On the infimum attained by a reflected L\'evy process

This paper considers a L\'evy-driven queue (i.e., a L\'evy process reflected at 0), and focuses on the distribution of $M(t)$, that is, the minimal value attained in an interval of length $t$ (where it is assumed that the queue is in stationarity at the beginning of the interval). The first contribution is an explicit characterization of this distribution, in terms of Laplace transforms, for spectrally one-sided L\'evy processes (i.e., either only positive jumps or only negative jumps). The second contribution concerns the asymptotics of \prob{M(T_u)> u} (for different classes of functions $T_u$ and $u$ large); here we have to distinguish between heavy-tailed and light-tailed scenarios

Low latency via redundancy

Low latency is critical for interactive networked applications. But while we know how to scale systems to increase capacity, reducing latency --- especially the tail of the latency distribution --- can be much more difficult. In this paper, we argue that the use of redundancy is an effective way to convert extra capacity into reduced latency. By initiating redundant operations across diverse resources and using the first result which completes, redundancy improves a system's latency even under exceptional conditions. We study the tradeoff with added system utilization, characterizing the situations in which replicating all tasks reduces mean latency. We then demonstrate empirically that replicating all operations can result in significant mean and tail latency reduction in real-world systems including DNS queries, database servers, and packet forwarding within networks

'I like money, I like many things'. The relationship between drugs and crime from the perspective of young people in contact with criminal justice systems

Based on research undertaken as part of the EU funded EPPIC project, this paper aims to update and elaborate on the relationship between drug use and offending behaviours by exploring variations within a cross-national sample of drug-experienced young people in touch with criminal justice systems. Adopting a trajectory-based approach, interviews were undertaken with 198 young people aged 15–25 in six European countries (Austria, Denmark, Germany, Italy, Poland, and UK). Data were analysed by applying the Bennett and Holloway categorization of the drugs-crime link, with a focus on the concept of social exclusion as developed by Seddon. Three main types of mechanisms (economic, pharmaceutical, and lifestyles) are used to interpret the data, showing how the relationship between drugs and offending can vary according to type of substances and over time. Furthermore, it can be associated with very different degrees of social exclusion and needs. The results suggest that while economic inequalities still play key roles in explaining drug use and offending, both behaviours can originate from a state of relative deprivation, resulting from the contradictions inherent in ‘bulimic societies’ that raise aspirations and desires while providing young people scarce opportunities for self-realisation and social recognition

Large deviations for a damped telegraph process

In this paper we consider a slight generalization of the damped telegraph process in Di Crescenzo and Martinucci (2010). We prove a large deviation principle for this process and an asymptotic result for its level crossing probabilities (as the level goes to infinity). Finally we compare our results with the analogous well-known results for the standard telegraph process

Implied volatility of basket options at extreme strikes

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function

Measurement-Adaptive Cellular Random Access Protocols

This work considers a single-cell random access channel (RACH) in cellular wireless networks. Communications over RACH take place when users try to connect to a base station during a handover or when establishing a new connection. Within the framework of Self-Organizing Networks (SONs), the system should self- adapt to dynamically changing environments (channel fading, mobility, etc.) without human intervention. For the performance improvement of the RACH procedure, we aim here at maximizing throughput or alternatively minimizing the user dropping rate. In the context of SON, we propose protocols which exploit information from measurements and user reports in order to estimate current values of the system unknowns and broadcast global action-related values to all users. The protocols suggest an optimal pair of user actions (transmission power and back-off probability) found by minimizing the drift of a certain function. Numerical results illustrate considerable benefits of the dropping rate, at a very low or even zero cost in power expenditure and delay, as well as the fast adaptability of the protocols to environment changes. Although the proposed protocol is designed to minimize primarily the amount of discarded users per cell, our framework allows for other variations (power or delay minimization) as well.Comment: 31 pages, 13 figures, 3 tables. Springer Wireless Networks 201