{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T09:22:58Z","timestamp":1648632178925},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,10,12]],"date-time":"2012-10-12T00:00:00Z","timestamp":1350000000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/2.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Wireless Com Network"],"published-print":{"date-parts":[[2012,12]]},"abstract":"Abstract<\/jats:title>\n \n Abstract<\/jats:title>\n In this article, we study the asymptotic behavior of flooding in large scale wireless networks. Specifically, we derive an upper bound on the coverage of flooding when the number of nodes n<\/jats:italic> in the network goes to infinity. We consider two different regimes of transmission radii: first, the case of constant transmission radius r<\/jats:italic> where the percentage of covered nodes scales as\n \n \n \n O<\/mml:mtext>\n (<\/mml:mo>\n n<\/mml:mi>\n \n \n r<\/mml:mi>\n <\/mml:mrow>\n \n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n \n \n e<\/mml:mi>\n <\/mml:mrow>\n \n \u2212<\/mml:mo>\n \n \n K<\/mml:mi>\n <\/mml:mrow>\n \n S<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n n<\/mml:mi>\n \n \n r<\/mml:mi>\n <\/mml:mrow>\n \n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mfenced>\n <\/mml:math>\n <\/jats:inline-formula> for a constant K<\/jats:italic>\n \n S<\/jats:italic>\n <\/jats:sub>> 0. In this case, as an important result, we observe that the percentage of covered nodes is upper bounded by a decreasing function, vanishing as the network size grows. Second, the case of vanishing r<\/jats:italic>\n \n n<\/jats:italic>\n <\/jats:sub>(i.e., r<\/jats:italic> decreases as n<\/jats:italic> increases) is considered where it is shown in the literature that the minimum value of r<\/jats:italic>\n \n n<\/jats:italic>\n <\/jats:sub>which maintains connectivity is\n \n \n \n \n \n log<\/mml:mo>\n n<\/mml:mi>\n \/<\/mml:mo>\n \u03a0<\/mml:mi>\n n<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msqrt>\n <\/mml:mrow>\n <\/mml:mfenced>\n <\/mml:math>\n <\/jats:inline-formula>. In this case, a coverage percentage of at most\n \n \n \n O<\/mml:mtext>\n (<\/mml:mo>\n \n \n n<\/mml:mi>\n <\/mml:mrow>\n \n \u2212<\/mml:mo>\n \n \n K<\/mml:mi>\n <\/mml:mrow>\n \n S<\/mml:mi>\n <\/mml:mrow>\n \n \u2032<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msubsup>\n <\/mml:mrow>\n <\/mml:msup>\n log<\/mml:mo>\n n<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mfenced>\n <\/mml:math>\n <\/jats:inline-formula> is expected for a constant value of\n \n \n \n \n \n K<\/mml:mi>\n <\/mml:mrow>\n \n S<\/mml:mi>\n <\/mml:mrow>\n \n \u2032<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msubsup>\n ><\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:mfenced>\n <\/mml:math>\n <\/jats:inline-formula>, leading to an infinite number of covered nodes. In such case, the rate at which the network coverage is decreased can be controlled and be considerably reduced by a proper choice of network parameters (\n \n \n \n \n \n K<\/mml:mi>\n <\/mml:mrow>\n \n S<\/mml:mi>\n <\/mml:mrow>\n \n \u2032<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msubsup>\n <\/mml:mrow>\n <\/mml:mfenced>\n <\/mml:math>\n <\/jats:inline-formula>). Consequently, this result shows that flooding is a suitable strategy even for large networks.<\/jats:p>\n <\/jats:sec>","DOI":"10.1186\/1687-1499-2012-312","type":"journal-article","created":{"date-parts":[[2012,10,12]],"date-time":"2012-10-12T16:14:15Z","timestamp":1350058455000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Asymptotic analysis of flooding in CSMA-based large scale ad-hoc wireless networks"],"prefix":"10.1186","volume":"2012","author":[{"given":"Hamed","family":"Shah-Mansouri","sequence":"first","affiliation":[]},{"given":"Babak Hossein","family":"Khalaj","sequence":"additional","affiliation":[]},{"given":"Seyed Pooya","family":"Shariatpanahi","sequence":"additional","affiliation":[]},{"given":"Javier Del","family":"Ser","sequence":"additional","affiliation":[]},{"given":"Susana","family":"P\u00e9rez-S\u00e1nchez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,10,12]]},"reference":[{"key":"511_CR1","volume-title":"ACM MOBICOM conference","author":"S Ni","year":"1999","unstructured":"Ni S, Tseng Y, Chen Y, Sheu J: The broadcast storm problem in a mobile ad hoc network, vol. 1. 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