On the optimality of field-line routing in massively dense wireless multi-hop networks

We consider the load balancing problem in large wireless multi-hop networks by applying the continuum approximation. The task is to find routes, geometric curves, such that the maximal traffic load in the network is minimized. In finite fixed networks, multi-path routes generally yield a lower congestion and thus allow higher throughput. In contrast, we show that in dense wireless multi-hop networks, the optimal load balancing can be achieved by a destination based single-path routing referred to as field-line routing. This is because any routing can be transformed to the corresponding field-line routing with the same or better performance, by using as paths, the field lines of the so-called destination flow associated with the original routing. The concepts are illustrated with two examples. In the case of a unit disk with unit traffic, the maximal load of 0.389 of a multi-path routing system is reduced to 0.343 by using the field-line routing. Similar improvements are also demonstrated for the unit square.     

Random waypoint mobility model in cellular networks

In this paper we study the so-called random waypoint (RWP) mobility model in the context of cellular networks. In the RWP model the nodes, i.e., mobile users, move along a zigzag path consisting of straight legs from one waypoint to the next. Each waypoint is assumed to be drawn from the uniform distribution over the given convex domain. In this paper we characterise the key performance measures, mean handover rate and mean sojourn time from the point of view of an arbitrary cell, as well as the mean handover rate in the network. To this end, we present an exact analytical formula for the mean arrival rate across an arbitrary curve. This result together with the pdf of the node location, allows us to compute all other interesting measures. The results are illustrated by several numerical examples. For instance, as a straightforward application of these results one can easily adjust the model parameters in a simulation so that the scenario matches well with, e.g., the measured sojourn times in a cell.     

Intake of fatty acids and risk of coronary heart disease in a cohort of Finnish men. The Alpha-Tocopherol, Beta-Carotene Cancer Prevention Study

The relation of intakes of specific fatty acids and the risk of coronary heart disease was examined in a cohort of 21,930 smoking men aged 50-69 years who were initially free of diagnosed cardiovascular disease. All men participated in the Finnish Alpha-Tocopherol, Beta-Carotene Cancer Prevention Study and completed a detailed and validated dietary questionnaire at baseline. After 6.1 years of follow-up from 1985-1988, the authors documented 1,399 major coronary events and 635 coronary deaths. After controlling for age, supplement group, several coronary risk factors, total energy, and fiber intake, the authors observed a significant positive association between the intake of trans-fatty acids and the risk of coronary death. For men in the top quintile of trans-fatty acid intake (median = 6.2 g/day), the multivariate relative risk of coronary death was 1.39 (95% confidence interval (CI) 1.09-1.78) (p for trend = 0.004) as compared with men in the lowest quintile of intake (median = 1.3 g/day). The intake of omega-3 fatty acids from fish was also directly related to the risk of coronary death in the multivariate model adjusting also for trans-saturated and cis-monounsaturated fatty acids (relative risk (RR) = 1.30, 95% CI 1.01-1.67) (p for trend = 0.06 for men in the highest quintile of intake compared with the lowest). There was no association between intakes of saturated or cis-monounsaturated fatty acids, linoleic or linolenic acid, or dietary cholesterol and the risk of coronary deaths. All the associations were similar but somewhat weaker for all major coronary events.     

The superposition of periodic cell arrival streams in an ATMmultiplexer

The authors consider the queue arising in a multiservice network using ATM (asynchronous transfer mode) when a superposition of periodic streams of constant-length cells is multiplexed on a high-speed link. An exact closed formula is derived for the queue length distribution in the case where all streams have the same period, and tight upper and lower bounds are obtained on this distribution when the periods are different. Numerical results confirm that the use of a Poisson approximation (i.e. the M/D/1 queue) can lead to a significant overestimation of buffer requirements, particularly in the case of heavy loads. Buffer requirements for a mixture of different period streams can be accurately estimated from the upper bound on the queue length distribution. For given load, requirements increase with the number of long-period (i.e. low-bit rate) sources. The results are deduced from a novel characterization of the single-server constant service time queue, which should be useful in other applications     

The effect of alpha-tocopherol and beta-carotene supplementation on COPD symptoms

The effects of alpha-tocopherol (50 mg/d) and beta-carotene (20 mg/d) supplementation on symptoms of chronic obstructive pulmonary disease were studied among the 29,133 participants of the Alpha-Tocopherol Beta-Carotene Cancer Prevention Study undertaken to investigate the effects of these two substances in the prevention of lung and other cancers. During the follow-up the supplementations did not affect the recurrence or incidence of chronic cough, phlegm, or dyspnea. The prevalence of chronic bronchitis and dyspnea at baseline was lower among those with high dietary intake of beta-carotene (OR = 0.78 and 0.67, respectively) or vitamin E (OR = 0.87 and 0.77) and high serum beta-carotene (OR = 0.59 and 0.62) and alpha-tocopherol (OR = 0.76 and 0.82). High intake and serum levels of retinol were associated with low prevalence of dyspnea (OR = 0.84 and 0.80, respectively) but not with chronic bronchitis. The results indicate no benefit from supplementation with alpha-tocopherol or beta-carotene on the symptoms of chronic obstructive pulmonary disorders but support the beneficial effect of dietary intake of fruits and vegetables rich in these compounds.     

Spatial node distribution of the random waypoint mobility model with applications

The random waypoint model (RWP) is one of the most widely used mobility models in performance analysis of ad hoc networks. We analyze the stationary spatial distribution of a node moving according to the RWP model in a given convex area. For this, we give an explicit expression, which is in the form of a one-dimensional integral giving the density up to a normalization constant. This result is also generalized to the case where the waypoints have a nonuniform distribution. As a special case, we study a modified RWP model, where the waypoints are on the perimeter. The analytical results are illustrated through numerical examples. Moreover, the analytical results are applied to study certain performance aspects of ad hoc networks, namely, connectivity and traffic load distribution.     

Effect of vitamin E and beta carotene on the incidence of primary nonfatal myocardial infarction and fatal coronary heart disease

BACKGROUND: Oxidized low-density lipoprotein is involved in the pathogenesis of atherosclerosis. In epidemiological studies antioxidants have been inversely related with coronary heart disease. Findings from controlled trials are inconclusive. METHODS: We studied the primary preventive effect of vitamin E (alpha tocopherol) and beta carotene supplementation on major coronary events in the Alpha-Tocopherol, Beta-Carotene Cancer Prevention Study, a controlled trial undertaken primarily to examine the effects of these agents on cancer. A total of 27 271 Finnish male smokers aged 50 to 69 years with no history of myocardial infarction were randomly assigned to receive vitamin E (50 mg), beta carotene (20 mg), both agents, or placebo daily for 5 to 8 years (median, 6.1 years). The end point was the first major coronary event, either nonfatal myocardial infarction (surviving at least 28 days; n = 1204) or fatal coronary heart disease (n = 907). RESULTS: The incidence of primary major coronary events decreased 4% (95% confidence interval, -12% to 4%) among recipients of vitamin E and increased 1% (95% confidence interval, -7% to 10%) among recipients of beta carotene compared with the respective nonrecipients. Neither agent affected the incidence of nonfatal myocardial infarction. Supplementation with vitamin E decreased the incidence of fatal coronary heart disease by 8% (95% confidence interval, -19% to 5%), but beta carotene had no effect on this end point. CONCLUSIONS: Supplementation with a small dose of vitamin E has only marginal effect on the incidence of fatal coronary heart disease in male smokers with no history of myocardial infarction, but no influence on nonfatal myocardial infarction. Supplementation with beta carotene has no primary preventive effect on major coronary events.     

A model of reservation systems

The author considers the performance evaluation of an advanced capacity reservation system using the CCITT defined reserved call establishment mode. A simple model for the traffic process is introduced: calls are assumed to be offered uniformly to the reservation book. The state of the system can then be described statistically in terms of the population of various types of islands of free time slots. The limit where the length of the reservation book tends to infinity is, in particular, considered. For single-server systems with a deterministic holding time of one or two time slots, a closed-form solution is found. For a general holding time distribution, an asymptotic analytical solution is derived and corrections to this asymptotic solution are calculated numerically. For multiserver systems with geometric holding time distribution, the author presents numerical results obtained by simulations. An interpolation formula valid for all traffic intensities is developed. A procedure is given to extrapolate the results to larger systems than were actually simulated     

Flow-optimized random access for wireless multihop networks

We study elastic traffic performance in time-slotted wireless random access networks, where the link access probabilities are adjusted at flow level each time a new flow (file transfer) arrives or a flow in progress terminates. By defining the capacity sets of such networks we carry out performance analysis in a dynamic setting, where the flows come and go and share the resources according to the balanced fairness principle. We derive flow throughput analytically for three special scenarios and devise an algorithm for general networks. At low loads, flow-optimized random access yields almost the same performance as optimal/deterministic scheduling.     

The superposition of variable bit rate sources in an ATMmultiplexer

When variable-bit-rate sources are multiplexed in an asynchronous transfer mode (ATM) network, there arise queues with a particular form of correlated arrival process. Such queues are analyzed by exploiting a result expressing the distribution of work in system of the G/G/1 queue originally derived by V.E. Benes (1963). A simple alternative demonstration of this result is analyzed and extended to the case of fluid input systems. The result is applied first to a queue where the arrival process is a superposition of periodic sources (the Σ D_i/D/1 queue), and then to a variable-input-rate constant-output-rate fluid system. The latter is shown to model the so-called burst component of the considered superposition queuing process. The difference between this and the real queue, the cell component, can be evaluated by means of the results obtained for the Σ D_i/D/1 queue. The relative importance of these two components is explored with reference to the particular case of a superposition of on/off sources