Related papers: Multi-component Matching Queues in Heavy Traffic
Motivated by application in wireless networks, cloud computing, data centers etc, Stochastic Processing Networks have been studied in the literature under various asymptotic regimes. In the heavy-traffic regime, the steady state mean queue…
The focus of this paper is on the asymptotics of large-time numbers of customers in time-periodic Markovian many-server queues with customer abandonment in heavy traffic. Limit theorems are obtained for the periodic number-of-customers…
This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The…
We present an analysis of large-scale load balancing systems, where the processing time distribution of tasks depends on both the task and server types. Our study focuses on the asymptotic regime, where the number of servers and task types…
We consider the FCFS $\mathit{GI}/\mathit{GI}/n$ queue in the so-called Halfin-Whitt heavy traffic regime. We prove that under minor technical conditions the associated sequence of steady-state queue length distributions, normalized by…
Motivated by applications that involve setting proper staffing levels for multi-server queueing systems with batch arrivals, we present a thorough study of the queue-length process $\{Q(t); t \geq 0\}$, departure process $\{D(t); t \geq…
We consider the model of a token-based joint auto-scaling and load balancing strategy, proposed in a recent paper by Mukherjee, Dhara, Borst, and van Leeuwaarden (SIGMETRICS '17, arXiv:1703.08373), which offers an efficient scalable…
We consider the heavy-traffic approximation to the $GI/M/s$ queueing system in the Halfin-Whitt regime, where both the number of servers $s$ and the arrival rate $\lambda$ grow large (taking the service rate as unity), with…
We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critical loading condition is assumed. Generally, the limit…
Inspired by quantum switches, we consider a discrete-time multi-way matching system with two classes of arrivals: requests for entangled pair of qubits between two nodes, and qubits from each node that can be used to serve the requests. An…
We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic…
This paper introduces and analyzes the notion of throughput suboptimality for many-server queueing systems in heavy traffic. The queueing model under consideration has multiple customer classes, indexed by a finite set $\mathcal{I}$, and…
This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate $\Lambda$ from a given distribution every $\Delta$…
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…
A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a…
We consider an infinite sequence consisting of agents of several types and goods of several types, with a bipartite compatibility graph between agent and good types. Goods are matched with agents that appear earlier in the sequence using…
This work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system is represented in terms of a process that describes the…
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…
In many different settings, requests for service can arrive in near or true simultaneity with one another. This creates batches of arrivals to the underlying queueing system. In this paper, we study the staffing problem for the batch…
We consider the processor sharing $M/M/1$-PS queue which also models balking. A customer that arrives and sees $n$ others in the system "balks" (i.e., decides not to enter) with probability $1-b_n$. If $b_n$ is inversely proportional to…