Related papers: Asymptotics of Insensitive Load Balancing and Bloc…
Dynamic affinity load balancing of multi-type tasks on multi-skilled servers, when the service rate of each task type on each of the servers is known and can possibly be different from each other, is an open problem for over three decades.…
Scheduling control problems for a family of unitary networks under heavy traffic with general interarrival and service times, probabilistic routing and an infinite horizon discounted linear holding cost are studied. Diffusion control…
We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…
We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean field…
We develop a heavy traffic diffusion limit theorem under nonstandard spatial scaling for the queue length process in a single server queue employing shortest remaining processing time (SRPT). For processing time distributions with unbounded…
We consider discrete, iterative load balancing via matchings on arbitrary graphs. Initially each node holds a certain number of tokens, defining the load of the node, and the objective is to redistribute the tokens such that eventually each…
We consider a system of processor-sharing queues with state-dependent service rates. These are allocated according to balanced fairness within a polymatroid capacity set. Balanced fairness is known to be both insensitive and…
We consider an automatic overload control for two large service systems modeled as multi-server queues, such as call centers. We assume that the two systems are designed to operate independently, but want to help each other respond to…
In parallel iterative applications, computational efficiency is essential for addressing large problems. Load imbalance is one of the major performance degradation factors of parallel applications. Therefore, distributing, cleverly, and as…
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 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…
We consider large-scale service systems with multiple customer classes and multiple server pools; interarrival and service times are exponentially distributed, and mean service times depend both on the customer class and server pool. It is…
We develop a Markovian framework for load balancing that combines classical algorithms such as Power-of-$d$ with auto-scaling mechanisms that allow the net service capacity to scale up or down in response to the current load on the same…
We consider a model inspired by compatibility constraints that arise between tasks and servers in data centers, cloud computing systems and content delivery networks. The constraints are represented by a bipartite graph or network that…
We study the scheduling polices for asymptotically optimal delay in queueing systems with switching overhead. Such systems consist of a single server that serves multiple queues, and some capacity is lost whenever the server switches to…
We consider N single server infinite buffer queues with service rate beta. Customers arrive at rate N times alpha,choose L queues uniformly, and join the shortest one. The stability condition is alpha strictly less than beta. We study in…
In this paper, motivated by considerations of server utilization and energy consumptions in cloud computing, we investigate a homogeneous queueing system with a threshold-based workload control scheme. In this system, a virtual machine will…
We consider several stochastic service systems, and study the asymptotic behavior of the moments of various quantities that have application to models for random interval graphs and algorithms for searching for an idle server or empty…
Consider a network of $n$ single-server queues where tasks arrive independently at each server at rate $\lambda_n$. The servers are connected by a graph that is resampled at rate $\mu_n$ in a way that is symmetric with respect to the…
We develop many-server asymptotics in the QED regime for models with admission control. The admission control, designed to reduce the incoming traffic in periods of congestion, scales with the size of the system. For a class of Markovian…