A probabilistic analysis of a leader election algorithm

A {\em leader election} algorithm is an elimination process that divides recursively into tow subgroups an initial group of n items, eliminates one subgroup and continues the procedure until a subgroup is of size 1. In this paper the biased case is analyzed. We are interested in the {\em cost} of the algorithm, i.e. the number of operations needed until the algorithm stops. Using a probabilistic approach, the asymptotic behavior of the algorithm is shown to be related to the behavior of a hitting time of two random sequences on [0,1]

Stationary Distribution Analysis of a Queueing Model with Local Choice

The paper deals with load balancing between one-server queues on a circle by a local choice policy. Each one-server queue has a Poissonian arrival of customers. When a customer arrives at a queue, he joins the least loaded queue between this queue and the next one, ties solved at random. Service times have exponential distribution. The system is stable if the arrival-to-service rate ratio called load is less than one. When the load tends to zero, we derive the first terms of the expansion in this parameter for the stationary probabilities that a queue has 0 to 3 customers. We investigate the error, comparing these expansion results to numerical values obtained by simulations. Then we provide the asymptotics, as the load tends to zero, for the stationary probabilities of the queue length, for a fixed number of queues. It quantifies the difference between policies with this local choice, no choice and the choice between two queues chosen at random

The determinants of banking regulation in the MENA region

Theoretical foundations in banks\u27 response to capital settlement suggest that the systems proposed by Basel are not sound. It is conceivable that regulators will consider alternative approaches to enhance the safety and soundness of the banking system. The regulation includes several decrees and ratios; the areas of interest encompassing the areas are subject to principal component analysis (PCA).The paper aims to present a regulatory framework based on balance sheet ratios, such as Capital requirements (equity ratio; Tier 1 ratio; Total Equity/Net Loans; Total Equity/Deposits); for liquidity needs (liquidity/deposits; liquidity/total assets; liquidity/deposits and loans, and net loans/total assets); for leverage requirements (total liabilities/total assets; total assets/equity; and total liabilities/equity); also banking restriction index; Official supervision index; Private surveillance index, finally global index of regulations and supervision. Besides, it performs a PCA analysis on a set of 13 financial ratios to exploit and compare the financial characteristics of 239 banks (175 Conventional and 64 Islamic commercial banks) in the MENA region over a 2004-2015 period. This gives the main indices EXIGCP, EXIGLIQ, LEVCP, and LEVP

Dynamic Tree Algorithms

In this paper, a general tree algorithm processing a random flow of arrivals is analyzed. Capetanakis-Tsybakov-Mikhailov's protocol in the context of communication networks with random access is an example of such an algorithm. In computer science, this corresponds to a trie structure with a dynamic input. Mathematically, it is related to a stopped branching process with exogeneous arrivals (immigration). Under quite general assumptions on the distribution of the number of arrivals and on the branching procedure, it is shown that there exists a {\em positive} constant $\lambda_c$ so that if the arrival rate is smaller than $\lambda_c$, then the algorithm is stable under the flow of requests, i.e. that the total size of an associated tree is integrable. At the same time a gap in the earlier proofs of stability of the literature is fixed. When the arrivals are Poisson, an explicit characterization of $\lambda_c$ is given. Under the stability condition, the asymptotic behavior of the average size of a tree starting with a large number of individuals is analyzed. The results are obtained with the help of a probabilistic rewriting of the functional equations describing the dynamic of the system. The proofs use extensively this stochastic background throughout the paper. In this analysis, two basic limit theorems play a key role: the renewal theorem and the convergence to equilibrium of an auto-regressive process with moving average

A mean field analysis of a stochastic model for reservation in car-sharing systems

International audienceOver the past decade, vehicle-sharing systems have appeared as a new answer to mobility challenges, like reducing congestion or pollution for numerous cities. In this paper we analyze a simple homogeneous stochastic model for station-based car-sharing systems with one-way trips where users reserve the parking space when the car is picked up. In these systems, users arrive at a station, pick up a vehicle while reserve a parking space at a destination station, use it for a while and then return it at the reserved parking space. Each station has a finite capacity and cannot host more vehicles and reserved parking spaces than its capacity. If the user cannot pick up a car or reserve at destination, he leaves the system. For this model, the large scale behavior is investigated via mean field approach. We derive asymptotics of the empirical measure process when the number of cars and stations are large together, such that their ratio tends to a constant. This gives the limiting distribution of the state of a station as the solution of a differential equation, called the Fokker-Planck equation. Then the main result is that the equilibrium point, characterized using queuing theory, exists and is unique. The proof uses a monotonicity argument as for bike-sharing systems, but also needs implicit function theorem and combinatorial arguments. It allows to study the system performance in terms of large scale stationary proportion of empty and full stations, especially the influence of the fleet size. For the optimal fleet size, we give asymptotics for this quantity in light and heavy traffic. We prove that, in light traffic case, reservation has little impact, unlike the heavy traffic case

Analyzing a Bloom Filter Algorithm via a join-the-shortest-queue queuing system

This paper deals with the problem of identifying elephants in the Internet Traffic. The aim is to analyze a new adaptive algorithm based on a Bloom Filter. This algorithm uses a so-called min-rule which can be described as in the supermarket model. This model consists of joining the shortest queue among d queues selected at random in a large number of m queues. In case of equality, one of the shortest queues is chosen at random. An analysis of a simplified model gives an insight into the error generated by the algorithm for the estimation of the number of the elephants. The main conclusion is that, as m gets large, there is a deterministic limit for the empirical distribution of the filter counters. Limit theorems are proved and the limit is identified. It depends on key parameters. The condition for the algorithm to perform well is discussed. Theoretical results are validated by experiments on a trac trace from France Telecom and by simulations

Thymoquinone, the Nigella sativa Bioactive Compound, Prevents Circulatory Oxidative Stress Caused by 1,2-Dimethylhydrazine in Erythrocyte during Colon Postinitiation Carcinogenesis

We have performed this study to investigate the modulatory effect of thymoquinone (TQ), the Nigella sativa active compound, on erythrocyte lipid peroxidation and antioxidant status during 1,2-dimethylhydrazine- (DMH-) induced colon carcinogenesis after initiation in male Wistar rats. Rats exposed to DMH showed an increase of malondialdehyde and conjugated diene levels, and an augmentation of enzyme activities like catalase, glutathione peroxidase, and superoxide dismutase activities was also noted. The TQ pretreatment restored the parameters cited above to near-normal values. However, the posttreatment shows an activity similar as that presented by DMH. Therefore, our investigation revealed that TQ was a useful compound preventing DMH-induced erythrocyte damages

Stochastic Modelling of Free-Floating Car-Sharing Systems

Car-sharing systems (CSSs) have gained popularity during the last decade as a flexible, efficient and ecological alternative mode of transportation. But for the operator, managing such systems is far to be simple. Due to heterogeneity of demand and also randomness, the user may face a lack of resources: no car or no parking space available. And the operator has to design the system in order to improve it. The total number of cars impact the performance of the system. We address the dimensioning issue. For that, mathematical models are needed. In many cities, two systems coexist: station-based and free-floating. The latter gives more flexibility to the user both to take or return the car. But he can reserve only the car for a short period, and not the parking space, as the car is parked on public space with no specific parking spaces. The car reservation is here to help the user. The aim of the paper is to study its influence on the system behavior. This study focuses on Communauto's Montreal free-floating car-sharing system (FFCSS). Data analysis investigates the main features of the system based on user preferences. It allows proposing a mathematical modelling. Then we present two analytical approaches. First the mean-field method could be used for different variants, and w gives first insights on the optimal fleet size in a homogeneous framework. Second the general inhomogeneous model is described as a closed Jackson network with blocking-rerouting policy. We prove that its state at stationarity is given by a product-form distribution. It allows in future work to obtain an explicit large-scale representation of the system which can be used both theoretically or numerically for optimization purposes

Influence of the drought on antioxidant and enzymatic activities of two Pinus species in humid and sub-humid climate

Pinus genus is widespread in the Mediterranean region and the most common in Tunisia. The impact of high temperatures in the mid-summer period (July 2015 and July 2016) on phenols and biological properties were examined in vitro. The study was carried out in two arboreta, in humid and sub-humid climates, dry needles of Pinus pinea and Pinus pinaster were used for secondary metabolites, antioxidant activities, and enzymatic inhibitory activities. The amount of all measured parameters increased from 2015 to 2016 in the two pine species in the two arboreta. Pinus pinea produced more phenols and showed higher antioxidant activity and a-amylase and lipoxygenase inhibitory activities than Pinus pinaster. Besides, both species generally presented better biological activities and higher phenol amounts in 2016 than in 2015, being 2016 warmer and drier than 2015 in both harvest zones. It was evident that both species in every bioclimatic zones adapted to the new climate conditions producing more secondary metabolites that rendered better antioxidant and inhibitory enzymatic activities. These findings confirmed the impact of mid-summer water deficits on pine species in the context of climate change and help to select the most resistant species for future reforestation.info:eu-repo/semantics/publishedVersio