Related papers: Convergence Rate of the Join-the-Shortest-Queue Sy…
In this paper, we present a condition to obtain instability for a class of queueing networks where the arrival rates in each server are constant and the departure rate in each server is a decreasing function of the queue lengths of other…
In this paper, we study the stability of light traffic achieved by a scheduling algorithm which is suitable for heterogeneous traffic networks. Since analyzing a scheduling algorithm is intractable using the conventional mathematical tool,…
We consider many-server queueing systems with heterogeneous exponential servers and renewal arrivals. The service rate of each server is a random variable drawn from a given distribution. We develop a framework for analyzing the heavy…
Join-the-Shortest-Queue (JSQ) is the scheduling policy of choice for many network providers, cloud servers and traffic management systems, where individual queues are served under processor sharing (PS) queueing discipline. A numerical…
Performance analysis of queueing networks is one of the most challenging areas of queueing theory. Barring very specialized models such as product-form type queueing networks, there exist very few results which provide provable…
Recent years have seen a great increase in the capacity and parallel processing power of data centers and cloud services. To fully utilize the said distributed systems, optimal load balancing for parallel queuing architectures must be…
Stochastic policies (also known as relaxed controls) are widely used in continuous-time reinforcement learning algorithms. However, executing a stochastic policy and evaluating its performance in a continuous-time environment remain open…
We consider a load balancing model where a Poisson stream of jobs arrive at a system of many servers whose service time distribution possesses a finite second moment. A small fraction of arrivals pass through the so called power-of-choice…
We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are inde- pendent and identically distributed. We call this the random scattering traffic model, and the…
The Join-the-Shortest-Queue-d routing policy is considered for a large system with $n$ servers. Moderate deviation principles (MDP) for the occupancy process and the empirical queue length process are established as $n\to \infty$. Each MDP…
In this article, we study the classical shortest queue problem under the influence of malicious attacks, which is relevant to a variety of engineering system including transportation, manufacturing, and communications. We consider a…
Obtaining estimates of the convergence rate of the regenerating process $Q(t)$ whose value at time $t$ is equal to the number of claims in the system $ M \backslash G \backslash \infty $ at this moment, to the limit (stationary) regime.
We study distributed load balancing in bipartite queueing systems where frontends route jobs to heterogeneous backends with workload-dependent service rates. The system's connectivity -- governed by compatibility constraints such as data…
We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered according to their speed, and arriving customers join the fastest idle server. A capacity allocation is…
We consider a one-dimensional stochastic reaction-diffusion generalizing the totally asymmetric simple exclusion process, and aiming at describing single lane roads with vehicles that can change speed. To each particle is associated a jump…
In this paper, energy efficiency of hybrid automatic repeat request (HARQ) schemes with statistical queuing constraints is studied for both constant-rate and random Markov arrivals by characterizing the minimum energy per bit and wideband…
We consider GI/Ph/n+M parallel-server systems with a renewal arrival process, a phase-type service time distribution, n homogenous servers, and an exponential patience time distribution with positive rate. We show that in the Halfin-Whitt…
A heterogeneous closed network with one-server queues with finite capacity and one infinite-server queue is studied. A target application is bike-sharing systems. Heterogeneity is taken into account through clusters whose queues have the…
This paper studies a 2-class, 2-server parallel server system under the recently introduced extended heavy traffic condition, which states that the underlying 'static allocation' linear program (LP) is critical, but does not require that it…
This paper studies the heavy-traffic joint distribution of queue lengths in two stochastic processing networks (SPN), viz., an input-queued switch operating under the MaxWeight scheduling policy and a two-server parallel server system…