TAILIEUCHUNG - witched Systems Part 11

Tham khảo tài liệu 'witched systems part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Effect of Switchover Time in Cyclically Switched Systems 123 Fig. 16. Simplified view of the transitions to and from a state when queue are not empty Fig. 17. Simplified view of the transitions to and from a state when queue are empty 124 Switched Systems E N1 í SE i1 P i1 2 1 1 i2 0 i1 1 Ễ i 1 P i1 0 2 0 S i1 P i1 i2 2 1 17 i1 0 i2 1 E 52 E i1 P i1 i2 j 2 j 1 i2 0 i1 0 E Q1 í SE i1 - 1 P i1 i2 1 1 i2 0 i1 1 Ễ i 1 P i1 0 2 0 E i1 P i1 i2 2 1 18 i1 0 i2 1 52 52 52 i1 P i1 i2 j 2 j 1 i2 0 i1 0 Applying Little s law Little 1961 the mean system time Ts1 and mean waiting time Tw1 can be found from 17 and 18 as follows TS1 Nr 19 a1 T E Q1 Tw1 a1 20 The probability of waiting W1 is obtained by summing up the probabilities of the state where on arrival a packet has to wait and is given by 21 for the packets of queue 1 while the probability of blocking B1 is obtained by summing up the state probabilities where queue 1 is full as given in 22 . W1 Ễ è P i1 i2 1 1 E I P i1 0 2 0 E P i1 i2 2 1 i2 0 i1 1 i1 0 i2 1 2 s s-1 EE EP i1 2 j 2 j 1 i2 0 i1 0 s s 1 B1 52 P s 1 i2 1 1 P s 0 2 0 52 P s i2 2 1 i2 0 i2 1 EE P s i2 j 2 21 22 Effect of Switchover Time in Cyclically Switched Systems 125 Results The effect of varying the switchover rate and input load on the mean number in system mean waiting time probability of waiting and probability of blocking is studied. In Figure 18 the input load for queue 2 is fixed at and queue size of both queues to 10. The resulting graph shows that for values of switchover rate comparable to the service rate the queue capacity is reached quickly and at a much lower load as compared to when the switchover rate is ten times that of the service rate. This effect is significantly reduced when the switchover rate is increased to hundred times that of the service rate and beyond. The same effect can also be noted in Figure 19 that shows the mean waiting time against the arrival rate for queue 1. In Figures 20 and 21 the load of queue 2 is also .

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