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1 Comuter Networks 55 (211) Contents lists available at ScienceDirect Comuter Networks journal homeage: Adative slee mode management in IEEE 82.16m wireless metroolitan area networks Sunggeun Jin a,b,, Xi Chen b, Daji Qiao b, Sunghyun Choi c a ETRI, Daejeon 35-7, Reublic of Korea b Deartment of Electrical and Comuter Engineering, Iowa State University, Ames, IA 511, United States c School of Electrical Engineering and INMC, Seoul National University, Seoul , Reublic of Korea article info abstract Article history: Received 15 May 21 Received in revised form 2 December 21 Acceted 1 March 211 Available online 11 March 211 Keywords: IEEE 82.16m Slee cycle Listening window Slee window The emerging IEEE 82.16m standard rovides a new slee mode oeration for Mobile Stations (MSs). It evolves from the slee mode oeration in the IEEE standard but with more advanced features, e.g., the listening window may be extended and the slee cycle length is adjustable. To fully exloit these advancements, we conduct a comrehensive analytical study on the ower consumtion and average acket delay under the new slee mode oeration. Then, based on the analytical results, we roose a novel adative slee mode management scheme called Adative Slee Mode Management (ASMM), which adjusts an MS s slee cycle and listening window in an adative manner based on online monitoring and estimation of the traffic condition. The goal is to minimize the ower consumtion by the MS while limiting the average acket delay under a user-secified level. The effectiveness of ASMM is demonstrated via simulation-based erformance evaluation. Ó 211 Elsevier B.V. All rights reserved. 1. Introduction In IEEE 82.16m [2] wireless metroolitan networks (WMANs), the slee mode is designed to save Mobile Stations (MSs) energy consumtion when they are serviced with lightly-loaded traffic. Basically, an MS in the slee mode wakes u to receive downlink data ackets and/or exchange signaling messages with the Base Station (BS) during a listening window, and owers down its transceiver during a slee window to reduce unnecessary ower consumtion. The interleaved listening and slee windows reeat every slee cycle as long as the MS is in the slee mode. While the 82.16m slee mode inherits most features from the [1] slee mode, it also introduces a number of new advanced features [3 6]. Among them, two of the key enhancements are that (1) the listening window may be extended uon new acket arrivals; and Corresonding author at: ETRI, Daejeon 35-7, Reublic of Korea. address: sunggeun.jin1@gmail.com (S. Jin). (2) the slee cycle length may be reconfigured to better service the dynamic traffic condition. The 82.16/m slee mode has been well-studied in the revious works [3 1]. Secifically, [6 1] deal with the slee mode oerations. The authors of [4] introduce an analytical model for the 82.16m slee mode oeration. However, their numerical analysis is based on an estimation obtained from an observation of simulation results, and hence, the numerical model may not be accurate. The authors of [3] rovided a more accurate model for the case that realtime and non-realtime ackets are serviced simultaneously. They assume that non-realtime acket service times follow an exonential distribution. In comarison, we rovide a more general model in this aer, where non-realtime acket service times may follow any general distribution. Then, based on this model, we design a novel adative algorithm for the 82.16m slee mode management. Concretely, to fully exloit the new features available in the 82.16m slee mode, we analyze the relation between traffic condition, slee cycle length and ower consumtion /$ - see front matter Ó 211 Elsevier B.V. All rights reserved. doi:1.116/j.comnet

2 S. Jin et al. / Comuter Networks 55 (211) as well as average acket delay in the 82.16m slee mode. We derive closed-form exressions for the ower consumtion and average acket delay, based on which we find the otimal value of the slee cycle length that minimizes an MS s ower consumtion while satisfying a user-secified delay constraint. Then, we roose a novel adative slee mode management (ASMM) scheme for 82.16m MSs. The basic idea of ASMM is to dynamically adjust the length of the slee cycle of an MS based on online monitoring and estimation of the acket arrival rate. Secifically, ASMM doubles the slee cycle length when there is no traffic in the revious cycle; otherwise, ASMM reconfigures the slee cycle towards the otimal value obtained from the theoretical analysis. The rest of the aer is organized as follows: In Section 2, we describe the 82.16m slee mode oeration in detail. In Section 3, we rovide a comrehensive numerical analysis for the 82.16m slee mode. In Section 4, we roose a management scheme for the 82.16m slee mode oeration, called ASMM, which is designed based on the numerical analysis derived in Section 3. The effectiveness of ASMM is demonstrated in Section 5 via simulation results. Finally, the aer concludes in Section IEEE 82.16m slee mode In this section, we summarize the key advancements in the 82.16m slee mode. Firstly, in the slee mode, it is ossible that the MS maintains a searate ower saving class for each of its connections. As a result, multile listening windows and slee windows may overla, which degrades the ower saving efficiency of the system and defeats the urose of having multile ower saving classes. For this reason, the 82.16m simlifies the slee mode oeration by offering a single ower saving class for each MS. It imlies that the MS maintains a single ower saving class for all of its connections. Note that, different MS s in the 82.16m network may have different ower saving classes. Traffics belonging to different connections are mixed together and served within the same ower saving class. In the slee mode, the listening window size is fixed. The second advancement in the new 82.16m slee mode is that the listening window may be extended if there are data ackets buffered at the BS for the MS. For examle, during the second cycle shown in Fig. 1, the ackets arriving during the initial listening window trigger the window extension, while the ackets arriving during the first extension of the listening window extend the window further. The third advancement is related to slee mode reconfiguration. As secified in the 82.16m standard, when there is no traffic destined for an MS, its slee cycle length doubles every cycle till reaching and remaining at a maximum value. In this case, the listening window length remains the same. For examle, in Fig. 1, the slee cycle length doubles after the first cycle as there is no traffic during the first cycle. However, whenever there is traffic destined for the MS, the 82.16m slee mode allows the slee cycle to be either reset to a minimum value or reconfigured to an arbitrary value. The third cycle shown in Fig. 1 is an examle of such reconfiguration. In 82.16m, slee mode reconfiguration may be done without disruting the ongoing ower saving class. In other words, the 82.16m slee mode allows the BS to convey the reconfiguration information to the MS via secial signaling messages (e.g., AAI-SLP- REQ) during the regular slee mode oeration (e.g., at the beginning of a slee cycle). This is different from the slee mode where the BS can only reconfigure the oerational arameters of an MS after it deactivates the ower saving class and via more comlicated signaling exchange. In this aer, we study the following tyical oeration of the 82.16m slee mode: An AAI-TRF-IND signaling message is sent at the beginning of each listening window to inform an MS of the ackets buffered at the BS for it. The listening window is extended as long as the transmission queue at the BS is nonemty. The entire listening window is fully utilized for acket transmissions. Slee mode reconfiguration is done via secial signaling messages without disruting the ongoing ower saving class, and the maximum length of the slee cycle is a configurable arameter. 3. Analytical study 3.1. Problem statement The ower consumtion of an 82.16m MS may be reduced via rolonging its slee cycle. However, as shown in [3], a longer slee cycle usually incurs higher acket Fig. 1. An examle of IEEE 82.16m slee mode.

3 3776 S. Jin et al. / Comuter Networks 55 (211) delays. So there is a tradeoff between ower conservation and acket delay. The goal of this work is to design an adative slee mode management scheme to adjust an 82.16m MS s slee cycle (T C ) so that its ower consumtion (P) can be minimized while the average acket delay (D) is bounded below a delay uer bound secified by user or alication. We first study the following otimization roblem in this section: Given k; s; r; P L ; P S ; find T y C ; to minimize PðT C Þ; subject to DðT C Þ 6 ; where (1) k is the acket arrival rate, which can be monitored and estimated by the BS; (2) s is the mean of acket transmission time; (3) r is the deviation of acket transmission time; (4) P L is the MS s ower consumtion during the listening window; (5) P S is the MS s ower consumtion during the slee window. Next, we derive closed-form exressions for P(T C ) and D(T C ) in Section 3.2, then discuss how to determine T y C in Section 3.3, followed by numerical results in Section Derivation of P(T C ) and D(T C ) ð1þ In order to determine T y C, we need to derive the ower consumtion P(T C ) and the average acket delay D(T C ). We make the following assumtions in the analysis: (1) the network is in the steady state and the slee cycle T C remains constant; (2) acket arrivals follow a Poisson distribution with an exected acket arrival rate of k; (3) acket transmission time follows a general distribution with a mean of s and a variance of r 2. For convenience, we summarize the notations used in the numerical analysis in Table Derivation of P(T C ) To hel analyze P(T C ), we first define a random variable t ðiþ. As shown in Fig. 2, tðiþ reresents the overall time for comleting the transmissions of acket i and all subsequent ackets that arrived during the transmissions of reviously arrived ackets. It is recursively defined as follows: t ðiþ ¼ t X þ X j2k i t ðjþ ; ð2þ where t X is the acket transmission time (for acket i) and K i is the set of ackets that arrived during the transmission of acket i. t ðjþ s are mutually indeendent random variables with the same distribution. Let k ¼jK i j. Then, we have the Lalace transform of t ðiþ by: " h i Ee stðiþ ktx ¼ t; jk i j¼k ¼ E ex s tþ X!!# t ðjþ j2k i k; ¼ e st F ðsþ ð3þ where F ðsþ is the Lalace Stieltjes transform of t. Based on our assumtions on acket arrival and acket transmission time, we have: Table 1 Notations used in the numerical analysis. h i Z 1 X 1 F ðsþ ¼Ee stðiþ ¼ e st F ðktþ k ðsþk e kt df X ðtþ k! k¼ Z 1 ¼ ex tðs þ k kf ðsþþ df X ðtþ ¼ F X ðs þ k kf ðsþþ; where F X (t) and F XðsÞ are cumulative distribution functions and L S transform of random variable t X, resectively. Furthermore, since E½t X Š¼ df X ðsþ=dsj s¼ ¼ s and F X ðþ ¼F ðþ ¼1, we have h i Et ðiþ ¼ df ðsþ=dsj s¼ ¼ ð1 qþ : s ð4þ ð5þ The listening window, denoted by t L, is the sum of the transmission time of all ackets buffered during the revious slee window. Hence, t L can be written as: t L ¼ X j2n t ðjþ ; where N is the set of ackets buffered during the revious slee window t S, and t ðjþ has the same hysical meaning as in Eq. (2). Let n ¼jNj. Since an AAI-TRF-IND signaling message is transmitted at the beginning of each listening window, the total number of ackets to be transmitted is n + 1. Similar to Eqs. (3) and (4), we can derive the L S transform of t L as follows: " Ee st L jt S ¼ t;jn j¼n ¼ E ex s t ðaai-trf-indþ þ X!!# t ðjþ j2n nþ1; ¼ F ðsþ ð7þ and Notation t L t S t X T C P(T C ) D(T C ) F L (t), F L ðsþ F S (t), F S ðsþ F X (t), F X ðsþ P S, P L s r 2 k q Meaning Listening window size (ms) Slee window size (ms) Packet transmission time (ms) Length of slee cycle (ms) Average ower consumtion with slee cycle T C (mw) Average acket delay with slee cycle T C (mw) User-secified uer bound for average acket delay (ms) c.d.f. and L S transform of random variable t L c.d.f. and L S transform of random variable t S c.d.f. and L S transform of random variable t X Power consumtion during slee window and listening window (mw) Mean of acket transmission time (ms) Variance of acket transmission time Packet arrival rate (1/ms) Traffic intensity: q = ks ð6þ

4 S. Jin et al. / Comuter Networks 55 (211) Fig. 2. Illustration of t ðiþ. X 1 Z F L ðsþ 1 ¼Ee st L ¼ F ðktþ n ðsþnþ1 e kt df S ðtþ n! n¼ Z 1 ¼ ðsþ ex k kf ðsþ df S ðtþ F ¼ F ðsþf S ðk kf ðsþþ; ð8þ where F S (t) and F SðsÞ are cumulative distribution function and L S transform of slee window size t S, resectively. From Eq. (8), we can obtain the exected listening window size E[t L ] by: s E½t L Š¼ df L ðsþ=dsj s¼ ¼ ð ð1 qþ 1 þ ke½t SŠÞ; ð9þ where s and E[t S ] are the exectations of random variables t X and t S, resectively. In the steady state, the length of the slee cycle is T C = t L + t S, which, together with Eq. (9), gives the following results: E½t L Š¼qT C þ s; E½t S Š¼ð1 qþt C s: ð1þ ð11þ The average ower consumtion P(T C ) can then be derived as: PðT C Þ¼ðP L E½t L ŠþP S E½t S ŠÞ=T C ¼ðP L P S Þq þðp L P S Þs=T C þ P S ; ð12þ where P L and P S are ower consumtion during listening window and slee window, resectively, as listed in Table Derivation of D(T C ) We now consider the average acket delay D(T C ). Let us first introduce a Markov chain with a random variable Q defined as the number of ackets in the transmission queue at the end of each acket transmission. The one-ste state transition robability for this Markov chain is jk = Pr(Q n+1 = k Q n = j), which, when k P j 1, is indeed the robability that there are k j + 1 acket arrivals between the ends of the revious and current acket transmissions. As shown in Fig. 3, the time interval between the ends of two adjacent acket transmissions may include (1) a slee window and one acket transmission time (in this case, the revious state is Q = since there is no acket in the queue at the end of a listening window when the network is in the steady state); or (2) one acket transmission time only. Note that there is at least one acket to be transmitted at each listening window: the AAI-TRF-IND signaling message. Therefore, if there are no ackets arriving during the revious slee window as well as the AAI- TRF-IND acket transmission time, the queue length is zero at the end of the AAI-TRF-IND transmission. Based on the above analysis, jk can be derived as: 8 P >< k a m b k m ; if j ¼ ; k P ; m¼ jk ¼ ð13þ b k jþ1 ; if k P j 1; >: ; if j P 1; 6 k < j 1; where a m is the robability that m ackets arrive during the revious slee window while b m is the robability that m ackets arrive during a acket transmission time. In the following we rovide some analysis on a m as well as b m, then find the steady-state robabilities of the defined Markov chain. Firstly, a m can be written as: Z 1 a m ¼ ðktþ m e kt df S ðtþ; m! ð14þ where F S (t) is the cumulative distribution function of the slee window size t S. We define aðzþ ¼ P 1 m¼a m z m. From this equation, a(z) is derived by: Fig. 3. Derivation of jk the robability that the number of ackets in the transmission queue changes from j to k between the ends of two adjacent acket transmissions.

5 3778 S. Jin et al. / Comuter Networks 55 (211) aðzþ ¼ X1 m¼ Z 1 X a 1 m z m ¼ m¼ ¼ F Sðk kzþ; ð15þ ðktþ m e kt z m df S ðtþ m! where F SðtÞ is the L S transform of the slee window size t S. Similarly, we can define bðzþ ¼ P 1 m¼ b mz m and obtain bðzþ ¼F X ðk kzþ where F XðtÞ is the L S transform of a single acket transmission time t X. Now, we analyze the steady-state robability k the robability that k ackets are left in the queue at the end of a acket transmission. k can be calculated with the state transition robabilities in the following way: k ¼ j X 1 j¼ jk ¼ X k m¼ a m b k m þ Xkþ1 j b k jþ1 : We define PðzÞ ¼ P 1 k¼ k z k and it is derived by: PðzÞ ¼ X 1 m¼ X1 k¼j 1 a m z m X1 k¼m b k jþ1 z k jþ1 j¼1 b k m z k m þ X1 ¼ aðzþbðzþþ PðzÞ bðzþ: z j¼1 j z j 1 ð16þ ð17þ By substituting a(z) and b(z) with F S ðk kzþ and F Xðk kzþ, resectively, we have: PðzÞ ¼ ½1 zf S ðk kzþšf Xðk kzþ F X ðk kzþ z : ð18þ Since P(1) = 1, can be obtained by alying the L Hôital s rule: ¼ 1 q 1 þ ke½t S Š : ð19þ From Eqs. (18) and (19), the average queue length E[L] is derived by: E½LŠ ¼ dpðzþ dz z¼1 ¼ ð1 qþðk2 E½t 2 S Šþ2kE½t SŠÞ þ 2qð1 qþn e þ k 2 NE½t e 2 2Nð1 e ; qþ ð2þ where e N ¼ 1 þ ke½ts Š, E½t 2 S Š¼E½t SŠ 2 þ Varðt S Þ, and E½t 2 X Š¼s2 þ r 2. Since T C = t S + t L in the steady state, we can derive the variance of t S (i.e., Var(t S )) as: Varðt S Þ¼Varð t L þ T C Þ¼Varðt L Þ: X Š ð21þ Moreover, since in the steady state, the total number of transmitted ackets is the same as the total number of acket arrivals during a slee cycle, the variance of t L is: Varðt L Þ¼ðkT C þ 1ÞVarðt X Þ¼ðkT C þ 1Þr 2 : Now, we have E½t 2 S Š as: E½t 2 S Š¼E½t SŠ 2 þðkt C þ 1Þr 2 : According to Little s Law, D(T C ) can be exressed by: DðT C Þ¼E½LŠ=k: ð22þ ð23þ ð24þ Now we have comleted the derivation of the closedform exressions for P(T C ) and D(T C ), which are the foundation of our roosed slee mode management scheme that will be discussed in detail in Section Calculation of otimal slee cycle T y C With P(T C ) and D(T C ) obtained in the revious section, we can calculate T y C with a tyical aroach using the Lagrangian dual function. In other words, we can (1) take the first-order derivative of P(T C )+m(d(t C ) ) with regard to T C ; (2) obtain a real-value solution (T C ) to the Lagrangian function by setting the derivative to zero; and then (3) obtain T y C by rounding down T C to the nearest integer value that is a multile of 5 ms, since the 82.16m standard mandates that T C is in the unit of frames and each frame is 5 ms. However, it is difficult, if not imossible, to derive a closed-form exression for the first-order derivative of the Lagrangian function with regard to T C (articularly the D(T C ) art). In this work, we instead take a numerical aroach to obtain T y C by enumerating all ossible T C values and finding the one that yields the lowest ower consumtion while satisfying the delay constraint. Since T C can only take discrete values, the number of choices for T C is limited. Hence, such a numerical aroach is simle and efficient Numerical results In this section, we rovide some numerical results for P(T C ) and D(T C ), and then show how the values of T y C and PðT y CÞ are affected by the traffic intensity q and the delay uer bound. Fig. 4 lots the results for P(T C ) and D(T C ) with varying q and T C values. We have the following observations. Firstly, when q increases (under a fixed T C ), the ower consumtion increases however the acket delay decreases. This is because a larger q indicates a higher traffic rate, hence the listening window gets extended more to serve the data ackets. As a result, the slee window becomes smaller during which less ackets are queued u. Secondly, as T C increases (with a fixed q), the ower consumtion decreases but the acket delay increases. This is because a larger T C reduces the er-slee cycle AAI-TRF-IND signaling overhead, hence conserving more ower; however it also yields a larger slee window during which more ackets are queued u and have to wait for a longer time before being served. Fig. 5 lots the results for T y C and PðTy CÞ with varying q and values. We can see that T y C increases with q. This is because a higher q indicates a higher traffic rate, hence the MS sends more time serving the data traffic. To achieve this goal, the MS needs to increase the slee cycle to reduce the signaling overhead. Another observation is that T y C also increases with. This is because a less stringent delay constraint allows the MS to oerate with a larger slee cycle (hence a larger slee window), which in turn reduces the signaling overhead and the average ower consumtion.

6 S. Jin et al. / Comuter Networks 55 (211) ρ=.1 ρ=.3 ρ=.5 ρ= ρ=.1 ρ=.3 ρ=.5 ρ=.7 P(T C ) (mw) D(T C ) (ms) T C (ms) T C (ms) Fig. 4. Numerical results for P(T C ) and D(T C ) with varying q and T C values. We assume that s =.5 ms, r =.25 ms, P A = 15 mw and P S = 2 mw. 2 =5 ms 15 =5 ms T C + (ms) D =1 ms T =2 ms =1 ms P(T C + ) (mw) 1 5 D =1 ms T =2 ms D =1 ms T ρ ρ Fig. 5. Numerical results for T y C and PðTy C Þ with varying q and values. We assume that s =.5 ms, r =.25 ms, P A = 15 mw and P S = 2 mw. 4. The roosed ASMM scheme In this section, we resent our roosed adative slee mode management scheme, called ASMM. ASMM is executed at the BS. It (1) monitors downlink ackets for each MS and estimates the acket arrival rate online, based on which (2) it adjusts the slee cycle for the MS and uses the AAI-SLP-REQ signaling message to notify the station of the new slee cycle length. Once the MS receives AAI- SLP-REQ, it starts the next slee cycle following the BS s instruction Estimation of the acket arrival rate ASMM emloys a modified moving average algorithm to estimate the acket arrival rate based on the observed acket arrival times. Let T n denote the time instance when the nth downlink acket for the MS arrives at the BS. Let k n denote the estimation of the acket arrival rate at time T n. ASMM estimates k n in the following manner: 8 k n 1 ð1 wþþ 1 T n T n 1 w; if a acket arrives within >< 1 the last k k n ¼ n 1 time; k n 1 ; if no acket arrives within 2 >: 1 the last k n 1 time; ð25þ where w( < w < 1) is a weighting factor. Basically, uon a acket arrival, k is udated with a weighted moving average. If there is no acket arrival during a certain time eriod (i.e., 1 ), k is reduced to one half of its revious value. k Initially, we set k = and T =. In the case when there exist multile connections with different delay requirements, we set to be the most stringent delay requirement in our roosed scheme since the 82.16m standard only allows a single ower saving class for each mobile station Adjustment of the slee cycle At the end of each slee cycle, ASMM makes an adjustment to the slee cycle length and the BS notifies the MS of the adjustment via the AAI-SLP-REQ message. As shown in Fig. 6, there are two oerating states for adjusting the slee cycle length: S 1 : when there are no acket arrivals during the revious slee cycle, the slee cycle length will be doubled; if the slee cycle length has reached the maximum value T max C, it remains unchanged. S 2 : when some ackets arrive during the revious slee cycle, the slee cycle length will be reconfigured. We assume that s and r of the acket transmission time as well as the ower consumtions P A and P S are known

7 378 S. Jin et al. / Comuter Networks 55 (211) Fig. 6. State transition diagram in ASMM. a riori. Then the length of the next slee cycle is set to the otimal value T y C based on the most recently estimated acket arrival rate k, i.e., the solution to the otimization roblem secified by Eq. (1) in Section 3. Moreover, the maximum value for the slee cycle length is udated to T max C ¼ ct y C, where c P 1 is a design arameter. We will evaluate the effects of c in Section 5. To hel further understand how ASMM works, we show an examle scenario in Fig. 7. In this examle, there are no acket arrivals during the first three cycles; therefore, the slee cycle length kees doubling (from 5 ms to 1 ms to 2 ms to 4 ms). In comarison, since ackets arrive during the next three cycles, the slee cycle length is reconfigured at the end of each one (to 15 ms, 1 ms and 3 ms, resectively). Then the slee cycle length is doubled at time 13 ms as no ackets arrive during the seventh cycle. MS. Fig. 8 comares the erformances of ASMM with different c values under different traffic arrival rates (k) and delay constraints ( ). It is very interesting to see that, when c has a large value (i.e., P2), the average acket delay is indeed higher than the delay bound, although ASMM is designed to converge to the otimal oint where the delay can be bounded while the ower consumtion is minimized. This counterintuitive observation is surrising at first sight, but rather reasonable for the following reason. In ASMM, when there are no acket arrivals during a slee cycle, the length of the slee cycle will be doubled. As a result, when ackets start arriving after a long idle eriod, the slee cycle and hence the slee window could be very large, which in turn results in large delivery delay for these newly-arrived ackets. As shown in the figure, this henomenon is articularly salient when the traffic load is light, since the MS may exerience a longer idle eriod under light traffic conditions than when the traffic load is heavy. On the other hand, when c takes a smaller value less than two, the delay constraint can be better satisfied, since the maximum length of the slee cycle and hence the slee window is effectively limited. Based on these observations, we emirically set c to 1.5 in ASMM. 5. Performance evaluation We evaluate the effectiveness of our roosed ASMM scheme using simulations. We comare ASMM with a naive scheme which (1) doubles the slee cycle T C when there is no traffic in the revious cycle; and (2) resets T C to 1 ms otherwise. T max C is set to s (= 5 ms 123) the maximum allowed by the IEEE 82.16m standard. The following arameters are used in the simulations: s =.5 ms, r =.25 ms, P A = 15 mw and P S = 2 mw, which are also used in [11] Effects of c in ASMM We evaluate the effects of c the design arameter in ASMM that determines the maximum slee cycle for an Average Packet Delay (ms) λ=.1 kts/ms, =1ms λ=.1 kts/ms, =2ms λ=.1 kts/ms, =1ms λ=.1 kts/ms, =2ms γ Fig. 8. The effects of c in ASMM. Fig. 7. An examle of the oeration of the roosed ASMM scheme.

8 S. Jin et al. / Comuter Networks 55 (211) Table 2 Performance comarison with different k values. k (ackets/ms).1.1 P (mw) D (ms) P (mw) D (ms) Naive scheme ASMM with = 1 ms ASMM with =2ms Performance comarison We simulate ASMM and the naive scheme under different traffic conditions: k =.1 (light traffic) and k =.1 (heavy traffic). For ASMM, we set different delay uer bounds: = 1 ms (loose delay constraint) and = 2 ms (tight delay constraint). Results are summarized in Table 2 and we have the following observations. 5 Naive Scheme 5 ASMM with =1 ms 5 ASMM with =2 ms Instant Power (mw) Instant Power (mw) Instant Power (mw) x x x Naive Scheme 4 ASMM with =1 ms 4 ASMM with =2 ms Packet Delay (ms) Packet Delay (ms) Packet Delay (ms) x x x 1 4 Fig. 9. Performance comarison with k =.1 ackets/ms. 1 λ x 1 4 Instant Power (mw) 1 ASMM with D =2 ms T x 1 4 Packet Delay (ms) 1 ASMM with D =2 ms T x 1 4 Fig. 1. ASMM behavior with k varying from.4 to.1 to.1 over time.

9 3782 S. Jin et al. / Comuter Networks 55 (211) When traffic load is light, the naive scheme yields a high acket delay (around 12 ms). This is because the naive scheme simly doubles or resets the slee cycle length without considering the delay erformance. In comarison, ASMM takes into consideration the delay constraint when adjusting the slee cycle. Hence, the delay constraint is always satisfied. We can see that, when the delay constraint is tight at = 2 ms, more ower is consumed as the tradeoff. However, when the delay constraint is loose at = 1 ms, ASMM yields a better erformance in both ower consumtion and acket delay than the naive scheme. This is due to the relatively stable and large slee cycle used by ASMM, comaring to the large variation range of the slee cycle (from 1 ms to s) in the naive scheme. When traffic load is heavy, the naive scheme is busy serving data ackets and rarely has the chance to double the slee cycle. As a result, the acket delay is low while the ower consumtion is high. In comarison, ASMM carefully adjusts the slee cycle for the MS so that the MS may slee for a longer eriod (with a larger slee cycle hence a large slee window) to save more ower while making sure that the delay constraint is satisfied. As shown in the table, ASMM allows a higher acket delay (than the naive scheme) to be around the delay constraint while saving about 15% ower. We investigate the behavior of ASMM and the naive scheme further by lotting their instant ower consumtion and average acket delay (in each slee cycle) when k =.1 in Fig. 9. In this figure, we can clearly observe (1) high ower consumtion and unredictable delay erformance with the naive scheme; (2) ASMM s acket delay around the desired delay constraint; and (3) low ower consumtion by ASMM. Finally, we study the behavior of ASMM when the traffic rate varies over time. As shown in Fig. 1, k is initially set to.4 in the simulation, then reduces to.1 at time 1 s, and then changes to.1 at time 2 s. Traces for instance ower consumtion as well as average acket delay show that ASMM is able to track the variation of k well and adjust the slee cycle accordingly. Over the entire 3 s eriod, the average acket delay is always around the target 2 ms, while the slee cycle is adjusted over time to conserve as much ower as ossible. For examle, between time instances 1 s and 2 s, larger slee cycles are used (which is evidenced by the sarse delay trace in the eriod) to deal with the light traffic condition and allow the MS to slee longer to save more ower (which is evidenced by the low ower trace in the eriod). 6. Conclusion In this aer, we investigate the slee mode management issues in IEEE 82.16m WMANs. We conduct a comrehensive analytical study on the ower consumtion and average acket delay for 82.16m MSs. Based on the analytical results, we roose a novel adative slee mode management scheme called Adative Slee Mode Management (ASMM) to minimize the ower consumtion of an 82.16m MS while satisfying a user-secified acket delay constraint. Simulation results show that ASMM erforms well under various traffic conditions and delay constraints, articularly when the traffic load is light and the delay constraint is less stringent. Acknowledgements This work was in art suorted by the MKE/KEIT, Korea, under both the ITRC suort rogram (IITA-28- C ) and the IT R&D rogram (KI2139, Develoment of cooerative oeration rofiles in multicell wireless systems). The research reorted in this aer was suorted in art by the Information Infrastructure Institute (icube) of Iowa State University and the National Science Foundation under Grant CNS References [1] IEEE , Part 16: Air Interface for Broadband Wireless Access Systems, May 29. [2] IEEE 82.16m/D7, Part 16: Air Interface for Broadband Wireless Access Systems: Advanced Air Interface, July 21. [3] S. Jin, M. Choi, S. Choi, Performance analysis of IEEE 82.16m slee mode for heterogeneous traffic, IEEE Commun. Lett., May 21. [4] E. Hwang, K.J. Kim, J.J. Son, B.D. Choi, The ower-save mechanism with eriodic traffic indications in the IEEE 82.16e/m, IEEE Trans. Veh. Tech., January 21. [5] S. Baek, J.J. Son, B.D. Choi, Performance analysis of slee mode oeration for IEEE 82.16m advanced WMAN, in: Proc. ICC 9, June 29. [6] R.K. Kalle, M. Raj, D. Das, A Novel Architecture for IEEE 82.16m subscriber station for joint ower saving class management, in: Proc. COMSNETS 9, January 29. [7] T.-C. Chen, J.-C. Chen, Y.-Y. Chen, Maximizing unavailability interval for energy saving in IEEE 82.16e wireless MANs, IEEE Trans. Mobile Comuting, Aril 29. [8] L. Kong, D.H.K. Tsang, Otimal selection of ower saving classes in IEEE 82.16e, in: Proc. IEEE WCNC 7, March 27. [9] Y. Zhang, Performance modeling of energy management mechanism in IEEE 82.16e mobile WiMAX, in: Proc. IEEE WCNC 7, March 27. [1] K. Han and S. Choi, Performance analysis of slee mode oeration in IEEE 82.16e mobile broadband wireless access systems, in: Proc. IEEE VTC 6-Fall, Setember 26. [11] <htt:// Sunggeun Jin is a senior engineer working for ETRI, which he joined in 1998, Korea. Prior to joining ETRI, he received his B.S. and M.S. degrees in School of Electrical Engineering and Comuter Science at Kyungook National University (KNU), Korea, in 1996 and 1998, resectively. He received his Ph.D. at School of Electrical and Comuter Engineering, Seoul National University (SNU), Korea, August, 28. He has articiated in standard develoments including IEEE 82.11v, IEEE 82.16j, IEEE 82.16m, and IEEE 82.11ad. He has served as a TPC member for IEEE WCNC 28, ICUFN 29, ICST BROADNETS 21, and IEEE GLOBECOM 211. Also, he comleted eer reviews for journals and conferences such as IEEE TMC, IEEE INFOCOM, IEEE ICC, IEEE GLOBECOM, and IEEE WCNC.

10 S. Jin et al. / Comuter Networks 55 (211) Xi Chen received the B.S. degree in Electrical Engineering and Information Science from University of Science and Technology of China, Hefei, China, in 26. He is currently working toward a Ph.D. degree in the Deartment of Electrical and Comuter Engineering, Iowa State University, Ames, Iowa. His research interests include rotocol design and erformance evaluation for based wireless/mobile networks. He is a student member of the IEEE. Daji Qiao is currently an Associate Professor in the Deartment of Electrical and Comuter Engineering, Iowa State University, Ames, Iowa. He received his Ph.D. degree in Electrical Engineering: Systems from The University of Michigan, Ann Arbor, Michigan, in February 24. His current research interests include algorithm and rotocol innovation and imlementation for IEEE wireless local area networks, system modeling and erformance analysis of wireless sensor networks, and ervasive comuting alications. He is a member of the IEEE and ACM. Sunghyun Choi is an associate rofessor at the School of Electrical Engineering, Seoul National University (SNU), Seoul, Korea. Before joining SNU in Setember 22, he was with Philis Research USA, Briarcliff Manor, New York, USA as a Senior Member Research Staff and a roject leader for three years. He was also a visiting associate rofessor at the Electrical Engineering deartment, Stanford University, USA from June 29 to June 21. He received his B.S. (summa cum laude) and M.S. degrees in electrical engineering from Korea Advanced Institute of Science and Technology (KAIST) in 1992 and 1994, resectively, and received Ph.D. at the Deartment of Electrical Engineering and Comuter Science, The University of Michigan, Ann Arbor in Setember, His current research interests are in the area of wireless/mobile networks with emhasis on wireless LAN/MAN/PAN, next-generation mobile networks, mesh networks, cognitive radios, resource management, data link layer rotocols, and cross-layer aroaches. He authored/coauthored over 14 technical aers and book chaters in the areas of wireless/mobile networks and communications. He has co-authored (with B. G. Lee) a book Broadband Wireless Access and Local Networks: Mobile WiMAX and WiFi, Artech House, 28. He holds 19 US atents, 1 Euroean atents, and 11 Korea atents, and has tens of atents ending. He has served as a General Co-Chair of COMSWARE 28, and a Technical Program Committee Co-Chair of ACM Multimedia 27, IEEE WoWMoM 27 and IEEE/Create-NetCOMSWARE 27. He was a Co-Chair of Cross- Layer Designs and Protocols Symosium in IWCMC 26, 27, and 28, the worksho co-chair of WILLOPAN 26, the General Chair of ACM WMASH 25, and a Technical Program Co-Chair for ACM WMASH 24. He has also served on rogram and organization committees of numerous leading wireless and networking conferences including ACM MobiCom, IEEE INFOCOM, IEEE SECON, IEEE MASS, and IEEE WoWMoM. He is also serving on the editorial boards of IEEE Transactions on Mobile Comuting, IEEE Wireless Communications, ACM SIGMOBILE Mobile Comuting and Communications Review (MC2R), Journal of Communications and Networks (JCN), Comuter Networks, and Comuter Communications. He has served as a guest editor for IEEE Journal on Selected Areas in Communications (JSAC), IEEE Wireless Communications, Pervasive and Mobile Comuting (PMC), ACM Wireless Networks (WINET), Wireless Personal Communications (WPC), and Wireless Communications and Mobile Comuting (WCMC). He gave a tutorial on IEEE in ACM MobiCom 24 and IEEE ICC 25. From 2 to 27, he was a voting member of IEEE WLAN Working Grou. He has received a number of awards including the Young Scientist Award awarded by the President of Korea (28); IEEK/IEEE Joint Award for Young IT Engineer (27); the Outstanding Research Award (28) and the Best Teaching Award (26) both from the College of Engineering, Seoul National University; the Best Paer Award from IEEE WoWMoM 28; and Recognition of Service Award (25, 27) from ACM. Dr. Choi was a reciient of the Korea Foundation for Advanced Studies (KFAS) Scholarshi and the Korean Government Overseas Scholarshi during and , resectively. He is a senior member of IEEE, and a member of ACM, KICS, IEEK, KIISE.