Related papers: On many-server queues in heavy traffic
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 have revealed general physical conditions for the {\it maximization} of the network throughput at which free flow conditions are ensured, i.e., traffic breakdown cannot occur in the whole traffic or transportation network. A physical…
Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent…
Multi-server queueing systems describe situations in which users require service from multiple parallel servers. Examples include check-in lines at airports, waiting rooms in hospitals, queues in contact centers, data buffers in wireless…
Following recent developments in the application of Stein's method in queueing theory, this paper is intended to be a short treatment showing how Stein's method can be developed and applied to the single server queue in heavy traffic. Here…
In this paper one presents method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically one considers inhomogeneous $M/M/S$ queueing system with…
In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…
We study a stochastic network that consists of a set of servers processing multiple classes of jobs. Each class of jobs requires a concurrent occupancy of several servers while being processed, and each server is shared among the job…
A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities. An optimal control problem is formulated, where the control corresponds to scheduling and routing,…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
We prove a heavy traffic scaling limit for a shortest remaining processing time queue. We are interested in the case where the processing time distribution has a tail that decays rapidly, i.e., has light tails. In particular, we revisit the…
Efficiently exploiting servers in data centers requires performance analysis methods that account not only for the stochastic nature of demand but also for server heterogeneity. Although several recent works proved optimality results for…
We define a minimal model of traffic flows in complex networks containing the most relevant features of real routing schemes, i.e. a trade--off strategy between topological-based and traffic-based routing. The resulting collective behavior,…
It is well-known that the power-of-d choices routing algorithm maximizes throughput and is heavy-traffic optimal in load balancing systems with homogeneous servers. However, if the servers are heterogeneous, throughput optimality does not…
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…
We provide upper bounds on the end-to-end backlog and delay in a network with heavy-tailed and self-similar traffic. The analysis follows a network calculus approach where traffic is characterized by envelope functions and service is…
We propose a model uncertainty approach to heavy traffic asymptotics that allows for a high level of uncertainty. That is, the uncertainty classes of underlying distributions accommodate disturbances that are of order 1 at the usual…
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 consider a natural scheduling problem which arises in many distributed computing frameworks. Jobs with diverse resource requirements (e.g. memory requirements) arrive over time and must be served by a cluster of servers, each with a…
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…