2,532 research outputs found
Exact results for the Barabasi model of human dynamics
Human activity patterns display a bursty dynamics, with interevent times
following a heavy tailed distribution. This behavior has been recently shown to
be rooted in the fact that humans assign their active tasks different
priorities, a process that can be modeled as a priority queueing system [A.-L.
Barabasi, Nature 435, 207 (2005)]. In this work we obtain exact results for the
Barabasi model with two tasks, calculating the priority and waiting time
distribution of active tasks. We demonstrate that the model has a singular
behavior in the extremal dynamics limit, when the highest priority task is
selected first. We find that independently of the selection protocol, the
average waiting time is smaller or equal to the number of active tasks, and
discuss the asymptotic behavior of the waiting time distribution. These results
have important implications for understanding complex systems with extremal
dynamics.Comment: 4 pages, 4 figures, revte
Ambiguity, Weakness, and Regularity in Probabilistic B\"uchi Automata
Probabilistic B\"uchi automata are a natural generalization of PFA to
infinite words, but have been studied in-depth only rather recently and many
interesting questions are still open. PBA are known to accept, in general, a
class of languages that goes beyond the regular languages. In this work we
extend the known classes of restricted PBA which are still regular, strongly
relying on notions concerning ambiguity in classical omega-automata.
Furthermore, we investigate the expressivity of the not yet considered but
natural class of weak PBA, and we also show that the regularity problem for
weak PBA is undecidable
Exact results for the Barabasi queuing model
Previous works on the queuing model introduced by Barab\'asi to account for
the heavy tailed distributions of the temporal patterns found in many human
activities mainly concentrate on the extremal dynamics case and on lists of
only two items. Here we obtain exact results for the general case with
arbitrary values of the list length and of the degree of randomness that
interpolates between the deterministic and purely random limits. The
statistically fundamental quantities are extracted from the solution of master
equations. From this analysis, new scaling features of the model are uncovered
Convergence to the maximal invariant measure for a zero-range process with random rates
We consider a one-dimensional totally asymmetric nearest-neighbor zero-range
process with site-dependent jump-rates - an environment. For each environment p
we prove that the set of all invariant measures is the convex hull of a set of
product measures with geometric marginals. As a consequence we show that for
environments p satisfying certain asymptotic property, there are no invariant
measures concentrating on configurations with critical density bigger than
, a critical value. If is finite we say that there is
phase-transition on the density. In this case we prove that if the initial
configuration has asymptotic density strictly above , then the
process converges to the maximal invariant measure.Comment: 19 pages, Revised versio
Stationary distributions of multi-type totally asymmetric exclusion processes
We consider totally asymmetric simple exclusion processes with n types of
particle and holes (-TASEPs) on and on the cycle . Angel recently gave an elegant construction of the stationary measures
for the 2-TASEP, based on a pair of independent product measures. We show that
Angel's construction can be interpreted in terms of the operation of a
discrete-time queueing server; the two product measures correspond to
the arrival and service processes of the queue. We extend this construction to
represent the stationary measures of an n-TASEP in terms of a system of queues
in tandem. The proof of stationarity involves a system of n 1-TASEPs, whose
evolutions are coupled but whose distributions at any fixed time are
independent. Using the queueing representation, we give quantitative results
for stationary probabilities of states of the n-TASEP on , and
simple proofs of various independence and regeneration properties for systems
on .Comment: Published at http://dx.doi.org/10.1214/009117906000000944 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- âŠ