20 research outputs found
A large-deviations analysis of the GI/GI/1 SRPT queue
We consider a GI/GI/1 queue with the shortest remaining processing time
discipline (SRPT) and light-tailed service times. Our interest is focused on
the tail behavior of the sojourn-time distribution. We obtain a general
expression for its large-deviations decay rate. The value of this decay rate
critically depends on whether there is mass in the endpoint of the service-time
distribution or not. An auxiliary priority queue, for which we obtain some new
results, plays an important role in our analysis. We apply our SRPT-results to
compare SRPT with FIFO from a large-deviations point of view.Comment: 22 page
Bounds for avalanche critical values of the Bak-Sneppen model
We study the Bak-Sneppen model on locally finite transitive graphs , in
particular on Z^d and on T_Delta, the regular tree with common degree Delta. We
show that the avalanches of the Bak-Sneppen model dominate independent site
percolation, in a sense to be made precise. Since avalanches of the Bak-Sneppen
model are dominated by a simple branching process, this yields upper and lower
bounds for the so-called avalanche critical value . Our main
results imply that 1/(Delta+1) <= \leq p_c^{BS}(T_Delta) \leq 1/(Delta -1)1/(2d+1)\leq p_c^{BS}(Z^d)\leq 1/(2d)+ 1/(2d)^2+O(d^{-3}), as
d\to\infty.Comment: 19 page
The effect of service time variability on maximum queue lengths in M^X/G/1 queues
We study the impact of service-time distributions on the distribution of the
maximum queue length during a busy period for the M^X/G/1 queue. The maximum
queue length is an important random variable to understand when designing the
buffer size for finite buffer (M/G/1/n) systems. We show the somewhat
surprising result that for three variations of the preemptive LCFS discipline,
the maximum queue length during a busy period is smaller when service times are
more variable (in the convex sense).Comment: 12 page
On Lossless Compression of 1-bit Audio Signals
In this paper we consider the problem of lossless compression of 1-bit audio signals. We study the properties of some existing proposed solutions. We also discuss possible improvements. Other methods have been considered, and the results are reported
Selection effects in forensic science
In this report we consider the following question: does a forensic expert need to know exactly how the evidential material was selected? We set up a few simple models of situations in which the way evidence is selected may influence its value in court. Although reality is far from a probabilistic model, and one should be very careful when applying theoretical results to real life situations, we believe that the results in our models indicate how the selection of evidence affects its value. We conclude that selection effects in forensic science can be quite important, and that from a statistical point of view, improvements can be made to court room practice
Math saves the forest
Wireless sensor networks are decentralised networks consisting of sensors that can detect events and transmit data to neighbouring sensors. Ideally, this data is eventually gathered in a central base station. Wireless sensor networks have many possible applications. For example, they can be used to detect gas leaks in houses or fires in a forest.\ud
In this report, we study data gathering in wireless sensor networks with the objective of minimising the time to send event data to the base station. We focus on sensors with a limited cache and take into account both node and transmission failures. We present two cache strategies and analyse the performance of these strategies for specific networks. For the case without node failures we give the expected arrival time of event data at the base station for both a line and a 2D grid network. For the case with node failures we study the expected arrival time on two-dimensional networks through simulation, as well as the influence of the broadcast range