General Load Under The Double Star Lan Mathematical Modeling Study

Generally, there is only one channel in star-LAN named single-star LAN, while multi-star LAN has more than one channels. Multi-star LAN can be considered consisting of several single star-LANs.The working principle of Multi-star LAN has been reported in some literature. During the research in multi-star LAN, a new famous media access mode named the contention-collision cancellation access mode (abbreviated as C-CC) has been presented. According to the different situations of customers requesting for service, re-requesting for service, and being served, the system model of C-CC can be classified as six types. The C-CC mode is very useful for the establishment of the standard access mode of star-LAN, which attracts more and more contention. At present, the studies about C-CC of the Ist, IInd, IIIrd, IVth, Vth types have been finished, which undoubtedly help develop the star LAN. But we can notice that, in order to make mathematical modeling and resolution of C-CC, papers published mostly deal with multi-star LAN as single-star LAN, which means those are the mathematical modeling research of single-star LAN of C-CC. From the viewpoint of innovation we know the value of developing multi-star LAN. However, because of mathematical difficulties, no paper has made any reports of multi-star LAN. In order to make innovation for the C-CC access mode, we have to study multi-star LAN deeply.The deep research starts from double-star LAN, which is a very important topology of multi-star LAN. And the research of double-star LAN under heavy load has been finished. This paper studies on extending of single-star LAN and double-star LAN, and successfully solves the mathematical model for double-star LAN with access mode of C-CC under normal load. At the same time we get expressions for the transfer probability P_ij of the customers, the mean waiting time of the customers in the system and carry onthe simulation for them. Then we compare the result of two servers under normal load with the one that is under heavy load. So far, the theory foundation of the contention-collision cancellation access mode has been established for its application. The result of this paper can give academic reference value to wire star-LAN and wireless star-LAN.