Related papers: On the Sojourn Time Distribution in a Finite Popul…
The model is motivated by the problem of load distribution in large-scale cloud-based data processing systems. We consider a heterogeneous service system, consisting of multiple large server pools. The pools are different in that their…
We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modelled as a stochastic process with a fat-tailed non-exponential distribution of waiting times, mimicking long-term…
We study a queueing network with a single shared server that serves the queues in a cyclic order. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the…
We consider maximizing the long-term average reward in a single server queue, where the reward obtained for a job is a non-increasing function of its sojourn time. The motivation behind this work comes from multiple applications, including…
We study the stationary sojourn time distribution in an M/G/1 queue operating under heavy traffic. It is known that the sojourn time converges to an exponential distribution in the limit. Our focus is on obtaining pre-asymptotic,…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
This paper studies the asymptotic behavior of the steady-state waiting time, W_infty, of the M/G/1 queue with subexponenential processing times for different combinations of traffic intensities and overflow levels. In particular, we provide…
Stochastic service systems describe situations in which customers compete for service from scarce resources. Think of check-in lines at airports, waiting rooms in hospitals or queues in supermarkets, where the scarce resource is human…
We investigate the long-run behavior of single-server queues with Hawkes arrivals and general service distributions and related optimization problems. In detail, utilizing novel coupling techniques, we establish finite moment bounds for the…
We consider a queue to which only a finite pool of $n$ customers can arrive, at times depending on their service requirement. A customer with stochastic service requirement $S$ arrives to the queue after an exponentially distributed time…
We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with nondegenerate slowdown. This regime is distinct from the well-studied heavy…
We consider the problem of efficiently simulating population protocols. In the population model, we are given a distributed system of $n$ agents modeled as identical finite-state machines. In each time step, a pair of agents is selected…
Frameworks, such as MapReduce and Hadoop are abundant nowadays. They seek to reap benefits of parallelization, albeit subject to a synchronization constraint at the output. Fork-Join (FJ) queuing models are used to analyze such systems.…
Given a growth rule which sequentially constructs random permutations of increasing degree, the stochastic process version of the rencontre problem asks what is the limiting proportion of time that the permutation has no fixed points…
Multiuser Multi-Packet Transmission (MPT) from an Access Point (AP) equipped with multiple antennas to multiple single-antenna nodes can be achieved by exploiting the spatial dimension of the channel. In this paper we present a queueing…
This report aims to characterise certain sojourn time distributions that naturally arise from semi-Markov models. To this end, it describes a family of discrete distributions that extend the geometric distribution for both finite and…
We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…
In the infinite servers queue with Poisson arrivals real life practical applications, the busy period and the busy cycle probabilistic study is of main importance. But it is a very difficult task. In this text, we show that by solving a…