TAILIEUCHUNG - Traffic Analysis and Design of Wireless IP Networks phần 4

Trong chuỗi Markov thời gian rời rạc, thời gian mà hệ thống chi tiêu trong cùng một trạng thái phân phối hình học [2]. Chúng tôi có thể dễ dàng chứng minh tuyên bố này. Hãy để chúng tôi giả định rằng hệ thống đã bước vào một nhà nước i. | Teletraffic Theory 99 In discrete-time Markov chains the time that the system spends in the same state is geometrically distributed 2 . We can easily prove this statement. Let us assume that the system has entered a state i. Then the probability that the system will remain in the same state is pịị. The probability that the system will leave its state at the next step is 1 pi . Due to the memoryless property of the Markov chains we may write the following P system remains in state i after m consecutive steps 1 piì piỉn For continuous-time Markov chain we have exponential distribution of the time in single state discrete-state continuous-time Markov process see Figure and we may write the following F t P I t 1 - e- where A is a parameter of the exponential distribution. The density function of the exponential distribution Figure is given by f t Ae - The probability that the interarrival time between two consecutive arrivals will be up to t after it was t0 may be calculated by Figure Probability density functions of discrete-state continuous-time Markov chain. 100 Traffic Analysis and Design of Wireless IP Networks Figure Probability density function of the exponential distribution. p I t tn II P t0 1 t t 0 I t to 11 to p t0 p I t t o -p I t0 r 1 - eẮ t t 0 - 1 - e -0 1 _ e-. 1 - p I t0 e -u 0 e If there is only one event from t 0 to time t t0 then the probability for a new event to occur in next time period t from t0 to t t0 does not depend upon t0. We will further apply Markov processes in telecommunications because most of the random events can be considered in a Markov chain fashion. The Birth-Death Process The birth-death process is a special case of the Markov processes. Here the transitions are permitted between adjacent states only. We are mainly interested in continuous-time processes so we consider birth-death processes in that fashion. The probability that more then one event will occur in an infinitesimal time .

TỪ KHÓA LIÊN QUAN
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.