Related papers: Asymptotics for the Late Arrivals Problem
A many-server queueing system is considered in which customers arrive according to a renewal process and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables.…
In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
A simple analytical solution is proposed for the stationary loss system of two parallel queues with finite capacity $K$, in which new customers join the shortest queue, or one of the two with equal probability if their lengths are equal.…
We consider an additive functional driven by a time-inhomogeneous Markov chain with a finite state space. Our study focuses on the joint distribution of the two-sided exit time and the state of the driving Markov chain at the time of exit,…
We consider a Markovian single server queue in which customers are preemptively scheduled by exogenously assigned priority levels. The novelty in our model is that the priority levels are randomly assigned from a continuous probability…
This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with…
In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…
This paper investigates the output synchronization problem for discrete-time heterogeneous multi-agent systems (MASs) subject to distinct communication delays. The presence of such delays prevents the instantaneous delivery of information…
We consider the delay properties of max-weight opportunistic scheduling in a multi-user ON/OFF wireless system, such as a multi-user downlink or uplink. It is well known that max-weight scheduling stabilizes the network (and hence yields…
We consider a load balancing system comprised of a fixed number of single server queues, operating under the well-known Join-the-Shortest Queue policy, and where jobs/customers are impatient and abandon if they do not receive service after…
To ensure the effective and objective development of transportation networks, it is crucial to identify performance limitations across various subsystems. A timetable-independent assessment of infrastructure capacity at railway junctions is…
In this paper, delay-optimal and energy-efficient communication is studied for a single link under Markov random arrivals. We present the optimal tradeoff between delay and power over Additive White Gaussian Noise (AWGN) channels and extend…
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…
A two-class Processor-Sharing queue with one impatient class is studied. Local exponential decay rates for its stationary distribution (N, M) are established in the heavy traffic regime where the arrival rate of impatient customers grows…
This paper is motivated by the observation that the average queueing delay can be decreased by sacrificing power efficiency in wireless communications. In this sense, we naturally wonder what is the minimum queueing delay when the available…
This paper considers a work-conserving FIFO single-server queue with multiple batch Markovian arrival streams governed by a continuous-time finite-state Markov chain. A particular feature of this queue is that service time distributions of…
We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with particular situations where the state space can be…
We consider a queueing system consisting of two non-identical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue…
Solving an output consensus problem in multi-agent systems is often hindered by multiple time-variant delays. To address such fundamental problems over time, we present a new optimal time-variant distributed control for linearly perturbed…