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Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling…
Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…
We introduce a novel single-server queue with general retrial times and event-dependent arrivals. This is a versatile model for the study of service systems, in which the server needs a non-negligible time to retrieve waiting customers upon…
Quantum annealing is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare…
We consider a horizontal traffic queue (HTQ) on a periodic road segment, where vehicles arrive according to a spatio-temporal Poisson process, and depart after traveling a distance that is sampled independently and identically from a…
We consider a processor shared $M/M/1$ queue that can accommodate at most a finite number $K$ of customers. We give an exact expression for the sojourn time distribution in the finite capacity model, in terms of a Laplace transform. We then…
We propose a new exact solution algorithm for closed multiclass product-form queueing networks that is several orders of magnitude faster and less memory consuming than established methods for multiclass models, such as the Mean Value…
This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to…
Prior work showed the efficacy of pausing midanneal: such a pause improved the probability of success by orders of magnitude in a class of native problem instances and improved the time to solution in a class of embedded problem instances.…
We study an M/G/1-type queueing model with the following additional feature. The server works continuously, at fixed speed, even if there are no service requirements. In the latter case, it is building up inventory, which can be interpreted…
This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. Specifically, every…
The $M/GI/m/n$ queueing system with $m$ homogeneous servers and the finite number $n$ of waiting spaces is studied. Let $\lambda$ be the customers arrival rate, and let $\mu$ be the reciprocal of the expected service time of a customer.…
We analyze the service times of customers in a stable M/M/1 queue in equilibrium depending on their position in a busy period. We give the law of the service of a customer at the beginning, at the end, or in the middle of the busy period.…
Time series forecasting is essential for many practical applications, with the adoption of transformer-based models on the rise due to their impressive performance in NLP and CV. Transformers' key feature, the attention mechanism,…
Uncertainty is ubiquitous in real-world data, and the assumptions underlying classical linear regression models are often violated in practice. Inspired by the theory of sublinear expectation, we consider a linear regression model where the…
We consider a one-dimensional stochastic reaction-diffusion generalizing the totally asymmetric simple exclusion process, and aiming at describing single lane roads with vehicles that can change speed. To each particle is associated a jump…
In many systems, servers do not turn on instantly; instead, a setup time must pass before a server can begin work. These "setup times" can wreak havoc on a system's queueing; this is especially true in modern systems, where servers are…
We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of…
We consider an M/M/1 queueing model where customers can strategically decide to enter or leave the queue. We characterize the class of queueing regimes such that, for any parameters of the model, the socially efficient behavior is an…
We present alternative approaches to routing and scheduling in Answer Set Programming (ASP), and explore them in the context of Multi-agent Path Finding. The idea is to capture the flow of time in terms of partial orders rather than time…