Related papers: The diffusion approximation of the Multiclass Proc…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump)…
We compare different approximations for the wait time in distribution networks, in which all warehouses use an (R,Q)-order policy. Reporting on the results of extensive computational experiments, we evaluate the quality of several…
Join-the-Shortest-Queue (JSQ) is the scheduling policy of choice for many network providers, cloud servers and traffic management systems, where individual queues are served under processor sharing (PS) queueing discipline. A numerical…
We consider the processor sharing $M/M/1$-PS queue which also models balking. A customer that arrives and sees $n$ others in the system "balks" (i.e., decides not to enter) with probability $1-b_n$. If $b_n$ is inversely proportional to…
Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…
These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…
Polling systems have been widely studied, however most of these studies focus on polling systems with renewal processes for arrivals and random variables for service times. There is a need driven by practical applications to study polling…
These days enterprise applications try to integrate online processing and batch jobs into a common software stack for seamless monitoring and driverless operations. Continuous integration of these systems results in choking of the poorly…
We consider a single server queue which has a threshold to change its arrival process and service speed by its queue length, which is referred to as a two-level single server queue. This model is motivated by an energy saving problem for a…
We consider a content-caching system thatis shared by a number of proxies. The cache could belocated in an edge-cloud datacenter and the proxies couldeach serve a large population of mobile end-users. Eachproxy operates its own LRU-list of…
Discriminatory Processor Sharing policy introduced by Kleinrock is of a great interest in many application areas, including telecommunications, web applications and TCP flow modelling. Under the DPS policy the job priority is controlled by…
We are given a set of jobs, each one specified by its release date, its deadline and its processing volume (work), and a single (or a set of) speed-scalable processor(s). We adopt the standard model in speed-scaling in which if a processor…
We study a single server queue under a processor-sharing type of scheduling policy, where the weights for determining the sharing are given by functions of each job's remaining service(processing) amount, and obtain a fluid limit for the…
We consider a large-scale parallel-server system, where each server independently adjusts its processing speed in a decentralized manner. The objective is to minimize the overall cost, which comprises the average cost of maintaining the…
Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…
Resource allocation is the problem that a process may enter a critical section CS of its code only when its resource requirements are not in conflict with those of other processes in their critical sections. For each execution of CS, these…
Master-worker distributed computing systems use task replication in order to mitigate the effect of slow workers, known as stragglers. Tasks are grouped into batches and assigned to one or more workers for execution. We first consider the…
Work sharing and work stealing are two scheduling paradigms to redistribute work when performing distributed computations. In work sharing, processors attempt to migrate pending jobs to other processors in the hope of reducing response…
A multi-class single-server system with general service time distributions is studied in a moderate deviation heavy traffic regime. In the scaling limit, an optimal control problem associated with the model is shown to be governed by a…