Related papers: Random Permutations and Queues
The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The…
Supermarket models with different servers become a key in modeling resource management of stochastic networks, such as, computer networks, manufacturing systems and transportation networks. While these different servers always make analysis…
We determine a set of permutation patterns $q$ so that the number of permutations with $r$ occurrences of $q$ is asymptotically $n^r$ times the number of permutations avoiding $q$, partially settling a conjecture of Conway and Guttman. We…
We consider the stochastic ranking process with space-time dependent jump rates for the particles. The process is a simplified model of the time evolution of the rankings such as sales ranks at online bookstores. We prove that the joint…
Progressive quenching (PQ) is the stochastic process in which the system's degrees of freedom are sequentially fixed. While such process does not satisfy the local detailed balance, it has been found that the some physical observable of a…
Hidden Markov chains are widely applied statistical models of stochastic processes, from fundamental physics and chemistry to finance, health, and artificial intelligence. The hidden Markov processes they generate are notoriously…
In this paper we consider the problem of maximum throughput for tandem queueing system. We modeled this system as a Quasi-Birth-Death process. In order to do this we named level the number of customers waiting in the first buffer (including…
We study scaling limits of random permutations ("permutons") constrained by having fixed densities of a finite number of patterns. We show that the limit shapes are determined by maximizing entropy over permutons with those constraints. In…
Subordinating a random walk to a renewal process yields a continuous time random walk (CTRW) model for diffusion, including the possibility of anomalous diffusion. Transition densities of scaling limits of power law CTRWs have been shown to…
Exclusion processes became paradigmatic models of nonequilibrium interacting particle systems of wide range applicability both across the natural and the applied, social and technological sciences. Usually they are defined as a…
We study an admissions control problem, where a queue with service rate $1-p$ receives incoming jobs at rate $\lambda\in(1-p,1)$, and the decision maker is allowed to redirect away jobs up to a rate of $p$, with the objective of minimizing…
In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in…
For the M/M/1+M model at the law-of-large-numbers scale, the long run reneging count per unit time does not depend on the individual (i.e., per customer) reneging rate. This paradoxical statement has a simple proof. Less obvious is a large…
In this lecture we present an overview of the physics of irreversible fractal growth process, with particular emphasis on a class of models characterized by {\em quenched disorder}. These models exhibit self-organization, with critical…
This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite cycle graph. The model can be regarded as a reinforced urn model with graph-based interactions. It is motivated…
We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…
We consider the $M/G/1$ queue with a processor sharing server. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, as well as the unconditional distribution, in various asymptotic limits.…
The embedding problem of Markov transition matrices into continuous-time Markov semigroups is a classic problem that regained a lot of impetus and activities in recent years. We consider it here for the following generalisation of the…
We study a stochastic scheduling on an unreliable machine with general up-times and general set-up times which is described by a group of partial differential equations with Dirac-delta functions in the boundary and initial conditions. In…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…