Related papers: Stability for Two-class Multiserver-job Systems
We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level…
The paper studies a multiserver retrial queueing system with $m$ servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon…
This paper studies a class of load balancing algorithms for many-server ($N$ servers) systems assuming finite buffer with size $b-1$ (i.e. a server can have at most one job in service and $b-1$ jobs in queue). We focus on steady-state…
Recently multiserver queues with setup times have been extensively studied because they have applications in power-saving data centers. The most challenging model is the M/M/$c$/Setup queue where a server is turned off when it is idle and…
We consider the stability of robust scheduling policies for multiclass queueing networks. These are open networks with arbitrary routing matrix and several disjoint groups of queues in which at most one queue can be served at a time. The…
We consider a distributed server system consisting of a large number of servers, each with limited capacity on multiple resources (CPU, memory, disk, etc.). Jobs with different rewards arrive over time and require certain amounts of…
In a large-scale computing cluster, the job completions can be substantially delayed due to two sources of variability, namely, variability in the job size and that in the machine service capacity. To tackle this issue, existing works have…
We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…
The paper studies a closed queueing network containing two types of node. The first type (server station) is an infinite server queueing system, and the second type (client station) is a single server queueing system with autonomous…
With multiple identical unit speed servers, the online problem of scheduling jobs that migrate between two phases, limitedly parallelizable or completely sequential, and choosing their respective speeds to minimize the total flow time is…
We provide a queueing-theoretic framework for job replication schemes based on the principle "\emph{replicate a job as soon as the system detects it as a \emph{straggler}}". This is called job \emph{speculation}. Recent works have analyzed…
We consider a distributed computing network consisting of a master and multiple workers processing tasks of different types. The master is running multiple applications. Each application stochastically generates real-time jobs with a strict…
In this paper, we study the stability of queues with impatient customers. Under general stationary ergodic assumptions, we first provide some conditions for such a queue to be regenerative (i.e. to empty a.s. an infinite number of times).…
We study a many-server queuing system with general service time distribution and state dependent service rates. The dynamics of the system are modeled using measure valued processes which keep track of the residual service times. Under…
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…
Distributed load balancing is the act of allocating jobs among a set of servers as evenly as possible. There are mainly two versions of the load balancing problem that have been studied in the literature: static and dynamic. The static…
The problem of scheduling jobs and choosing their respective speeds with multiple servers under a sum power constraint to minimize the flow time + energy is considered. This problem is a generalization of the flow time minimization problem…
We consider the problem of scheduling non preemptively a set of jobs on parallel identical machines with prior setup operations on a single shared server, where the objective is to minimise the makespan. We develop an arc-flow formulation…
Most data generated by modern applications is stored in the cloud, and there is an exponential growth in the volume of jobs to access these data and perform computations using them. The volume of data access or computing jobs can be…
We consider a load balancing system comprised of a fixed number of single server queues, operating under the well-known Join-the-Shortest Queue policy, and where jobs/customers are impatient and abandon if they do not receive service after…