Accuracy of state space collapse for earliest-deadline-first Queues

This paper presents a second-order heavy traffic analysis of a single server queue that processes customers having deadlines using the earliest-deadline-first scheduling policy. For such systems, referred to as real-time queueing systems, performance is measured by the fraction of customers who meet their deadline, rather than more traditional performance measures, such as customer delay, queue length or server utilization. To model such systems, one must keep track of customer lead times (the time remaining until a customer deadline elapses) or equivalent information. This paper reviews the earlier heavy traffic analysis of such systems that provided approximations to the system's behavior. The main result of this paper is the development of a second-order analysis that gives the accuracy of the approximations and the rate of convergence of the sequence of real-time queueing systems to its heavy traffic limit.Comment: Published at http://dx.doi.org/10.1214/105051605000000809 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Earliest-deadline-first service in heavy-traffic acyclic networks

This paper presents a heavy traffic analysis of the behavior of multi-class acyclic queueing networks in which the customers have deadlines. We assume the queueing system consists of J stations, and there are K different customer classes. Customers from each class arrive to the network according to independent renewal processes. The customers from each class are assigned a random deadline drawn from a deadline distribution associated with that class and they move from station to station according to a fixed acyclic route. The customers at a given node are processed according to the earliest-deadline-first (EDF) queue discipline. At any time, the customers of each type at each node have a lead time, the time until their deadline lapses. We model these lead times as a random counting measure on the real line. Under heavy traffic conditions and suitable scaling, it is proved that the measure-valued lead-time process converges to a deterministic function of the workload process

Gaussian approximations to service problems : a communication system example

Messages arrive at a group of service channels in accordance with a time-dependent Poisson process. An arrival either (1) immediately begins k-stage Markovian service if an empty channel is reached, or (2) balks and enters a retrial population if the channel sought is busy. Diffusion approximations to the number of messages in service (each stage) and in the retrial population are derived by writing stochastic differential (I+0) equations. Steady-state distributions are found and compared with certain simulation resultssupported in part by the National Science Foundation, Grant AG46 7, at the Naval Postgraduate School, and the Air Force Office of Scientific Research, Grant AFOSR74-2642, at Carnegie Mellon University.http://archive.org/details/gaussianapproxim00gaveN

Second order approximation for the customer time in queue distribution under the FIFO service discipline

A single server with one customer class, serviced by the FIFO protocol, is considered and the instantaneous time in the queue profile of the customers is investigated. We provide the second order approximation for the random measure describing the customer time in the queue distribution under heavy traffic conditions

Use of beneficial bacteria and their secondary metabolites to control grapevine pathogen diseases

Grapevine is one of the most important economic crops yielding berries, wine products as well as derivates. However, due to the large array of pathogens inducing diseases on this plant, considerable amounts of pesticides—with possible negative impact on the environment and health—have been used and are currently used in viticulture. To avoid negative impacts of such products and to ensure product quality, a substantial fraction of pesticides needs to be replaced in the near future. One solution can be related to the use of beneficial bacteria inhabiting the rhizo- and/or the endosphere of plants. These biocontrol bacteria and their secondary metabolites can reduce directly or indirectly pathogen diseases by affecting pathogen performance by antibiosis, competition for niches and nutrients, interference with pathogen signaling or by stimulation of host plant defenses. Due to the large demand for biocontrol of grapevine diseases, such biopesticides, their modes of actions and putative consequences of their uses need to be described. Moreover, the current knowledge on new strains from the rhizo- and endosphere and their metabolites that can be used on grapevine plants to counteract pathogen attack needs to be discussed. This is in particular with regard to the control of root rot, grey mould, trunk diseases, powdery and downy mildews, pierce’s disease, grapevine yellows as well as crown gall. Future prospects on specific beneficial microbes and their secondary metabolites that can be used as elicitors of plant defenses and/or as biocontrol agents with potential use in a more sustainable viticulture will be further discussed

Initial sequencing and analysis of the human genome

The human genome holds an extraordinary trove of information about human development, physiology, medicine and evolution. Here we report the results of an international collaboration to produce and make freely available a draft sequence of the human genome. We also present an initial analysis of the data, describing some of the insights that can be gleaned from the sequence.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62798/1/409860a0.pd

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead