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Wireless Mesh Networks 2010 Part 2

Tham khảo tài liệu 'wireless mesh networks 2010 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Optimal Control of Transmission Power Management in Wireless Backbone Mesh Networks 9 A A1 21 12 1E 22 2E 1 Ae1 E2 EE It should be recalled that the power optimization phase requires information about the queue load and energy level dynamics Denote X n xn i n j n as a two dimensional Markov chain sequence where i n and j n are respectively the energy level available for packet transmission and the number of packets in the buffer at the nth time step Let the packet arrival and the energy-charging discharging process at each interface in time step n 1 be independent of the chain X n Arrivals are assumed to occur at the end of the time step so that new arrivals cannot depart in the same time step that they arrive Olwal et aL 2010a Figure 3 depicts the two dimensional Markov chain evolution diagram with the transition probability matrix PT n whose elements are Ản n 1 i j for all i 1 2 E and j 0 1 2 B The notation Ản n 1 i j represents the transition probability of the ith energy level and the jth buffer level from state at n to state at n 1 In general similar Markov chain representations can be assumed for other queues in a multiqueue systemr Fig 3 Markov chain diagram The transition probability E B 1 xE B 1 matrix of the Markov chain X n is yielded by Bo PT n A2 0 B1 0 A1 A0 A 2 A1 0 A0 0 Ì 0 2 10 A1 A0 0 A2 F1 B where PT n consists of B 1 block rows and B 1 block columns each of size E X E The matrices B0 B1 A0 A1 A2 and F1 are all E X E non-negative matrices denoted as B0 ỘA B1 ỘA A0 diag ộ ỹi i 1 E A A1 diag ộipị ộộị i 1 e a 10 Wireless Mesh Networks A2 diag ộpị i 1 . . . e a and F1 diag ộpi pỊ i 1 . . . E A. Here ộ 1 - ộ and p 1 - Pị respectively denote the probability that no packet arrives in the queue and no packet is transmitted into the channel when the available energy level is i. If one assumes that the energy level transition matrix A is irreducible and aperiodic1 and that ộ 0 then the Markov chain X n is aperiodic and contains a single ergodic class2. A .