Related papers: Proportional fairness and its relationship with mu…
We study many-server queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measure- valued processes, to keep track of the residual service and patience…
Queueing networks are gaining attraction for the performance analysis of parallel computer systems. A Jackson network is a set of interconnected servers, where the completion of a job at server i may result in the creation of a new job for…
Recently, Atar and Miyazawa [2] introduced a multi-level GI/G/1 queue with a finite number of levels, where both the arrival and service rates depend on the level corresponding to the current queue length. For this model, they proved that…
In this paper we analyze an $M/M/1$ queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a…
We investigate a stochastic model hierarchy for pedestrian flow. Starting from a microscopic social force model, where the pedestrians switch randomly between the two states stop-or-go, we derive an associated macroscopic model of…
In this paper we show that in a multiclass Markovian network with unit rate servers, the condition that the average load $\rho$ at every server is less than unity is indeed sufficient for the stability or positive recurrence for \emph{any}…
The paper deals with a sharing economy system with various management factors by using a bulk input G/M/1 type queuing model. The effective management of operating costs is vital for controlling the sharing economy platform and this…
In traditional federated learning, a single global model cannot perform equally well for all clients. Therefore, the need to achieve the client-level fairness in federated system has been emphasized, which can be realized by modifying the…
Modern processing networks often consist of heterogeneous servers with widely varying capabilities, and process job flows with complex structure and requirements. A major challenge in designing efficient scheduling policies in these…
Algorithmic decision making systems are ubiquitous across a wide variety of online as well as offline services. These systems rely on complex learning methods and vast amounts of data to optimize the service functionality, satisfaction of…
The paper investigates the throughput behavior of single-commodity dynamical flow networks governed by monotone distributed routing policies. The networks are modeled as systems of ODEs based on mass conversation laws on directed graphs…
Stochastic reaction networks are dynamical models of biochemical reaction systems and form a particular class of continuous-time Markov chains on $\mathbb{N}^n$. Here we provide a fundamental characterisation that connects structural…
The upper bound for the convergence rate of the distribution of the state of a queuing system with infinitely many servers is obtained, in the case when the intensity of the incoming flow and the intensity of the service depend on the state…
A queueing model has $J\ge2$ heterogeneous service stations, each consisting of many independent servers with identical capabilities. Customers of $I\ge2$ classes can be served at these stations at different rates, that depend on both the…
The interconnection network is a key element in High-Performance Computing (HPC) and Datacenter (DC) systems whose performance depends on several design parameters, such as the topology, the switch architecture, and the routing algorithm.…
We consider a stable open queuing network as a steady non-equilibrium system of interacting particles. The network is completely specified by its underlying graphical structure, type of interaction at each node, and the Markovian transition…
Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…
This paper considers a multiclass processor-sharing queue with feedback. Jobs arrive according to renewal processes, and service times follow general distributions. Upon service completion, jobs may either depart the system or re-enter as a…
We study distributed load balancing in bipartite queueing systems where frontends route jobs to heterogeneous backends with workload-dependent service rates. The system's connectivity -- governed by compatibility constraints such as data…
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…