Related papers: Two-Parameter Heavy-Traffic Limits for Infinite-Se…

We consider a sequence of single-server queueing models operating under a service policy that incorporates batches into processor sharing: arriving jobs build up behind a gate while waiting to begin service, while jobs in front of the gate…

We consider a two-dimensional stochastic fluid model with $N$ ON-OFF inputs and temporary assistance, which is an extension of the same model with $N = 1$ in Mahabhashyam et al. (2008). The rates of change of both buffers are piecewise…

A service system with multiple types of customers, arriving according to Poisson processes, is considered. The system is heterogeneous in that the servers also can be of multiple types. Each customer has an independent exponentially…

We present methodology for estimating the stochastic intensity of a doubly stochastic Poisson process. Statistical and theoretical analyses of traffic traces show that these processes are appropriate models of high intensity traffic…

In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of…

Stochastic service systems describe situations in which customers compete for service from scarce resources. Think of check-in lines at airports, waiting rooms in hospitals or queues in supermarkets, where the scarce resource is human…

We investigate a processor sharing queue with renewal arrivals and generally distributed service times. Impatient jobs may abandon the queue, or renege, before completing service. The corresponding stochastic processes are represented by…

This paper studies the input queued switch operating under the MaxWeight algorithm when the arrivals are according to a Markovian process. We exactly characterize the heavy-traffic scaled mean sum queue length in the heavy-traffic limit,…

We suggest an approach to obtaining general two-sided bounds on the rate of convergence in terms of special "weighted" norms related to total variation. Some important classes of continuous-time Markov chains are considered:…

This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale…

This paper considers the mean waiting times in discrete-time preemptive-resume and nonpreemptive priority single-server queues fed by K independent batch Markovian arrival streams with geometrically distributed idle periods. While being…

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks…

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…

A parallel server system is a stochastic processing network with applications in manufacturing, supply chain, ride-hailing, call centers, etc. Heterogeneous customers arrive in the system, and only a subset of servers can serve any customer…

Many stochastic systems have arrival processes that exhibit clustering behavior. In these systems, arriving entities influence additional arrivals to occur through self-excitation of the arrival process. In this paper, we analyze an…

In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in…

Code-division multiple-access (CDMA) has the potential to support traffic sources with a wide range of quality of service (QoS) requirements. The traffic carrying capacity of CDMA channels under QoS constraints (such as delay guarantee) is,…

Atar and Miyazawa recently introduced a single server queue with queue length dependent arrival and service processes, and name it a multi-level queue. They prove that the heavy traffic limit of its queue length process weakly converges to…

We consider an M/M/Infinity service system in which an arriving customer is served by the first idle server in an infinite sequence S_1, S_2, ... of servers. We determine the first two terms in the asymptotic expansions of the moments of L…

Consider a first-come, first-served single server queue with an initial workload $x>0$ and customers who arrive according to an inhomogeneous Poisson process with rate function $\lambda:[0,\infty)\rightarrow[0,\lambda_h ]$ for some…