service system with time-varying arrivals and customer feedback}, volume={256}, ISSN={["1872-6860"]}, DOI={10.1016/j.ejor.2016.07.018}, abstractNote={Analytical offered-load and modified-offered-load (MOL) approximations are developed to determine staffing levels that stabilize performance at designated targets in a non-Markovian many-server queueing model with time-varying arrival rates, customer abandonment from queue and random feedback with additional feedback delay in an infinite-server or finite-server queue. To provide a flexible model that can be readily fit to system data, the model has Bernoulli routing, where the feedback probabilities, service-time, patience-time and feedback-delay distributions all are general and may depend on the visit number. Simulation experiments confirm that the new MOL approximations are effective. A many-server heavy-traffic FWLLN shows that the performance targets are achieved asymptotically as the scale increases.}, number={2}, journal={EUROPEAN JOURNAL OF OPERATIONAL RESEARCH}, author={Liu, Yunan and Whitt, Ward}, year={2017}, month={Jan}, pages={473–486} }
 @article{liu_whitt_yu_2016, title={Approximations for Heavily Loaded G/GI/n plus GI Queues}, volume={63}, ISSN={["1520-6750"]}, DOI={10.1002/nav.21688}, abstractNote={Abstract}, number={3}, journal={NAVAL RESEARCH LOGISTICS}, author={Liu, Yunan and Whitt, Ward and Yu, Yao}, year={2016}, month={Apr}, pages={187–217} }
 @article{he_liu_whitt_2016, title={STAFFING A SERVICE SYSTEM WITH NON-POISSON NON-STATIONARY ARRIVALS}, volume={30}, ISSN={["1469-8951"]}, DOI={10.1017/s026996481600019x}, abstractNote={Motivated by non-Poisson stochastic variability found in service system arrival data, we extend established service system staffing algorithms using the square-root staffing formula to allow for non-Poisson arrival processes. We develop a general model of the non-Poisson non-stationary arrival process that includes as a special case the non-stationary Cox process (a modification of a Poisson process in which the rate itself is a non-stationary stochastic process), which has been advocated in the literature. We characterize the impact of the non-Poisson stochastic variability upon the staffing through the heavy-traffic limit of the peakedness (ratio of the variance to the mean in an associated stationary infinite-server queueing model), which depends on the arrival process through its central limit theorem behavior. We provide simple formulas to quantify the performance impact of the non-Poisson arrivals upon the staffing decisions, in order to achieve the desired service level. We conduct simulation experiments with non-stationary Markov-modulated Poisson arrival processes with sinusoidal arrival rate functions to demonstrate that the staffing algorithm is effective in stabilizing the time-varying probability of delay at designated targets.}, number={4}, journal={PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES}, author={He, Beixiang and Liu, Yunan and Whitt, Ward}, year={2016}, month={Oct}, pages={593–621} }
 @article{guo_liu_2015, title={A law of iterated logarithm for multiclass queues with preemptive priority service discipline}, volume={79}, ISSN={["1572-9443"]}, DOI={10.1007/s11134-014-9419-5}, number={3-4}, journal={QUEUEING SYSTEMS}, author={Guo, Yongjiang and Liu, Yunan}, year={2015}, month={Apr}, pages={251–291} }
 @article{liu_whitt_2014, title={Algorithms for Time-Varying Networks of Many-Server Fluid Queues}, volume={26}, ISSN={["1526-5528"]}, DOI={10.1287/ijoc.1120.0547}, abstractNote={ Motivated by large-scale service systems with network structure, we introduced in a previous paper a time-varying open network of many-server fluid queues with customer abandonment from each queue and time-varying proportional routing among the queues, and showed how performance functions can be determined. The deterministic fluid model serves as an approximation for the corresponding non-Markovian stochastic network of many-server queues with Markovian routing, experiencing periods of overloading at the queues. In this paper we develop a new algorithm for the previous model and generalize the model to include non-exponential service-time distributions. In this paper we report results of implementing the algorithms and studying their computational complexity. We also conduct simulation experiments to confirm that the algorithms are effective in computing the performance functions and that these performance functions provide useful approximations for the corresponding stochastic models. }, number={1}, journal={INFORMS JOURNAL ON COMPUTING}, author={Liu, Yunan and Whitt, Ward}, year={2014}, pages={59–73} }
 @article{liu_whitt_2014, title={MANY-SERVER HEAVY-TRAFFIC LIMIT FOR QUEUES WITH TIME-VARYING PARAMETERS}, volume={24}, ISSN={["1050-5164"]}, DOI={10.1214/13-aap927}, abstractNote={+GI queueing model, having time-varying arrival rate and staffing, ageneral arrival process satisfying a FCLT, exponential service timesand customer abandonment according to a general probability dis-tribution. The FCLT provides theoretical support for the approxi-mating deterministic fluid model the authors analyzed in a previouspaper and a refined Gaussian process approximation, using varianceformulas given here. The model is assumed to alternate between un-derloaded and overloaded intervals, with critical loading only at theisolated switching points. The proof is based on a recursive analy-sis of the system over these successive intervals, drawing heavily onprevious results for infinite-server models. The FCLT requires carefultreatment of the initial conditions for each interval.}, number={1}, journal={ANNALS OF APPLIED PROBABILITY}, author={Liu, Yunan and Whitt, Ward}, year={2014}, month={Feb}, pages={378–421} }
 @article{liu_whitt_2014, title={STABILIZING PERFORMANCE IN NETWORKS OF QUEUES WITH TIME-VARYING ARRIVAL RATES}, volume={28}, ISSN={["1469-8951"]}, DOI={10.1017/s0269964814000084}, abstractNote={This paper investigates extensions to feed-forward queueing networks of an algorithm to set staffing levels (the number of servers) to stabilize performance % at Quality of Service (QoS) targets in anMt/GI/st+GImulti-server queue with a time-varying arrival rate. The model has a non-homogeneous Poisson process (NHPP), customer abandonment, and non-exponential service and patience distributions. For a single queue, simulation experiments showed that the algorithm successfully stabilizes abandonment probabilities and expected delays over a wide range of Quality-of-Service (QoS) targets. A limit theorem showed that stable performance at fixed QoS targets is achieved asymptotically as the scale increases (by letting the arrival rate grow while holding the service and patience distributions fixed). Here we extend that limit theorem to a feed-forward queueing network. However, these fixed QoS targets provide low QoS as the scale increases. Hence, these limits primarily support the algorithm with a low QoS target. For a high QoS target, effectiveness depends on the NHPP property, but the departure process never is exactly an NHPP. Thus, we investigate when a departure process can be regarded as approximately an NHPP. We show that index of dispersion for counts is effective for determining when a departure process is approximately an NHPP in this setting. In the important common case when all queues have high QoS targets, we show that both: (i) the departure process is approximately an NHPP from this perspective and (ii) the algorithm is effective.}, number={4}, journal={PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES}, author={Liu, Yunan and Whitt, Ward}, year={2014}, month={Oct}, pages={419–449} }
 @article{liu_whitt_2012, title={A many-server fluid limit for the G(t)/GI/s(t) + GI queueing model experiencing periods of overloading}, volume={40}, ISSN={["1872-7468"]}, DOI={10.1016/j.orl.2012.05.010}, abstractNote={A many-server heavy-traffic functional weak law of large numbers is established for the Gt/GI/st+GI queueing model, which has customer abandonment (the +GI), time-varying arrival rate and staffing (the subscript t) and non-exponential service and patience distributions (the two GI’s). This limit provides support for a previously proposed deterministic fluid approximation, and extends a previously established limit for the special case of exponential service times.}, number={5}, journal={OPERATIONS RESEARCH LETTERS}, author={Liu, Yunan and Whitt, Ward}, year={2012}, month={Sep}, pages={307–312} }
 @article{liu_whitt_2012, title={Stabilizing Customer Abandonment in Many-Server Queues with Time-Varying Arrivals}, volume={60}, ISSN={["0030-364X"]}, DOI={10.1287/opre.1120.1104}, abstractNote={ An algorithm is developed to determine time-dependent staffing levels to stabilize the time-dependent abandonment probabilities and expected delays at positive target values in the Mt/GI/st + GI many-server queueing model, which has a nonhomogeneous Poisson arrival process (the Mt), has general service times (the first GI), and allows customer abandonment according to a general patience distribution (the +GI). New offered-load and modified-offered-load approximations involving infinite-server models are developed for that purpose. Simulations show that the approximations are effective. A many-server heavy-traffic limit in the efficiency-driven regime shows that (i) the proposed approximations achieve the goal asymptotically as the scale increases, and (ii) it is not possible to simultaneously stabilize the mean queue length in the same asymptotic regime. }, number={6}, journal={OPERATIONS RESEARCH}, author={Liu, Yunan and Whitt, Ward}, year={2012}, pages={1551–1564} }
 @article{liu_whitt_2012, title={The G(t)/GI/s(t)+GI many-server fluid queue}, volume={71}, ISSN={["1572-9443"]}, DOI={10.1007/s11134-012-9291-0}, abstractNote={This paper introduces a deterministic fluid model that approximates the many-server G t /GI/s t +GI queueing model, and determines the time-dependent performance functions. The fluid model has time-varying arrival rate and service capacity, abandonment from queue, and non-exponential service and patience distributions. Two key assumptions are that: (i) the system alternates between overloaded and underloaded intervals, and (ii) the functions specifying the fluid model are suitably smooth. An algorithm is developed to calculate all performance functions. It involves the iterative solution of a fixed-point equation for the time-varying rate that fluid enters service and the solution of an ordinary differential equation for the time-varying head-of-line waiting time, during each overloaded interval. Simulations are conducted to confirm that the algorithm and the approximation are effective.}, number={4}, journal={QUEUEING SYSTEMS}, author={Liu, Yunan and Whitt, Ward}, year={2012}, month={Aug}, pages={405–444} }