相关论文: Uniform Moment Bounds for Generalized Jackson Netw…

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…

In the seminal paper of Gamarnik and Zeevi (2006), the authors justify the steady-state diffusion approximation of a generalized Jackson network (GJN) in heavy traffic. Their approach involves the so-called limit interchange argument, which…

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…

In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…

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 give uniform proofs of tightness and exponential tightness of the sequences of stationary queue lengths in generalised Jackson networks in a number of setups which concern large, normal and moderate deviations.

We study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For {\em finite} networks we establish stability and some steady-state moment bounds under natural…

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 consider a stochastic network with mobile users in a heavy-traffic regime. We derive the scaling limit of the multi-dimensional queue length process and prove a form of spatial state space collapse. The proof exploits a recent result by…

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…

For a class of large closed Jackson networks submitted to capacity constraints, asymptotic independence of the nodes in normal traffic phase is proved at stationarity under mild assumptions, using a Local Limit Theorem. The limiting…

A general moment bound for sums of products of Gaussian vector's functions extending the moment bound in Taqqu (1977, Lemma 4.5) is established. A general central limit theorem for triangular arrays of nonlinear functionals of…

This paper serves as a companion to "Asymptotic Product-form Steady-state for Multiclass Queueing Networks with SBP Service Policies in Multi-scale Heavy Traffic." In this short paper, we illustrate the main results of the main paper…

This paper proves a large deviation principle (LDP) for the stationary distribution of queue lengths in a subcritical generalised Jackson network assuming a Cramer condition on the interarrival and service times. The deviation function is…

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,…

We study the load balancing system operating under Join the Shortest Queue (JSQ) in the many-server heavy-traffic regime. If $N$ is the number of servers, we let the difference between the total service rate and the total arrival rate be…

Queueing networks are gaining attraction for the performance analysis of parallel computer systems. A Jackson network is a set of interconnected servers, where the completion of a job at server i may result in the creation of a new job for…

We establish conditions for uniform $r$-th moment bound of certain $\R^d$-valued functions of a discrete-time stochastic process taking values in a general metric space. The conditions include an appropriate negative drift together with a…

Bounding the queue length in a multiserver queue is a central challenge in queueing theory. Even for the classical $G/G/n$ queue with homogeneous servers, it is highly non-trivial to derive a simple and accurate bound for the steady-state…

We provide the first perfect sampling algorithm for a Generalized Jackson Network of FIFO queues under arbitrary topology and non-Markovian assumptions on the input of the network. We assume (in addition to stability) that the interarrival…