In this paper, we investigate and characterize the effects of multi-channel and rendezvous protocols on the connectivity of dynamic spectrum access networks using percolation theory. In particular, we focus on the scenario where the secondary nodes have plenty of vacant channels to choose from a phenomenon which we define as channel abundance. To cope with the existence of multi-channel, we use two types of rendezvous protocols: naive ones which do not guarantee a common channel and advanced ones which do. We show that, with more channel abundance, even with the use of either type of rendezvous protocols, it becomes difficult for two nodes to agree on a common channel, thereby, potentially remaining invisible to each other. We model this invisibility as a Poisson thinning process and show that invisibility is even more pronounced with channel abundance. Following the disk graph model, we represent the multiple channels as parallel edges in a graph and build a multi-layered graph (MLG) in R2. In order to study the connectivity, we show how percolation occurs in the MLG by coupling it with a typical discrete percolation. Using a Boolean model and the MLG, we study both cases of primaries' absence and presence. For both cases, we define and characterize connectivity of the secondary network in terms of the available number of channels, deployment densities, number of simultaneous transmissions per node, and communication range. When primary users are absent, we derive the critical number of channels which maintains supercriticality of the secondary network. When primary users are present, we characterize and analyze the connectivity for all the regions: channel abundance, optimal, and channel deprivation. For each region we show the requirement and the outcome of using either type of rendezvous techniques. Moreover, we find the tradeoff between deployment-density versus rendezvous probability which results in a connected network. Our results can be used to decide on the goodness of any channel rendezvous algorithm by computing the expected resultant connectivity. They also provide a guideline for achieving connectivity using minimal resources.
المقدمة
الحمد لله رب العالمين، وأفضل السلام وأتم التسليم على سيدنا محمد، وعلى آله وصحبه، أجمعين، وعلى من تبعهم بإحسان إلى يوم الدين، أما بعد.
فإن مسألة التعارض بين الرواية، والفتوى، من المسائل المشهورة عند الأصوليين والفقهاء،وهي من مباحث السنة عند الأصوليين، والتي تبنى عليها مسائل متعددة، وهي من أسباب اختلاف الفقهاء، فإذا ما روى أحد الرواة حديثاً معيناً، ثم عمل بخلاف ما روى، فللعل
... Show MoreDielectric measurements were carried on pure and doping potassium sulfate with copper and iron ions samples at 1wt.% and 3wt.% for both of copper and iron. The dielectric constant (ε') decreases exponentially from 2.8 to 1.5 as frequency increase for both dopant which is attributed to the space charge and structural distortion. The dielectric loss (ε") for Cu dopant decrease gradually with frequency. The same behavior for 1%Fe dopant while its 3%Fe doping started from 0.27 then decrease exponential. Band gaps for all samples almost constant around 6 eV.
This research addresses the relevance of men and women and the consequent provisions
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The paper is highlighting the athletics and heroic sports which encouraged and played at Greek and Islamic period. The paper is identifying the Islamic athletics and heroic sport and compare them with Greek sports, as it is the model of sports while the sport during the Islamic period was not undertaken by scientific researches or articles even in Wikipedia. Although, this period was encouraged and practice many sports such as archery, sword grappling and wrestling, equestrianism, jogging and running whereas there are many Arabic references revealed during the Islamic 610 A.D. while the Greek and Olympic was known at 732 A.D. The paper is followed the literature review and historical to shied a light scientifically about traditional sports
... Show MoreModern asphalt technology has adopted nanomaterials as an alternative option to assert that asphalt pavement can survive harsh climates and repeated heavy axle loading during service life and prolong pavement life. This work aims to elucidate the behavior of the modified asphalt mixture fracture model and assess the fatigue and Rutting performance of Hot Mix Asphalt (HMA) mixes using the outcomes of indirect Tensile Strength (IDT), Semicircular bend (SCB) and rutting resistance; for this, a single PG (64−16) nanomodified asphalt binder with 5 % SiO2 and TiO2 have been investigated through a series of laboratory tests, including: Resilient modulus, Creep compliance, and tensile strength, SCB, and Flow Number (FN) to study their potential
... Show MoreBoth religions have urged (honoring parents and kin) through the texts that came in their original sources, as honoring parents means showing respect to them In word and deed, and carrying in our hearts an appreciation for their status, and God commands to honor parents; Becausee this is Important in the eyes of God that he includeincludeed it in the Ten Commandmen.
The study aims to identify the bargaining differences between the governmental and private kindergarteners; the rivalry differences between the governmental and private kindergarteners; the rivalry and bargaining differences among private kindergarteners; and the rivalry and bargaining differences among governmental kindergarteners. The researchers had raised a question; is there any difference of rivalry and bargaining between governmental and private kindergarteners?. A total of (150) kindergarteners ranged from 5 to 6 years old, (90) student from governmental kindergarten and (60) student from private kindergarten, were selected as a sample of this study. Fifteen governmental and private kindergarten were chosen from al-rasafa directo
... Show MoreThe new media scene reveals that the unprecedented overlap of a number of technical, economic, and political factors has made the new media a very complicated issue; and the focus of specialized and public debates about its impact on traditional means of communication and forms of social media and social relations. Then, the same scene discloses the reality of the relationship between the new and the traditional. These are the axes that will be will be discussed in this study.
MS Elias, RGM AL-helfy, Plant Archives, 2019