38 research outputs found
Analysis of Push-type Epidemic Data Dissemination in Fully Connected Networks
Consider a fully connected network of nodes, some of which have a piece of
data to be disseminated to the whole network. We analyze the following
push-type epidemic algorithm: in each push round, every node that has the data,
i.e., every infected node, randomly chooses other nodes
in the network and transmits, i.e., pushes, the data to them. We write this
round as a random walk whose each step corresponds to a random selection of one
of the infected nodes; this gives recursive formulas for the distribution and
the moments of the number of newly infected nodes in a push round. We use the
formula for the distribution to compute the expected number of rounds so that a
given percentage of the network is infected and continue a numerical comparison
of the push algorithm and the pull algorithm (where the susceptible nodes
randomly choose peers) initiated in an earlier work. We then derive the fluid
and diffusion limits of the random walk as the network size goes to
and deduce a number of properties of the push algorithm: 1) the number of newly
infected nodes in a push round, and the number of random selections needed so
that a given percent of the network is infected, are both asymptotically normal
2) for large networks, starting with a nonzero proportion of infected nodes, a
pull round infects slightly more nodes on average 3) the number of rounds until
a given proportion of the network is infected converges to a constant
for almost all . Numerical examples for theoretical results
are provided.Comment: 28 pages, 5 figure
Application of Stochastic Flows to the Sticky Brownian Motion Equation
We show how the theory of stochastic flows allows to recover in an elementary
way a well known result of Warren on the sticky Brownian motion equation
An optimal stopping problem for spectrally negative Markov additive processes
Previous authors have considered optimal stopping problems driven by the
running maximum of a spectrally negative L\'evy process , as well as of a
one-dimensional diffusion. Many of the aforementioned results are either
implicitly or explicitly dependent on Peskir's maximality principle. In this
article, we are interested in understanding how some of the main ideas from
these previous works can be brought into the setting of problems driven by the
maximum of a class of Markov additive processes (more precisely Markov
modulated L\'evy processes). Similarly to previous works in the L\'evy setting,
the optimal stopping boundary is characterised by a system of ordinary
first-order differential equations, one for each state of the modulating
component of the Markov additive process. Moreover, whereas scale functions
played an important role in the previously mentioned work, we work instead with
scale matrices for Markov additive processes here. We exemplify our
calculations in the setting of the Shepp-Shiryaev optimal stopping problem, as
well as a family of capped maximum optimal stopping problems.Comment: 31 page
MAPPING OF VEHICLE EMISSIONS IN ZONGULDAK PROVINCE
Increase in the rate of individual vehicle use and decrease in the usage habits of public transportation results in significant increase in traffic-related emissions. One of the most important factor among these is the number of vehicles that increases day by day especially in developing countries. In Zonguldak, the number of vehicles have also increased by 21% in the last five years. For that reason we focused on to determine the effects of urban transportation on air quality in the city center of Zonguldak/Turkey. The main objective of the study was to determine pollutant emissions in different parts of a highway and present it on emission maps. In this context, hourly vehicle counts were conducted at Zonguldak D010 highway in four zones in the coastal area. In addition, speed counts were carried out in the same zones. Emissions were calculated by the obtained data and IPCC guidance was used for these calculations. The IPCC guidelines include main headings such as energy, industrial processes, agriculture and waste. In this study, emission related data under the head of “energy” were used. Emission intensity maps for Zonguldak province were established by using the obtained values. The results of the study show that fuel consumption was the highest between 08:00 and 09:00 a.m. It decreases between 12:00 and 13:00 at noon and then tends to increase again between 18:00 and 19:00 p.m. Pollutant emissions were also higher in the morning and evening hours, depending on fuel consumption. In this study only the main arterial road was selected as study area. In future studies, by choosing whole road segments, the study area can be expanded and more accurate and reliable results can be obtained