Related papers: Heavy traffic approximation for the stationary dis…
We consider a single class open queueing network, also known as a generalized Jackson network (GJN). A classical result in heavy-traffic theory asserts that the sequence of normalized queue length processes of the GJN converge weakly to a…
The basic adjoint relationship (BAR) approach is an analysis technique based on the stationary equation of a Markov process. This approach was introduced to study heavy-traffic, steady-state convergence of generalized Jackson networks in…
We establish uniform moment bounds for steady-state queue lengths of generalized Jackson networks (GJNs) in multi-scale heavy traffic as recently proposed by Dai et al. [2023]. Uniform moment bounds lay the foundation for further analysis…
We consider a single server queue which has a threshold to change its arrival process and service speed by its queue length, which is referred to as a two-level single server queue. This model is motivated by an energy saving problem for a…
We consider Palm distributions arising in a Markov process with time homogeneous transitions which is jointly stationary with multiple point processes. Motivated by a BAR approach studied in the recent paper Braverman, Dai and Miyazawa…
This paper examines a continuous-time routing system with general interarrival and service time distributions, operating under the join-the-shortest-queue and power-of-two-choices policies. Under a weaker set of assumptions than those…
We prove that under a multi-scale heavy traffic condition, the stationary distribution of the scaled queue length vector process in any generalized Jackson network has a product-form limit. Each component in the product form follows an…
Inspired by the work of Atar and Miyazawa [1] (2026) as well as applications to energy-saving problems, we are interested in the heavy-traffic limit of the stationary queue length distribution, which is not addressed in [1]. In this paper,…
Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove,…
Various empirical and theoretical studies indicate that cumulative network traffic is a Gaussian process. However, depending on whether the intensity at which sessions are initiated is large or small relative to the session duration tail,…
Atar and Miyazawa recently introduced a single server queue with queue length dependent arrival and service processes, and name it a multi-level queue. They prove that the heavy traffic limit of its queue length process weakly converges to…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
We study the tail asymptotic of the stationary joint queue length distribution for a generalized Jackson network (GJN for short), assuming its stability. For the two station case, this problem has been recently solved in the logarithmic…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
We consider a connection-level model proposed by Massouli\'{e} and Roberts for bandwidth sharing among file transfer flows in a communication network. We study weighted proportionally fair sharing policies and establish explicit-form bounds…
Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…
We investigate the functional limits of generalized Jackson networks in a multi-scale heavy traffic regime where stations approach full utilization at distinct, separated rates. Our main result shows that the appropriately scaled queue…
We investigate the steady-state diffusion-approximation error for continuous-time queueing systems with generally distributed primitives. Across four canonical systems -- the $G/G/1$ and $G/M/\infty$ queues, the join-the-shortest-queue…
We extend the Markov additive methodology developed in [Ann. Appl. Probab. 9 (1999) 110-145, Ann. Appl. Probab. 11 (2001) 596-607] to obtain the sharp asymptotics of the steady state probability of a queueing network when one of the nodes…
Introduced by Bean and O'Reilly (2014), a stochastic fluid-fluid process is a Markov processes $\{X_t, Y_t, \varphi_t\}_{t \geq 0}$, where the first fluid $X_t$ is driven by the Markov chain $\varphi_t$, and the second fluid $Y_t$ is driven…