Related papers: Random Permutations and Queues

We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…

Define the non-overlapping return time of a random process to be the number of blocks that we wait before a particular block reappears. We prove a Central Limit Theorem based on these return times. This result has applications to entropy…

For a widely used hub-and-spoke closed product-form network consisting of an infinite-server node and several single-server queues, we characterize the maximum queue-length distribution in various operational regimes by leveraging a novel…

We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…

Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the…

We consider the problem of selfish agents in discrete-time queuing systems, where competitive queues try to get their packets served. In this model, a queue gets to send a packet each step to one of the servers, which will attempt to serve…

We consider a Markovian evolution on point processes, the $\Psi$--process, on the unit interval in which points are added according to a rule that depends only on the spacings of the existing point configuration. Having chosen a spacing, a…

Consider the continuous-time Markov Branching Process. In critical case we consider a situation when the generating function of intensity of transformation of particles has the infinite second moment, but its tail regularly varies in sense…

We consider an infinite server queue where the arrival and the service rates are both modulated by a stochastic environment governed by an $S$-valued stochastic process $X$ that is ergodic with a limiting measure $\pi\in \mathcal{P}(S)$.…

Proper management of resources whose arrival and consumption are subject to environmental randomness is an intrinsic process in both natural and artificial systems. This phenomenon can be modeled as a queuing process whose arrival…

We consider a non-conserving zero-range process with hopping rate proportional to the number of particles at each site. Particles are added to the system with a site-dependent creation rate, and removed from the system with a uniform…

The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…

We consider a finite population processor-sharing (PS) queue, with Markovian arrivals and an exponential server. Such a queue can model an interactive computer system consisting of a bank of terminals in series with a central processing…

We consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive…

This paper attempts to find out numerically the distribution of the queue-length ratio in the context of a model of preferential attachment. Here we consider two restaurants only and a large number of customers (agents) who come to these…

We study the rare event behavior of the workload process in a transitory queue, where the arrival epochs (or points) of a finite number of jobs are assumed to be the ordered statistics of independent and identically distributed (i.i.d.)…

We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to…

In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends…

We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…