In this paper, we study a queueing process for which the dynamics are changed once the workload in the queue exceeds a predefined threshold, and these new dynamics stay in force until the queue is emptied, at which point the previous dynamics are again reinstalled. For general spectrally positive Lévy processes in each case, we derive expressions for the workload at an independent exponentially distributed random time horizon and study in detail properties of the workload in stationarity. We work out explicit formulas as well as expressions for the optimal changing threshold for special cases of the underlying process dynamics and a chosen set of involved switching, holding, and service cost functions. Funding: The research of O. Boxma and M. Mandjes has been partly funded by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek Gravitation [Project Networks, Grant 024.002.003]. The research of O. Kella is partially funded by Israel Science Foundation [Grant 3336/24] and the Vigevani Chair in Statistics.
In this paper, we study the fluid limit of many-server queues with abandonment (with traffic intensity [Formula: see text]) via a class of nonlinear Volterra equations. For a broad class of service time distributions, we establish the asymptotic behavior of the solutions to the class of nonlinear Volterra equations, which in turn implies the large time behavior of the fluid limit of the many-server queues with abandonment.
This paper studies the applications of state-dependent importance sampling in pricing exotic rainbow options. We demonstrate that for many rainbow options, efficient dynamic importance sampling schemes can be constructed from subsolutions to appropriate partial differential equations. We also introduce an alternative large deviations scaling, which leads to universal importance sampling for rainbow options.
We study optimal coordination in quality-driven rework systems, where each station contributes to an item’s quality and the likelihood of rework depends on these contributions through a production function. Our model links quality targets to processing times via Brownian hitting times and aggregates quality into rework probability. By setting quality targets, a planner jointly shapes processing times and rework rates, determining overall workload. We characterize the attainable workload region and use it to minimize effort costs in two-station networks. The optimal policy depends on (i) complementarity versus substitutability of quality contributions, (ii) each station’s quality impact, and (iii) relative operational costs. We identify three operating regimes: two corner regimes (one active station) and a network regime (both active). As complementarity increases, effort shifts toward the more cost-effective station, whereas finite capacity modifies this threshold, pushing effort toward the less constrained station. The analysis highlights how complementarity shapes efficiency trade-offs and capacity requirements. To illustrate the model’s practical relevance, we calibrate it using published operational statistics from industrial maintenance settings, in which equipment undergoes repair followed by preventive service while offline. The results show that the optimal design is robust to parameter misspecification, achieves substantial cost savings relative to benchmark policies, and can be estimated from standard operational data. Funding: Partial financial support was provided by the Israel Science Foundation [Grant 277/21] and the Bernard M. Gordon Center for Systems Engineering at the Technion. Supplemental Material: The online appendix is available at https://doi.org/10.1287/stsy.2025.0111 .
We consider a basic balls-and-bins question in which you have to distribute n balls into k bins. Then, round by round, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. The goal is to minimize the expected number of remaining balls. An open problem posed by Will Ma asks whether the initial assignment that minimizes the expected number of remaining balls is one that is as balanced as possible. Using a coupling argument, we answer this conjecture positively, and we discuss the case of non-uniform choice among the non-empty bins.
