Related papers: Rare events in a polling system: Rays and Spirals
We study a single-lane traffic model that is based on human driving behavior. The outflow from a traffic jam self-organizes to a critical state of maximum throughput. Small perturbations of the outflow far downstream create emergent traffic…
Motivated by the growing interest in today's massive parallel computing capabilities we analyze a queueing network with many servers in parallel to which jobs arrive a according to a Poisson process. Each job, upon arrival, is split into…
The dynamics of pedestrian crowds has been studied intensively in recent years, both theoretically and empirically. However, in many situations pedestrian crowds are rather static, e.g. due to jamming near bottlenecks or queueing at ticket…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
This paper considers a parallel system of queues fed by independent arrival streams, where the service rate of each queue depends on the number of customers in all of the queues. Necessary and sufficient conditions for the stability of the…
We have introduced excluded volume effect, which is an important factor to model a realistic pedestrian queue, into queueing theory. The probability distributions of pedestrian number and pedestrian waiting time in a queue have been…
We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are inde- pendent and identically distributed. We call this the random scattering traffic model, and the…
We consider an ergodic process on finitely many states, with positive entropy. Our first main result asserts that the distribution function of the normalized waiting time for the first visit to a small (i.e., over a long block) cylinder set…
We calculate asymptotics of the distribution of the number of customers in orbit in a two-class priority retrial $M/G/1$-type queueing model. In this model, priority customers wait in line while non-priority customers join an orbit and…
We consider a service system with two Poisson arrival queues. A server chooses which queue to serve at each moment. Once a queue is served, all the customers will be served within a fixed amount of time. This model is useful in studying…
In the supermarket model, there are $n$ queues, each with a single server. Customers arrive in a Poisson process with arrival rate $\lambda n$, where $\lambda = \lambda (n) \in (0,1)$. Upon arrival, a customer selects $d=d(n)$ servers…
Motivated by applications such as urban traffic control and make-to-order systems, we study a fluid model of a single-server, on-off system that can accommodate multiple queues. The server visits each queue in order: when a queue is served,…
Upon arrival to a ticket queue, a customer is offered a slip of paper with a number on it and is told the number of the customer currently in service. The arriving customer then chooses whether to take the slip or balk, a decision based on…
This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…
To perform a queuing analysis or design in a communications context, we need to estimate the values of the input parameters, specifically the mean of the arrival rate and service time. In this paper, we propose an approach for estimating…
Elections involving a very large voter population often lead to outcomes that surprise many. This is particularly important for the elections in which results affect the economy of a sizable population. A better prediction of the true…
We study rare events in networks with both internal and external noise, and develop a general formalism for analyzing rare events that combines pair-quenched techniques and large-deviation theory. The probability distribution, shape, and…
We investigate in this paper the performance of a simple file sharing principle. For this purpose, we consider a system composed of N peers becoming active at exponential random times; the system is initiated with only one server offering…
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of…
In discrete time, customers arrive at random. Each waits until one of three servers is available; each thereafter departs at random. We seek the distribution of maximum line length of idle customers. Algebraic expressions obtained for the…