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 $G$, 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 $p_c^{BS}(G)$. Our main results imply that 1/(Delta+1) <= \leq p_c^{BS}(T_Delta) \leq 1/(Delta -1)$, and that$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