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1. k-Nearest Neighbor Queues with Delayed Information

   https://doi.org/10.1142/S0218127422501747  

   Pender, Jamol (September 2022, International Journal of Bifurcation and Chaos)

   In this paper, we analyze a model called the k-nearest neighbor queue with the possibility of having delayed queue length feedback. We prove fluid limits for the stochastic queueing model and show that the fluid limit converges to a system of delay differential equations. Using the properties of circulant matrices, we derive a closed form expression for the value of the critical delay, which governs whether the delayed information will induce oscillations or a Hopf bifurcation in our queueing system. 

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2. Breaking the Symmetry in Queues with Delayed Information

   https://doi.org/10.1142/S0218127421300275  

   Doldo, Philip; Pender, Jamol; Rand, Richard (July 2021, International Journal of Bifurcation and Chaos)

   Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze a two-dimensional deterministic fluid model that incorporates customer choice behavior based on delayed queue length information. Reports in the existing literature always assume that all queues have identical parameters and the underlying dynamical system is symmetric. However, in this paper, we relax this symmetry assumption by allowing the arrival rates, service rates, and the choice model parameters to be different for each queue. Our methodology exploits the method of multiple scales and asymptotic analysis to understand how to break the symmetry. We find that the asymmetry can have a large impact on the underlying dynamics of the queueing system. 

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3. SRPT Scheduling Discipline in Many-Server Queues with Impatient Customers

   https://doi.org/10.1287/mnsc.2021.4110  

   Dong, Jing; Ibrahim, Rouba (October 2021, Management Science)

   The shortest-remaining-processing-time (SRPT) scheduling policy has been extensively studied, for more than 50 years, in single-server queues with infinitely patient jobs. Yet, much less is known about its performance in multiserver queues. In this paper, we present the first theoretical analysis of SRPT in multiserver queues with abandonment. In particular, we consider the M/GI/s+GI queue and demonstrate that, in the many-sever overloaded regime, performance in the SRPT queue is equivalent, asymptotically in steady state, to a preemptive two-class priority queue where customers with short service times (below a threshold) are served without wait, and customers with long service times (above a threshold) eventually abandon without service. We prove that the SRPT discipline maximizes, asymptotically, the system throughput, among all scheduling disciplines. We also compare the performance of the SRPT policy to blind policies and study the effects of the patience-time and service-time distributions. This paper was accepted by Baris Ata, stochastic models & simulation. 

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4. Stable isotope values of consumers, producers, and organic matter in the Shark River Slough and Taylor Slough, Everglades National Park (FCE LTER), Florida, USA, 2019 – ongoing

   https://doi.org/10.6073/pasta/da36c97eccd5461ba32eecce23a53892  

   Rezek, Ryan (January 2024, Environmental Data Initiative)

   {"Abstract":["Wetland food webs have often been characterized as detrital-based ‘brown’ energy pyramids, whereas the relative role of autotrophic (‘green’) vs. microbial (‘brown’) energy sources falls along a continuum set by physical drivers, as well as autochthonous and allochthonous inputs (Moore et al. 2004; Evans-White & Halvorson 2017) that change with ecosystem development (Schmitz et al. 2006). In the Florida Coastal Everglades (FCE), metabolic imbalances, including the collapse of calcareous periphyton mats, begin with a loss of foundation species primary production and legacy organic matter (Gaiser et al. 2006). This process likely enhances heterotrophic microbial productivity (Schulte 2016) and the supply of detrital energy to consumers by changing bioavailable and recalcitrant carbon supplies (Baggett et al. 2013). A shift from complex periphyton communities to transient planktonic communities under elevated P exposure reduces habitat structure and animal refuges but increases ‘green’ energy supplies and edibility (Trexler et al. 2015; Naja et al. 2017). Multiple sites (n=9) within the FCE were selected to document changes in coastal food webs as a result of eutrophication and increasing hydrologic variability. The project began in 2019 and is currently ongoing.\n \n References:\n Baggett, L. P., Heck, K. L., Frankovich, T. A., Armitage, A. R., & Fourqurean, J. W. (2013). Stoichiometry, growth, and fecundity responses to nutrient enrichment by invertebrate grazers in sub-tropical turtle grass (Thalassia testudinum) meadows. Marine biology, 160, 169-180.\n Evans-White, M. A., and H. M. Halvorson. 2017. Comparing the Ecological Stoichiometry in Green and Brown Food Webs – A Review and Meta-analysis of Freshwater Food Webs. Frontiers in Microbiology 8:1184. \n Gaiser, E. E., Childers, D. L., Jones, R. D., Richards, J. H., Scinto, L. J., & Trexler, J. C. (2006). Periphyton responses to eutrophication in the Florida Everglades: cross‐system patterns of structural and compositional change. Limnology and Oceanography, 51(1part2), 617-630.\n Moore, J. C., E. L. Berlow, D. C. Coleman, P. C. Ruiter, Q. Dong, A. Hastings, N. C. Johnson, K. S. McCann, K. Melville, P. J. Morin, K. Nadelhoffer, A. D. Rosemond, D. M. Post, J. L. Sabo, K. M. Scow, M. J. Vanni, and D. H. Wall. 2004. Detritus, trophic dynamics and biodiversity: Detritus, trophic dynamics and biodiversity. Ecology Letters 7:584–600. \n Naja, M., Childers, D. L., & Gaiser, E. E. (2017). Water quality implications of hydrologic restoration alternatives in the Florida Everglades, United States. Restoration Ecology, 25, S48-S58.\n Schmitz, O. J., Kalies, E. L., & Booth, M. G. (2006). Alternative dynamic regimes and trophic control of plant succession. Ecosystems, 9, 659-672.\n Schulte, Nicholas O., "Controls on Benthic Microbial Community Structure and Assembly in a Karstic Coastal Wetland" (2016). FIU Electronic Theses and Dissertations. 2447. 10.25148/etd.FIDC000233\n Trexler, J. C., Gaiser, E. E., Kominoski, J. S., & Sanchez, J. (2015). The role of periphyton mats in consumer community structure and function in calcareous wetlands: lessons from the Everglades. Microbiology of the everglades ecosystem, 155-179."]} 

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5. Optimal Signaling Mechanisms in Unobservable Queues with Strategic Customers

   https://doi.org/10.1145/3033274.3085135  

   Lingenbrink, David; Iyer, Krishnamurthy (June 2017, Proceedings of the 2017 ACM Conference on Economics and Computation (EC))

   We study the problem of optimal information sharing in the context of a service system. In particular, we consider an unobservable single server queue offering a service at a fixed price to a Poisson arrival of delay-sensitive customers. The service provider can observe the queue, and may share information about the state of the queue with each arriving customer. The customers are Bayesian and strategic, and incorporate any information provided by the service provider into their prior beliefs about the queue length before making the decision whether to join the queue or leave without obtaining service. We pose the following question: which signaling mechanism and what price should the service provider select to maximize her revenue? We formulate this problem as an instance of Bayesian persuasion in dynamic settings. The underlying dynamics make the problem more difficult because, in contrast to static settings, the signaling mechanism adopted by the service provider affects the customers' prior beliefs about the queue (given by the steady state distribution of the queue length in equilibrium). The core contribution of this work is in characterizing the structure of the optimal signaling mechanism. We summarize our main results as follows. (1) Structural characterization: Using a revelation-principle style argument, we find that it suffices to consider signaling mechanisms where the service provider sends a binary signal of "join" or "leave", and under which the equilibrium strategy of a customer is to follow the service provider's recommended action. (2) Optimality of threshold policies: For a given fixed price for service, we use the structural characterization to show that the optimal signaling mechanism can be obtained as a solution to a linear program with a countable number of variables and constraints. Under some mild technical conditions on the waiting costs, we establish that there exists an optimal signaling mechanism with a threshold structure, where service provider sends the "join" signal if the queue length is below a threshold, and "leave" otherwise. (In addition, at the threshold, the service provider randomizes.) For the special case of linear waiting costs, we derive an analytical expression for the optimal threshold i terms of the two branches of the Lambert-W function. (3) Revenue comparison: Finally, we show that with the optimal choice of the fixed price and using the corresponding optimal signaling mechanism, the service provider can achieve the same revenue as with the optimal state-dependent pricing mechanism in a fully-observable queue. This implies that in settings where state-dependent pricing is not feasible, the service provider can effectively use optimal signaling (with the optimal fixed price) to achieve the same revenue. 

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