Related papers: Delay Bounds for Multiclass FIFO

Stochastic gradient descent (SGD) performed in an asynchronous manner plays a crucial role in training large-scale machine learning models. However, the generalization performance of asynchronous delayed SGD, which is an essential metric…

In this article statistical bounds for certain output characteristics of the $M/GI/1/n$ and $GI/M/1/n$ loss queueing systems are derived on the basis of large samples of an input characteristic of these systems, such as service time in the…

Explicit numerical methods based on Lax-Friedrichs and Leap-Frog finite difference approximations are constructed to find the numerical solution of the first-order hyperbolic partial differential equation with point-wise delay or advance,…

Classical list scheduling is a very popular and efficient technique for scheduling jobs in parallel and distributed platforms. It is inherently centralized. However, with the increasing number of processors, the cost for managing a single…

We establish matching upper and lower generalization error bounds for mini-batch Gradient Descent (GD) training with either deterministic or stochastic, data-independent, but otherwise arbitrary batch selection rules. We consider smooth…

We study nonstochastic bandits and experts in a delayed setting where delays depend on both time and arms. While the setting in which delays only depend on time has been extensively studied, the arm-dependent delay setting better captures…

Upper and lower class functions for the maximum likelihood estimator of the arrival and the service rates in a $GI/G/1$ queue are studied and the results are verified for M/M/1 queue.

For a given independent and identically distributed (i.i.d.) source, Huffman code achieves the optimal average codeword length in the class of instantaneous code with a single code table. However, it is known that there exist time-variant…

Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…

We give a novel, unified derivation of conditional PAC-Bayesian and mutual information (MI) generalization bounds. We derive conditional MI bounds as an instance, with special choice of prior, of conditional MAC-Bayesian (Mean Approximately…

In cognitive radio systems, secondary users can utilize multiple dispersed bands that are not used by primary users. In this paper, time delay estimation of signals that occupy multiple dispersed bands is studied. First, theoretical limits…

This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to…

We study critical GI/G/1 queues under finite second moment assumptions. We show that the busy period distribution is regularly varying with index half. We also review previously known M/G/1/ and M/M/1 derivations, yielding exact asymptotics…

Queue length monitoring is a commonly arising problem in numerous applications such as queue management systems, scheduling, and traffic monitoring. Motivated by such applications, we formulate a queue monitoring problem, where there is a…

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates…

This paper studies a scheduling problem in a parallel machine setting, where each machine must adhere to a predetermined fixed order for processing the jobs. Given $n$ jobs, each with processing times and deadlines, we aim to minimize the…

In this paper, we adopt a cross layer design approach for analyzing the throughput-delay tradeoff of the multicast channel in a single cell system. To illustrate the main ideas, we start with the single group case, i.e., pure multicast,…

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…

This paper considers the stationary distribution of the age of information (AoI) in information update systems. We first derive a general formula for the stationary distribution of the AoI, which holds for a wide class of information update…

Consider a multihop wireless network serving multiple flows in which wireless link interference constraints are described by a link interference graph. For such a network, we design routing-scheduling policies that maximize the end-to-end…