TY - JOUR AU - Sultana, Basra AU - Khandker, Mamun-ur-Rashid PY - 2008/12/20 Y2 - 2024/03/29 TI - On Number of Planes of Rearrangeably Nonblocking Optical Banyan Networks with Link Failures JF - Journal of Scientific Research JA - J. Sci. Res. VL - 1 IS - 1 SE - Section A: Physical and Mathematical Sciences DO - 10.3329/jsr.v1i1.1070 UR - https://banglajol.info/index.php/JSR/article/view/1070 SP - 43-54 AB - <span style="font-size: 9pt; font-family: "><p class="MsoNormal" style="margin: 0cm 17.85pt 0pt; text-align: justify;"><span style="font-family: Times New Roman;"><span style="font-size: 9pt; color: #000000;">Vertically stacked optical banyan (VSOB) networks are attractive for serving as optical switching systems due to the desirable properties (such as the small depth and self-routing capability) of banyan network structures. Although banyan-type networks result in<strong> </strong>severe blocking and crosstalk, both these problems can be minimized by using sufficient number of banyan planes in the VSOB network structure. The number of banyan planes is minimum for rearrangeably nonblocking and maximum for strictly nonblocking<strong> </strong>structure. Both results are available for VSOB networks when there exist no internal link-failures. Since the issue of link-failure is unavoidable, we intend to find the minimum number of planes required to make a VSOB network nonblocking when some links are broken or failed in the structure. This paper presents the approximate number of planes required to make a VSOB networks rearrangeably nonblocking allowing link-failures. We also show an interesting behavior of the<span style="mso-spacerun: yes;">  </span>blocking<span style="mso-spacerun: yes;">  </span>probability of a faulty VSOB networks that the blocking probability may not<span style="mso-spacerun: yes;">  </span>always<span style="mso-spacerun: yes;">  </span>increase monotonously with<span style="mso-spacerun: yes;">  </span>the<span style="mso-spacerun: yes;">  </span>increase<span style="mso-spacerun: yes;">  </span>of<span style="mso-spacerun: yes;">  </span>link-failures; blocking probability<span style="mso-spacerun: yes;">  </span>decreases<span style="mso-spacerun: yes;">  </span>for<span style="mso-spacerun: yes;">  </span>certain range of<span style="mso-spacerun: yes;">  </span>link-failures, and then increases again. We believe that such fluctuating behavior of blocking probability with the increase of link failure probability deserves special attention in switch design</span><span style="font-size: 9pt; mso-bidi-font-weight: bold;" lang="EN-US">. </span></span></p><p class="MsoNormal" style="margin: 0cm 17.85pt 0pt 14.2pt; text-align: justify;"><em style="mso-bidi-font-style: normal;"><span style="font-size: 4pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 9.0pt;" lang="EN-US"><span style="font-family: Times New Roman;"> </span></span></em></p><p class="MsoNormal" style="margin: 0cm 17.85pt 0pt 14.2pt; text-align: justify;"><span style="font-family: Times New Roman;"><em style="mso-bidi-font-style: normal;"><span style="font-size: 9pt; mso-bidi-font-weight: bold;" lang="EN-US">Keywords: </span></em><span style="font-size: 9pt; mso-bidi-font-weight: bold;" lang="EN-US">Banyan networks; Blocking probability; Switching networks; Vertical stacking; Link-failures.</span></span></p><p class="MsoNormal" style="margin: 0cm 17.85pt 0pt 14.2pt; text-align: justify;"><span style="font-size: 6pt; mso-bidi-font-weight: bold; mso-bidi-font-size: 9.0pt;" lang="EN-US"><span style="font-family: Times New Roman;"> </span></span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt 14.2pt; text-align: justify; mso-layout-grid-align: none;"><span style="font-size: 8pt; mso-ansi-language: EN-SG; mso-fareast-language: EN-SG;"><span style="font-family: Times New Roman;">©</span></span><span style="font-size: 8pt; font-family: Symbol;"> </span><span style="font-size: 8pt; mso-ansi-language: EN-SG; mso-fareast-language: EN-SG;"><span style="font-family: Times New Roman;">2009 JSR Publications. ISSN: 2070-0237(Print); 2070-0245 (Online). All rights reserved.</span></span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt 14.2pt; mso-layout-grid-align: none;"><span style="font-size: 2pt; mso-ansi-language: EN-SG; mso-fareast-language: EN-SG; mso-bidi-font-size: 8.0pt;"><span style="font-family: Times New Roman;"> </span></span></p><p class="MsoNormal" style="margin: 0cm 0cm 0pt 14.2pt; text-align: justify;"><span style="font-size: 8pt; mso-ansi-language: EN-SG; mso-fareast-language: EN-SG;"><span style="font-family: Times New Roman;">DOI: 10.3329/jsr.v1i1.1070</span></span></p></span> ER -