Related papers: On Exponential Ergodicity of Multiclass Queueing N…

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…

Estimating delay tail probabilities in scheduling and load balancing systems is a critical but computationally prohibitive task due to the rarity of violation events. Quantum Amplitude Estimation (QAE) offers a generic quadratic reduction…

We carry out a delay stability analysis (i.e., determine conditions under which expected steady-state delays at a queue are finite) for a simple 3-queue system operated under the Max-Weight scheduling policy, for the case where one of the…

In this paper we study time semi-discrete approximations of a class of exponentially stable infinite dimensional systems with unbounded feedbacks. It has recently been proved that for time semi-discrete systems, due to high frequency…

In this thesis, we propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction $p$ of an available resource is deployed in a centralized manner…

We consider stability and network capacity in discrete time queueing systems. Relationships between four common notions of stability are described. Specifically, we consider rate stability, mean rate stability, steady state stability, and…

In this work, we consider the existence of global solution and the exponential decay of a nonlinear porous elastic system with time delay. The nonlinear term as well as the delay acting in the equation of the volume fraction. In order to…

In this paper, by the singular-perturbation technique, we investigate the heavy-traffic behavior of a priority polling system consisting of three M/M/1 queues with threshold policy. It turns out that the scaled queue-length of the…

We consider the stability of robust scheduling policies for multiclass queueing networks. These are open networks with arbitrary routing matrix and several disjoint groups of queues in which at most one queue can be served at a time. The…

We consider a single server queueing system with two classes of jobs: eager jobs with small sizes that require service to begin almost immediately upon arrival, and tolerant jobs with larger sizes that can wait for service. While blocking…

We consider the problem of selfish agents in discrete-time queuing systems, where competitive queues try to get their packets served. In this model, a queue gets to send a packet each step to one of the servers, which will attempt to serve…

Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…

We study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the XY model of finite size. In two-dimensions this system is critical over the whole of the low temperature…

Consider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an i.i.d. process. A key step is to show that any…

In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten [12] and Goldie [8] all discount factors in the model are mutually independent. We prove that the tails of the…

Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…

We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not…

In this work, the achievable rate of three-node relay systems with selection relaying under statistical delay constraints, imposed on the limitations of the maximum end-to-end delay violation probabilities, is investigated. It is assumed…

Gaitonde and Tardos recently studied a model of queueing networks where queues compete for servers and re-send returned packets in future rounds. They quantify the amount of additional processing power that guarantees a decentralized…

We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…