1. Maximizing Unavailability Interval for Energy Saving in IEEE 802.16e Wireless MANs Tuan-Che Chen ( 陳端哲 ), Ying-Yu Chen ( 陳盈佑 ), and Jyh-Cheng Chen ( 陳志成 ) Department of Computer Science College of Electrical Engineering and Computer Science National Tsing Hua University

2. Outline Introduction PSC of Type II in IEEE 802.16e Maximum Unavailability Interval (MUI) –Chinese Remainder Theorem –Table-based Algorithm Experiments on Time Complexity Conclusion

3. Introduction An important issue in mobile environment –To extend the life of mobile devices. There are three types of power saving class in IEEE 802.16e. An energy conservation scheme to improve the energy efficiency for PSC of Type II in IEEE 802.16e –Be fully compatible with the IEEE 802.16e standard. –Do not change QoS requirements. –Maximum Unavailability Interval (MUI) for MS.

4. Introduction - Maximum Unavailability Interval (MUI) Connection 1 : Power Saving Class A : Connection 2 : Power Saving Class B : State of MS as a whole availability intervalssleep windowslistening windows unavailability intervals

5. PSC of Type II in IEEE 802.16e Three parameters for IEEE 802.16e PSC of Type II : –Sleep window (according to QoS of the connections) –Listening window (according to QoS of the connections) –Start frame number Sleep cycle is equal to the sum of sleep window size and listening window size. … Start frameSleep windowListening window Normal operation Sleep cycle

6. PSC of Type II in IEEE 802.16e Start frame number ： f Sleep cycle ： m Sleep window ： s 123456789101112131415161718192021222324252627282930313233343536 1 Class A ： f a = 1, m a = 9, s a = 5 sleep windows listening windows availability intervals unavailability intervals 11 Class B ： f b =1, m b = 6, s b = 4 Class C ： f c =1, m c = 4, s c = 3 State of MS as a whole 12345678910 case 1

7. PSC of Type II in IEEE 802.16e Start frame number ： f Sleep cycle ： m Sleep window ： s 123456789101112131415161718192021222324252627282930313233343536 3 Class A ： f a = 3, m a = 9, s a = 5 11 Class B ： f b =1, m b = 6, s b = 4 Class C ： f c =1, m c = 4, s c = 3 State of MS as a whole 1234567891011 sleep windows listening windows availability intervals unavailability intervals case 2

8. PSC of Type II in IEEE 802.16e If the first sleep window of a Power Saving Class is initiated at different frame, the unavailability interval of the MS may be change. –The change of the start frame number will not change the QoS of the connections.

9. PSC of Type II in IEEE 802.16e Start Frame NumberSleep WindowListening WindowSleep Cycle First Class27815 Second Class3152035 Third Class1 to 5varies from 1 to 20varies from 20 to 121 Length of Sleep Windows Start Frame Number Sleep Window Listening Window Sleep Cycle Third Class 1 to 515621 紀錄 MUI 最大值 紀錄 MUI 最小值

10. MUI using Chinese Remainder Theorem The steps of the Chinese Remainder Theorem –Give some modulus and remainders –The modulus are pairwise relatively prime –Apply extended Euclidean algorithm to find the solutions Example x ≡ 2 (mod 3 ) x ≡ 3 (mod 5 ) x ≡ 2 (mod 7 ) The minimum positive solutions is 23. How to apply it to power saving classes of type II ?

11. MUI using Chinese Remainder Theorem The form and example of Chinese Remainder Theorem Form x ≡ r 1 (mod m 1 ) r 2 (mod m 2 ) … r t (mod m t ) m 1, m 2, …, m t (pairwise relatively prime) m = lcm (m 1, m 2, …, m t ) B i = m / m i Apply extended Euclidean algorithm to B i to find integers c i such that : c 1 B 1 + c 2 B 2 + … + c k B k = 1 Compute x 0 = r 1 c 1 B 1 + r 2 c 2 B 2 + … + r k c k B k (mod m) Example x ≡ 2 (mod 3 ) x ≡ 3 (mod 5 ) x ≡ 2 (mod 7 ) m = lcm ( 3, 5, 7 ) = 105 B 1 = m / m 1 = 105/3 = 35 B 2 = m / m 2 = 105/5 = 21 B 3 = m / m 3 = 105/7 = 15 Apply extended Euclidean algorithm to B i to find integers c i such that : c 1 = -1 ; c 2 = 1 ; c 3 = 1 Compute x 0 = r 1 c 1 B 1 + r 2 c 2 B 2 + … + r k c k B k (mod m) = 2*(-1)*35+3*1*21+2*1*15 (mod 105) = 23

12. MUI using Chinese Remainder Theorem The form of the Chinese Remainder Theorem apply to Power Saving Class of Type II. 2 Class A ： f a = 2, m a = 3, s a = 1 3 Class B ： f b =3, m b = 5, s b = 1 State of MS as a whole 123456789101112131415 sleep windows listening windows availability intervals unavailability intervals x Class A x ≡ 2 (mod 3 ) Class B x ≡ 3 (mod 5 ) Solution x = 8

13. MUI using Chinese Remainder Theorem The form of the Chinese Remainder Theorem apply to Power Saving Class of Type II. 23 Class A ： f a = 2, m a = 3, s a = 2 345 Class B ： f b =3, m b = 5, s b = 3 State of MS as a whole 123456789101112131415 sleep windows listening windows availability intervals unavailability intervals x Class A ： x ≡ 2 (mod 3 ) Class B ： x ≡ 3 (mod 5 ) Solutions x = 3, 5, 8, 9, 14, 15 Class B ： x ≡ 4 (mod 5 ) Class B ： x ≡ 5/0 (mod 5 ) Class A ： x ≡ 3/0 (mod 3 )

14. MUI using Chinese Remainder Theorem x ≡ r i (mod m i ) – 第 x 個 frame 落在 sleep cycle m i 中的 sleep window r i 內 – f i ≤ r i ≤ f i + sleep window – 1 – 對所有可能的 f i 和 sleep window 排列組合做檢查的動作 Drawback : –According to the Chinese Remainder Theorem, if all of the sleep cycle lengths m i are pairwise relatively prime, all of the solutions of x can be found. –The computational complexity may be too high. –On the other hand, if the lengths of sleep cycles m i are not pairwise relatively prime, the existence of solutions of x is no longer guaranteed.

15. MUI using Table-based Algorithm The same concept for table-based algorithm. –A table can be constructed with m a rows and m b columns –Table elements are denoted as c i,j. –c i,j is a blank or a value satisfying that c i,j ≡ i (mod m a ) c i,j ≡ j (mod m b ) index12…j…mbmb 1 2 … i … mama c i,j

16. MUI using Table-based Algorithm c i,j ≡ i (mod m a ) c i,j ≡ j (mod m b ) sleep windows listening windows availability intervals unavailability intervals case 1 4/0 3 2 1 6/054321index mbmb mcmc 123456789101112 1 1 Class B ： f b =1, m b = 6, s b = 4 Class C ： f c =1, m c = 4, s c = 3 State of MS as a whole 123456123 4 56 1248 1137 6102 591 123412341 2 34 j i c i,j

17. MUI using Table-based Algorithm Extend the table to solve t Power Saving Classes of Type II. 123456789101112131415161718192021222324252627282930313233343536 1 Class A ： f a = 1, m a = 9, s a = 5 sleep windowslistening windows availability intervals unavailability intervals 11 Class B ： f b =1, m b = 6, s b = 4 Class C ： f c =1, m c = 4, s c = 3 State of MS as a whole 12345678910 case 1 123456789101112 Class B+C ： f b,c = 1, m b,c = 12, s b,c = 1,2,3,7,9,10 1 123456789101112

18. MUI using Table-based Algorithm Class A ： f a = 1, m a = 9, s a = 5 Class B+C ： f b,c = 1, m b,c = 12, s b,c = 1,2,3,7,9,10 123456789101112 1 1 123456789 24 33 6 15 23 32 5 14 22 31 4 13 1830 1729 1628 273 262 251 3612 3511 3410 921 820 719 123456789101112131415161718192021222324252627282930313233343536 12345678910

19. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 5, s c = 3 1 4 10 1284 11373 622 591 index465321 Class AB1 ： m ab1 = 12, s ab1 = 1, 9 (f a = 1, f b = 1) Class AB2 ： m ab2 = 12, s ab2 = 5, 9 (fa = 1, fb = 2) Class AB3 ： m ab3 = 12, s ab3 = 5, 9 (fa = 1, fb = 3) Class AB4 ： m ab4 = 12, s ab4 = 1, 5 (fa = 1, fb = 4) Class AB5 ： m ab5 = 12, s ab5 = 1, 5 (fa = 1, fb = 5) Class AB6 ： m ab6 = 12, s ab6 = 1, 9 (fa = 1, fb = 6) Class AB7 ： m ab7 = 12, s ab7 = 2, 10 (fa = 2, fb = 1) Class AB8 ： m ab8 = 12, s ab8 = 2, 10 (fa = 2, fb = 2) Class AB9 ： m ab9 = 12, s ab9 = 6, 10 (fa = 2, fb = 3) Class AB10 ： m ab10 = 12, s ab10 = 6, 10 (fa = 2, fb = 4) Class AB11 ： m ab11 = 12, s ab11 = 2, 6 (fa = 2, fb = 5) Class AB12 ： m ab12 = 12, s ab12 = 2, 6 (fa = 2, fb = 6) Class AB13 ： m ab13 = 12, s ab13 = 3, 7 (fa = 3, fb = 1) Class AB14 ： m ab14 = 12, s ab14 = 3, 11 (fa = 3, fb = 2) Class AB15 ： m ab15 = 12, s ab15 = 3, 11 (fa = 3, fb = 3) Class AB16 ： m ab16 = 12, s ab16 = 7, 11 (fa = 3, fb = 4) Class AB17 ： m ab17 = 12, s ab17 = 7, 11 (fa = 3, fb = 5) Class AB18 ： m ab18 = 12, s ab18 = 3, 7 (fa = 3, fb = 6) Class AB19 ： m ab19 = 12, s ab19 = 4, 8 (fa = 4, fb = 1) Class AB20 ： m ab20 = 12, s ab20 = 4, 8 (fa = 4, fb = 2) Class AB21 ： m ab21 = 12, s ab21 = 4, 12 (fa = 4, fb = 3) Class AB22 ： m ab22 = 12, s ab22 = 4, 12 (fa = 4, fb = 4) Class AB23 ： m ab23 = 12, s ab23 = 8, 12 (fa = 4, fb = 5) Class AB24 ： m ab24 = 12, s ab24 = 8, 12 (fa = 4, fb = 6)

20. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 Class AB1 ： m ab1 = 12, s ab1 = 1, 9 (f a = 1, f b = 1) Class AB6 ： m ab6 = 12, s ab6 = 1, 9 (fa = 1, fb = 6) f c = 1, MUI = 1, 9, 13, 21 f c = 2, MUI = 13, 21 f c = 3, MUI = 13, 21 f c = 4, MUI = 13, 21 f c = 5, MUI = 1, 9, 13, 21 f c = 6, MUI = 1, 9 f c = 7, MUI = 1, 9 f c = 8, MUI = 1, 9 No. of MUI : 4

21. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 f c = 1, MUI = 5, 9, 17, 21 f c = 2, MUI = 5, 21 f c = 3, MUI = 5, 21 f c = 4, MUI = 5, 21 f c = 5, MUI = 5, 9, 17, 21 f c = 6, MUI = 9, 17 f c = 7, MUI = 9, 17 f c = 8, MUI = 9, 17 Class AB2 ： m ab2 = 12, s ab2 = 5, 9 (fa = 1, fb = 2) Class AB3 ： m ab3 = 12, s ab3 = 5, 9 (fa = 1, fb = 3) No. of MUI : 4

22. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 f c = 1, MUI = 1, 5, 13, 17 f c = 2, MUI = 5, 13 f c = 3, MUI = 5, 13 f c = 4, MUI = 5, 13 f c = 5, MUI = 1, 5, 13, 17 f c = 6, MUI = 1, 17 f c = 7, MUI = 1, 17 f c = 8, MUI = 1, 17 Class AB4 ： m ab4 = 12, s ab4 = 1, 5 (fa = 1, fb = 4) Class AB5 ： m ab5 = 12, s ab5 = 1, 5 (fa = 1, fb = 5) No. of MUI : 4

23. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 Class AB7 ： m ab7 = 12, s ab7 = 2, 10 (fa = 2, fb = 1) Class AB8 ： m ab8 = 12, s ab8 = 2, 10 (fa = 2, fb = 2) f c = 1, MUI = 2, 10 f c = 2, MUI = 2, 10, 14, 22 f c = 3, MUI = 14, 22 f c = 4, MUI = 14, 22 f c = 5, MUI = 14, 22 f c = 6, MUI = 2, 10, 14, 22 f c = 7, MUI = 2, 10 f c = 8, MUI = 2, 10 No. of MUI : 4

24. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 Class AB9 ： m ab9 = 12, s ab9 = 6, 10 (fa = 2, fb = 3) Class AB10 ： m ab10 = 12, s ab10 = 6, 10 (fa = 2, fb = 4) f c = 1, MUI = 10, 18 f c = 2, MUI = 6, 10, 18, 22 f c = 3, MUI = 6, 22 f c = 4, MUI = 6, 22 f c = 5, MUI = 6, 22 f c = 6, MUI = 6, 10, 18, 22 f c = 7, MUI = 10, 18 f c = 8, MUI = 10, 18 No. of MUI : 4

25. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 Class AB11 ： m ab11 = 12, s ab11 = 2, 6 (fa = 2, fb = 5) Class AB12 ： m ab12 = 12, s ab12 = 2, 6 (fa = 2, fb = 6) f c = 1, MUI = 2, 18 f c = 2, MUI = 2, 6, 14, 18 f c = 3, MUI = 6, 14 f c = 4, MUI = 6, 14 f c = 5, MUI = 6, 14 f c = 6, MUI = 2, 6, 14, 18 f c = 7, MUI = 2, 18 f c = 8, MUI = 2, 18 No. of MUI : 4

26. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 Class AB13 ： m ab13 = 12, s ab13 = 3, 7 (fa = 3, fb = 1) Class AB18 ： m ab18 = 12, s ab18 = 3, 7 (fa = 3, fb = 6) f c = 1, MUI = 3, 19 f c = 2, MUI = 3, 19 f c = 3, MUI = 3, 7, 15, 19 f c = 4, MUI = 7, 15 f c = 5, MUI = 7, 15 f c = 6, MUI = 7, 15 f c = 7, MUI = 3, 7, 15, 19 f c = 8, MUI = 3, 19 No. of MUI : 4

27. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 f c = 1, MUI = 3, 11 f c = 2, MUI = 3, 11 f c = 3, MUI = 3, 11, 15, 23 f c = 4, MUI = 15, 23 f c = 5, MUI = 15, 23 f c = 6, MUI = 15, 23 f c = 7, MUI = 3, 11, 15, 23 f c = 8, MUI = 3, 11 Class AB14 ： m ab14 = 12, s ab14 = 3, 11 (fa = 3, fb = 2) Class AB15 ： m ab15 = 12, s ab15 = 3, 11 (fa = 3, fb = 3) No. of MUI : 4

28. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 f c = 1, MUI = 11, 19 f c = 2, MUI = 11, 19 f c = 3, MUI = 7, 11, 19, 23 f c = 4, MUI = 7, 23 f c = 5, MUI = 7, 23 f c = 6, MUI = 7, 23 f c = 7, MUI = 7, 11, 19, 23 f c = 8, MUI = 11, 19 Class AB16 ： m ab16 = 12, s ab16 = 7, 11 (fa = 3, fb = 4) Class AB17 ： m ab17 = 12, s ab17 = 7, 11 (fa = 3, fb = 5) No. of MUI : 4

29. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 f c = 1, MUI = 4, 20 f c = 2, MUI = 4, 20 f c = 3, MUI = 4, 20 f c = 4, MUI = 4, 8, 16, 20 f c = 5, MUI = 8, 16 f c = 6, MUI = 8, 16 f c = 7, MUI = 8, 16 f c = 8, MUI = 4, 8, 16, 20 Class AB19 ： m ab19 = 12, s ab19 = 4, 8 (fa = 4, fb = 1) Class AB20 ： m ab20 = 12, s ab20 = 4, 8 (fa = 4, fb = 2) No. of MUI : 4

30. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 f c = 1, MUI = 4, 12 f c = 2, MUI = 4, 12 f c = 3, MUI = 4, 12 f c = 4, MUI = 4, 12, 16, 24 f c = 5, MUI = 16, 24 f c = 6, MUI = 16, 24 f c = 7, MUI = 16, 24 f c = 8, MUI = 4, 12, 16, 24 Class AB21 ： m ab21 = 12, s ab21 = 4, 12 (fa = 4, fb = 3) Class AB22 ： m ab22 = 12, s ab22 = 4, 12 (fa = 4, fb = 4) No. of MUI : 4

31. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 index12345678 1113 2214 3315 4416 5175 6186 7197 8208 9921 10 22 11 23 12 24 f c = 1, MUI = 12, 20 f c = 2, MUI = 12, 20 f c = 3, MUI = 12, 20 f c = 4, MUI = 8, 12, 20, 24 f c = 5, MUI = 8, 24 f c = 6, MUI = 8, 24 f c = 7, MUI = 8, 24 f c = 8, MUI = 8, 12, 20, 24 Class AB23 ： m ab23 = 12, s ab23 = 8, 12 (fa = 4, fb = 5) Class AB24 ： m ab24 = 12, s ab24 = 8, 12 (fa = 4, fb = 6) No. of MUI : 4

32. Table-based Algorithm – Example Class A ： m a = 4, s a = 1 Class B ： m b = 6, s b = 3 Class C ： m c = 8, s c = 5 No. of MUIMUIfafa fbfb fcfc 4 1, 9, 13, 21191 195 5, 9, 17, 21591 595 1, 5, 13, 17151 155 2, 10, 14, 222102 2, 10, 14, 222106 6, 10, 18, 226102 6, 10, 18, 226106 2, 6, 14, 18262 266 3, 7, 15, 19373 377 3, 11, 15, 233113 3, 11, 15, 233117 7, 11, 19, 237113 7, 11, 19, 237117 4, 8, 16, 20484 488 4, 12, 16, 244124 4, 12, 16, 244128 8, 12, 20, 248124 8, 12, 20, 248128 MS 可調整 connections 參數 (start frame number)

33. Experiments on Time Complexity Code : C++ ( gcc version 3.22 ) Experimental parameters : –T ( the number of Power Saving Classes ) : 2 6 = 64 –M ( the maximum length of sleep cycle) : 6 ~ 15 (1000 samples) –C ( sleep cycle length ) : 2 ~ M –S ( sleep window lengrh ) : 1 ~ C –1 ≤ S < C ≤ M –Pick 2 ~ 5 Power Saving Classes from T Compare the time consumption of three schemes –Brute force scheme –MUI using Chinese Remainder Algorithm –MUI using Table-based Algorithm

34. Experiments on Time Complexity

38. Conclusion It is important to configure the parameters properly so the battery life of an MS can be extended. Maximum Unavailability Interval algorithm improves the energy efficiency for Type II. MUI is fully compatible with the IEEE 802.16e standard and does not change the parameters of QoS of connections.

39. The End THANK YOU