Tham khảo tài liệu 'wireless mesh networks 2010 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The Performance of Wireless Mesh Networks with Apparent Link Failures 169 We are now able to find the probability of being in state X0 which is the case for which none of the hidden nodes have packets awaiting transmission pC . Using standard queuing theory Kleinrock 1975 it can easily be shown that this probability is given by 1 pC 1 mpý n i 1 1 Ac 3 N p 7 where zn i is the average number of the m nodes transmitting simultaneously and is calculated according to yn i- m 1 1 nm k 1k k k 1 1 p n m Ln m n-1 p Ac ụ k 1 k k 1 . 7 m 1 J n 1 fl _ m k 1 k k 1 1 p m n m yvn 1 n 1 p p Ac 7 k 1 k 1 The probability that one or more of the m nodes having zero packets in its buffer given the sum of packets in the buffers is n is given by the term 1 pm in Eq. 4 . The combinations of k of m buffers containing packets constrained by a total sum of n packets is given by n 1 . By substituting P0 in Eq. 1 with pC Eq. 3 the probability that transmissions from the connected hidden nodes overlap with a beacon can be calculated as PC 1 pC e AcWb Tp. 5 Before attempting to model more complex traffic patterns . arbitrary packet flows between different nodes we must ensure that the basic model is capturing all possible transmission configurations. In fact the initial model did not take into account the possibility that a neighbouring node receiving the beacon could be transmitting any data packets. Therefore an approximate model will be provided where the channel access time of the neighbouring node receiving the beacon is also taken into account. This model will be used in the next sub-section when random traffic patterns is analysed. Again consider the sample topology illustrated in Fig. 3 a . Let us assume that node -1 has a traffic load with the rate Ac and the probability that it gains access to the channel in order to transmit a packet is pS1. If the nodes s1 S2 -4 -6 are modelled as M M 1 queues the probability that . node 2 has no packets in its buffer can be expressed as .
