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IEICE TRANS. COMMUN., VOL.Exx–??, NO.xx XXXX 200x 1 PAPER An eﬃcient power saving mechanism for delay-guaranteed services in IEEE 802.16e∗ Yunju PARK† , Nonmember and Gang Uk HWANG†a) , Member SUMMARY As the IEEE 802.16e Wireless Metropolitan Ac- services. Power Saving Class of type II is recommended cess Network (WMAN) supports the mobility of a mobile station for the connections of Unsolicited grant service (UGS) (MS), increasing MS power eﬃciency has become an important and Real-Time Variable Rate (RT-VR) services. Power issue. In this paper, we analyze the sleep-mode operation for an eﬃcient power saving mechanism for delay-guaranteed services in Saving Class of type III is recommended for multicast the IEEE 802.16e WMAN and observe the eﬀects of the operating connections and for management operations. parameters related to this operation. For the analysis we use the Regarding the analysis of the sleep-mode opera- M/GI/1/K queueing system with multiple vacations, exhaus- tion in IEEE 802.16e, Nga et al. [4] analyzed a numeri- tive services and setup times. In the analysis, we consider the power consumption during the wake-mode period as well as the cal model to determine the operating parameters in the sleep-mode period. As a performance measure for the power con- sleep-mode operation and proposed a delay guaranteed sumption, we propose the power consumption per unit time per energy saving algorithm to minimize energy consump- eﬀective arrival which considers the power consumption and the tion with a given MAC (Medium Access Control) SDU packet blocking probability simultaneously. In addition, since we (Service Data Unit) response delay. Xiao [5] considered consider delay-guaranteed services, the average packet response delay is also considered as a performance measure. Based on the a sleep-mode scheme for the power saving mechanism performance measures, we obtain the optimal sleep-mode opera- and analyzed the eﬀects of the operating parameters. tion which minimizes the power consumption per unit time per Seo et al. [6] used the M/GI/1/K queueing system with eﬀective arrival with a given delay requirement. Numerical stud- multiple vacations and considered the dropping proba- ies are also provided to investigate the system performance and to show how to achieve our objective. bility of packets and the mean waiting times of packets key words: sleep-mode operation, power saving, IEEE 802.16e, as the performance measures. Jang et al. [7] simulated power consumption, average packet response delay the sleep-mode operation of the Power Saving Class of type I and II, and found the optimal values of oper- 1. Introduction ating parameters to satisfy diﬀerent QoS requirements. Kim et al. [8] introduced an eﬃcient power management As wireless internet services are rapidly expanding, it mechanism which takes into account the remaining en- is an important task to provide high speed and high ergy. Kim et al. [9] modeled the sleep mode operation in quality wireless services. To meet these demands, in the IEEE 802.16e MAC and evaluated the eﬀect of op- the Wireless Metropolitan Access Network (WMAN), erating parameters on the performance of power man- mobility and power management of a Mobile Station agement by considering the average interarrival time (MS) become important issues, and to solve the issues of MAC frames. They used simulation to evaluate the the IEEE 802.16 standard [1, 2] has been extended to performance. Xu et al. [10] discussed a novel adaptive the IEEE 802.16e standard where the handover process sleep-mode scheme which considered quick responses to and the sleep mode operation are included [3]. the packet arrival events. Dong et al. [11] modelled the In the IEEE 802.16e standard [3], the sleep-mode sleep-mode operation where two-type-returning from operation has three types of the Power Saving Classes. sleep mode is considered. Most studies modelled the Power Saving Class is a group of connections which sleep-mode period, but they focused on the analysis of have common demand properties. Power Saving Class the sleep-mode period only and did not consider the of type I is recommended for the connections of Best Ef- wake-mode period and the queueing eﬀect of the sys- fort (BE) and Non-Real-Time Variable Rate (NRT-VR) tem. However, in our paper, we analyze the packet † response delay and the power consumption during the The authors are with the Department of Mathemati- cal Sciences and Telecommunication Engineering Program wake-mode period as well as the sleep-mode period. in Korea Advanced Institute of Science and Technology The operation of IEEE 802.16e system is based on (KAIST), Daejeon, Republic of Korea frame units of 5 ms, and the sleep-mode operation in † This paper was presented in part at the 65th IEEE IEEE 802.16e is performed between one base station Vehicular Technology Conference VTC2007-spring, Dublin, (BS) and one MS. In this paper, we focus on downlink Ireland, April 22-25, 2007. transmission from a BS to an MS, and assume that a) E-mail: guhwang@kaist.edu ∗ This research was supported by the Korea Science and there is a ﬁnite size buﬀer in the BS to develop a sys- Engineering Foundation (KOSEF) grant funded by the Ko- tem model close to the real one. The ﬁnite size buﬀer rea government (MOST) (No. R01-2007-000-20053-0). in the BS accommodated packets addressed to the MS IEICE TRANS. COMMUN., VOL.Exx–??, NO.xx XXXX 200x 2 with the Power Saving Class of type I packets. The detailed sleep-mode operation of this type will be given buffer one frame in section 2. In an IEEE 802.16e network, the resources BS time are shared by all MS in the network, and some amount of resources are assigned to our MS at each frame. So, n ate) e pep s m g s e rqu tm g ( e te) se r s one s (eg v epe es s i v pt) ( ose n gai t cdi a m g t cdi a m g t cdi a m g v i rfin c tn s rfin c tn s rfin c tn s the downlink transmission system can be modelled by a ai o ai o ai o i i i l l single server queueing system. The amount of resources MS active sleep awake sleep awake sleep awake active allocated to our MS determines the packet transmission T0 L T1 L T2 L time time. The amount of resources allocated to our MS is v0 v1 v2 S not ﬁxed in general. In addition, the mobility and the wake mode start time of sleep mode start time of wake mode wireless channel condition may aﬀect the packet ser- sleep mode wake mode vice process through packet transmission errors. Such vacation period setup time busy period eﬀects can be approximately taken into consideration Fig. 1 The sleep-mode operation in IEEE802.16e by using a suitable service time distribution. Here, the service time is deﬁned by the time period needed to transmit the HOL (Head Of Line) packet in the buﬀer successfully. Accordingly, to consider such eﬀects, we 2. The Operation of Sleep-Mode in IEEE802.16e assume that the service times of packets have a gen- eral service time distribution. As the arrival process We consider downlink transmission from a BS to an MS to the buﬀer in BS, we adopt the Poisson process for where the Power Saving Class of type I is used. In this the convenience in the analysis [4–11]. In addition, due case, the MS has two modes: sleep-mode and wake- to the sleep-mode operation, our queueing system has mode. During a sleep-mode period, the MS powers vacations. down to reduce the battery consumption and there is Based on above assumptions, to analyze the sleep- no packet transmission between the BS and the MS. So, mode operation mathematically, the buﬀer in the BS the buﬀer in the BS accommodates incoming packets is modelled by the M/GI/1/K queueing system with addressed to the MS until the sleep-mode period ends. multiple vacations, exhaustive services and setup times When the sleep-mode period ends, a wake-mode period [12, 13]. The contributions of this paper are as fol- starts immediately and there are packet transmissions lows. First, we mathematically model the sleep-mode between the BS and the MS during the wake-mode pe- operation as exactly as possible and obtain the packet riod. After the wake-mode period, a new sleep-mode blocking probability, the power consumption per unit period begins again and this alternating procedure will time and the average packet response delay. Second, as continue. performance measures, we consider the average packet To enter a new sleep-mode period after a wake- response delay and the power consumption per unit mode period, the MS sends a Sleep Request message time per eﬀective arrival, which is newly proposed to (MOB SLP-REQ) to the BS and waits for a Sleep Re- combine the average packet blocking probability and sponse message (MOB SLP-RSP) from the BS. The the power consumption per unit time simultaneously. MOB SLP-REQ contains the relevant parameters re- Third, we provide a detailed procedure to get the opti- garding the sleep-mode period such as initial-sleep win- mal sleep-mode operation which satisﬁes the delay re- dow, ﬁnal-sleep window base, listening window, ﬁnal- quirement and minimizes the power consumption per sleep window exponent and start frame number for unit time per eﬀective arrival. the ﬁrst sleep window. When the BS receives the The rest of this paper is organized as follows. MOB SLP-REQ, if there is no downlink traﬃc for the In section 2, the sleep-mode operation in the IEEE MS, then the BS sends a positive MOB SLP-RSP mes- 802.16e standard is described. In section 3, we use sage to the MS with the same parameters as in the the M/GI/1/K queueing system with multiple vaca- MOB SLP-REQ message that it has received. Other- tions, exhaustive services and setup times to analyze wise, the BS sends a negative MOB SLP-RSP message. the sleep-mode operation. In section 4 and 5, we ana- After receiving the MOB SLP-RSP, the MS can deter- lyze the system behaviors during the vacation and busy mine whether to begin a new sleep-mode period or not. periods, respectively. In section 6, we obtain the packet If it has received a negative MOB SLP-RSP (i.e., no blocking probability, the power consumption per unit approval message), it continues to be in wake-mode time and the average packet response delay. Based on and waits for another packet transmissions. If it has our analysis, we propose a detailed procedure to get the received a positive MOB SLP-RSP (i.e., approval mes- optimal sleep-mode operation. In section 7, we give our sage), it begins a new sleep-mode period at the frame conclusions. speciﬁed as start frame number for the ﬁrst sleep win- dow. A sleep-mode period may consist of a single or multiple sleep intervals as shown in Fig. 1. The length of the ﬁrst sleep interval is equal to the initial-sleep PARK and HWANG: AN EFFICIENT POWER SAVING MECHANISM FOR DELAY-GUARANTEED SERVICES IN IEEE 802.16E 3 window, denoted by T0 . After the ﬁrst sleep interval, the ﬁrst sub-vacation interval. Similarly, the MS has the MS wakes for a ﬁxed time period, called the lis- the (i + 1)-th sub-vacation interval if there is no packet tening interval, of length listening window L, to check during the i-th sub-vacation interval which consists of the Traﬃc Indication message (MOB TRF-IND). The a listening interval and the (i + 1)-th sleep interval. message is broadcasted by the BS during the listening Now, assume that the MS is at the end of the n- interval. It indicates the presence of the buﬀered traﬃc th sub-vacation interval and that there is at least one addressed to the MS in the BS. If the MS has received a packet arrival during the n-th sub-vacation interval. In negative MOB TRF-IND, i.e., no buﬀered traﬃc for it, this case, the MS receives a positive MOB TRF-IND it goes back to the sleep-mode again to start the second message from the BS during the listening interval fol- sleep interval with the doubled length T1 (= 2T0 ). Oth- lowing the n-th sub-vacation interval. So, the MS ends erwise, the MS begins a new wake-mode period after the sleep-mode period consisting of n + 1 sub-vacation the listening interval. The MS keeps the above pro- intervals, called a vacation period in our model, and cedure during the sleep-mode period until it receives starts a new wake-mode period, called a busy period in a positive MOB TRF-IND. In the IEEE 802.16e stan- our model, to receive packets from the BS. Note that dard [3], the length Ti of the i-th sleep interval in a there is always a listening interval between a vacation sleep-mode period, if any, is computed as follows: period and the following busy period, which is called the setup time period in our model. For details, refer to T0 = initial-sleep window, Fig. 1. Ti = min{2Ti−1 , Tmax }, i ≥ 1, From the above assumptions and explanation, Tmax = ﬁnal-sleep window base · 2ﬁnal-sleep window exponent . our system can be modelled by the discrete time M/GI/1/K queueing system with multiple vacations, exhaustive services and setup times [12, 13]. Here, GI 3. Mathematical Modelling of The Sleep-Mode implies that service times are general and independent. Operation Note that our system has the exhaustive service disci- pline because the MS begins the vacation period only In this section, we consider the buﬀer in the BS which when there is no packet for the BS to transmit. If accommodates packets addressed to the MS, and ana- we assume that the time to transmit the control mes- lyze the operation of the sleep-mode in IEEE 802.16e sages such as MOB SLP-REQ, MOB SLP-RSP and explained in section 2. MOB TRF-IND is zero, the i-th sub-vacation interval, We assume that the packet arrival process follows denoted by vi , is given by a Poisson process with rate λ and the service times of packets are independent and identically distributed T0 , i = 0, vi = (i.i.d) with common distribution function F (x). We L + Ti , i = 1, 2, .... also assume that the buﬀer in the BS for the MS is of ﬁnite size K − 1, and single server for packet trans- Recall that L is the length of a listening interval, T0 is mission. Then, if there are K packets in the system the initial sleep interval, and Ti is given by including the packet being transmitted, newly arriving Ti = min{2Ti−1 , Tmax }, i = 1, 2, .... packets are blocked and discarded. For this reason, K is called the system size from now on. The packets in Since Ti ’s are all ﬁxed, all sub-vacation intervals, vi , i = the buﬀer are transmitted based on the FCFS (First- 0, 1, 2, ..., are of ﬁxed lengths. Come-First-Served) service discipline. Let V , S and B be the vacation period, setup Since the operation of IEEE 802.16e is based on time period and busy period in our model, respectively. frame times, a frame time is considered as a unit time Then, we can deﬁne a service cycle C by C = V +S +B, and we assume that the time axis is divided into unit i.e., a service cycle consists of a vacation period, a setup times in our analysis. To model our system, we ﬁrst time period and a busy period. consider a sleep-mode period. The sleep-mode period In the subsequent sections, we analyze the system starts with the ﬁrst sleep interval of length T0 . This behaviors during the vacation period and busy period ﬁrst sleep interval is called the 0-th sub-vacation in- separately and obtain the performance measures such terval in our model. If there is no packet during the as the power consumption per unit time per eﬀective 0-th sub-vacation interval, the MS receives a negative arrival and the average packet response delay. MOB TRF-IND message during the following listening interval and starts immediately the second sleep inter- 4. The Vacation Period Analysis val after the listening interval. Since the switching to the wake-mode for the MS after the second sleep inter- In this section, we analyze the length of a vacation pe- val depends on whether there is at least one packet ar- riod and the number of sub-vacation intervals in steady rival during the listening and second sleep intervals, the state. To do this, we ﬁrst obtain the probability mass sum of the listening and second sleep intervals is called function of a vacation period. By the deﬁnition of a IEICE TRANS. COMMUN., VOL.Exx–??, NO.xx XXXX 200x 4 vacation period V given in section 3, the probability steady state. Observing that there should be at least mass function of V is given by one packet at the end of a vacation period, we have the probability mass function of NV as follows: S0 with prob. 1 − e−λS0 , V = (1) Theorem 1: The probability mass function of the Sn with prob. e−λSn−1 (1 − e−λvn ), n ≥ 1, number NV of backlogged packets at the end of a va- n cation period is given by where Sn = i=0 vi and S0 = v0 . For our analysis, we use M to denote the index of M (λvn )i e−λSn (λvM )i −λvM e the sub-vacation interval such that vj = L + Tmax for Pr[NV = i] = + i! −λvM e−λSM , i! 1−e all j ≥ M and vj < L + Tmax for all 0 ≤ j < M . That n=0 is, M = min{j : vj = L + Tmax }. Note that the value (i = 1, 2, ..., K − 1) of M depends on T0 and Tmax . For example, if T0 = 2 K−1 and Tmax = 1024, then M = 9. Then, from equation Pr[NV = K] = 1 − Pr[NV = i]. (1) the expectation E[V ] of a vacation period is given i=1 by The proof of Theorem 1 is given in Appendix A.3. ∞ E[V ] = Sj Pr[V = Sj ] 5.2 Distribution of the number of packets at the be- j=0 ginning of a busy period M vM = S0 + e−λSj−1 vj + e−λSM . Let NS be the number of backlogged packets in the j=1 1 − e−λvM system at the beginning of a busy period in steady state. Since there is always a setup time period be- The detail derivation is given in Appendix A.1. tween a vacation period and a busy period, NS satis- Next, let NI denote the maximum of sub-vacation ﬁes NS = NV + AS where AS denotes the number of interval indexes during a vacation period in steady packets newly arriving during the setup time period. state. By a similar argument as above, we also obtain Then, by Theorem 1 the distribution of NS is derived the expectation E[NI ] as follows: as follows. ∞ Theorem 2: The probability mass function of the E[NI ] = jPr[V = Sj−1 ] number NS of backlogged packets at the beginning of j=1 a busy period is given by M e−λvM = 1+ e−λSj + e−λSM . j (λS)j−i e−λS j=0 1 − e−λvM Pr[NS = j] = × i=1 (j − i)! The detail derivation is given in Appendix A.2. M (λvM )i e−λSM −λvM (λvn )i e−λSn i! e + , 5. The Busy Period Analysis n=0 i! 1 − e−λvM (j = 1, 2, ..., K − 1) In this section, we analyze the length of a busy period K−1 in steady state. Since the length of a busy period is Pr[NS = K] = 1 − Pr[NS = j]. closely related with the number of backlogged packets j=1 at the beginning of the busy period, we start with the analysis of the number of backlogged packets at the end The proof of Theorem 2 is given in Appendix A.4. of a vacation period. 5.3 The length of a busy period 5.1 Distribution of the number of packets at the end of a vacation period In this subsection, we analyze the length of a busy pe- riod based on the results obtained in subsections 5.1 Let NV be the number of backlogged packets at the end and 5.2. Recall that packets in the buﬀer are transmit- of a vacation period in steady state. By the deﬁnition, ted based on the FCFS discipline. However, the length the distribution of NV is obtained as follows: of a busy period does not depend on the order in which packets in the buﬀer are transmitted [12, 14–16]. That ∞ is, the length of a busy period of the system with the Pr[NV = i] = Pr[NV = i|NI = n]Pr[NI = n]. FCFS discipline is identical to that of the system with n=0 the LCFS (Last-Come-First-Served) discipline. So, for Here, recall that NI denotes the maximum of sub- convenience in the analysis, we consider a new system vacation interval indexes during a vacation period in which is identical to our system except that the LCFS PARK and HWANG: AN EFFICIENT POWER SAVING MECHANISM FOR DELAY-GUARANTEED SERVICES IN IEEE 802.16E 5 discipline is used. Note that the method of considering 3, we can derive the expectation of a busy period B in a system with the LCFS discipline is widely used for our system as follows. the busy period analysis, e.g., [14]. Now we assume that there are j backlogged packets Theorem 4: The expectation of a busy period in our in the buﬀer at the beginning of a busy period. Then, system is given by due to the LCFS service discipline the busy period gen- erated by the j backlogged packets can be divided into K−1 K−1 j sub-busy periods, each of which is generated by the E[B] = E[Bi ]Pr [NS = j] service of a backlogged packet as follows. When a busy j=1 i=K−j period starts, our system immediately starts the ser- K−1 vice of the j-th backlogged packet and continue its ser- + E[X] + E[Bi ] Pr[NS = K], vice for all subsequent packets that newly arrive at the i=1 system until it can start the service of the (j − 1)-th backlogged packet. That is, the service of the j-th where X is the service time of a packet. backlogged packet generates the ﬁrst sub-busy period which ends with the start of the service of the (j − 1)- th backlogged packet. In addition, since there are only The proof of Theorem 4 is given in Appendix A.5. K − j empty waiting rooms in the buﬀer for this case, the length of the ﬁrst sub-busy period in our system is identical to the length of a busy period of the ordi- 6. Performance Analysis nary M/GI/1/K − j + 1 queueing system. Similarly, the i-th sub-busy period is generated by the service In this section, we propose two performance measures, of the (j − i + 1)-th backlogged packet. Since there called the the power consumption per unit time per ef- are K − j + i − 1 empty waiting rooms in the buﬀer fective arrival and the average packet response delay. for this case, the length of the i-th sub-busy period is Based on these two performance measures, for given identical to the length of a busy period of the ordinary arrival rate λ, the ﬁrst sleep interval T0 , the system M/GI/1/K − j + i queueing system. ∗ size K and the mean service time of a packet E[X], we Let Bm and Bm (s) be the length of a busy period obtain the optimal Tmax value. Then, by using the re- and its LST (Laplace-Stieltjes Transform) in the ordi- sults of Tmax for each T0 , we will determine the optimal nary M/GI/1/m + 1 queueing system. Then, we have set of (T0 , Tmax ) for a given delay requirement to mini- the following Theorem [16]. mize the power consumption per unit time per eﬀective Theorem 3: The LST of the length of a busy period arrival. for the ordinary M/GI/1/m + 1 queueing system with The parameters related with the power consump- m waiting rooms is tion are as follows. Let ES , EW and EL be the power u0 (s) Bm ∗ (s) = . consumption units per unit time in sleep-mode, wake- m−1 m−1 ∞ m−1 ∗ ∗ mode and a listening interval, respectively. In addition, 1− uk (s) Bj (s) − uk (s) Bj (s) k=1 j=m−k+1 k=m j=1 since the MS consumes the power to switch the mode, let Eon−switch and Eof f −switch be the power consump- The expectation E[Bm ] is tion units for the switch-on action and the switch-oﬀ action, respectively. The switch-on (switch-oﬀ, resp.) 1 m−1 action means that the MS changes its state from sleep E[Bm ] = E[X] + E[Bj ]Qm−j , q0 (wake or listen, resp.) to listen (sleep, resp.). j=1 ∞ k where uk (s) = 0 (λx) e−(λ+s)x dF (x), F (x) is the dis- k! 6.1 The power consumption per unit time per eﬀective tribution function of the service time, qk = uk (0) and arrival j Qj = 1 − k=0 qk . (Note that when the lower limit of a product (a summation, resp.) is greater that the upper limit, the product (the summation, resp.) is taken to In this subsection, we obtain the power consumption be 1 (0, resp.).) per unit time per eﬀective arrival in our system. To do this, we ﬁrst derive the power consumption per unit Then, from our observation above the length of a time of an MS. Then, we get the packet blocking prob- busy period B(j) generated by j backlogged packets in ability. Let pV , pS and pB be the amounts of total the buﬀer is given by power consumption during a vacation period, a setup d B(j) = BK−j + BK−j+1 + · · · + BK−1 . (2) time period and a busy period, respectively. Then, by the deﬁnitions the expectations E[pV ], E[pS ] and E[pB ] Therefore, using equation (2), Theorem 2 and Theorem are given as follows: IEICE TRANS. COMMUN., VOL.Exx–??, NO.xx XXXX 200x 6 M packets leave the system after service completion. Let E[pV ] = ES S0 + e−λSj−1 (ES Tj + EL L) d πj be the steady state probability that j packets are j=1 left in the system immediately after service completion ES TM + EL L −λSM (0 ≤ j ≤ K − 1). Let Ln be the number of packets + e , 1 − e−λvM left behind in the system immediately after the n-th d E[pS ] = EL E[S] = EL L, Markov point (n = 1, 2, ...). Then the πj is represented E[pB ] = EW E[B]. as follows. d Theorem 5: The steady state probability πj that j Note that E[pV ] can be derived from E[V ] in section 4. packets are left in the system immediately after a ser- Then, the power consumption per unit time of the MS, vice completion is given by which is denoted by P C and deﬁned by d E[total power consumption in a cycle] πj = lim Pr[Ln = j], 0≤j ≤K −1 n→∞ PC = , E[total length of a cycle] 1 K−1 , j=0 is given by = j=0 πj d π0 πj , 1 ≤ j ≤ K − 1, E[pV ]+ E[pS ]+ E[pB ]+ E[NI ](Eon−switch + Eof f −switch ) PC = (3) . E[C] where Let PB and ρ be the packet blocking probability and π0 = 1, the probability that the server is busy at an arbitrary j j+1 1 time in steady state, respectively. Since our system has πj+1 = πj − πi aj−i+1 − aj−k+1 Pr[NS = k] , a0 a single server and is of ﬁnite size K, it satisﬁes that i=1 k=1 for 0 ≤ j ≤ K − 2, ρ = λ(1 − PB )E[X] (4) ∞ (λx)k −λx ∆ ak = e dF (x), k = 0, 1, ..., where E[X] denotes the mean service time of a packet. 0 k! On the other hand, by its deﬁnition ρ can be also ob- and Pr[NS = k] are given in Theorem 2. tained as follows: The proof of Theorem 5 is given in Appendix A.6. E[B] Let Qk be the probability that there are k packets ρ= . (5) E[C] in the system including the packet being transmitted Then, by combining equations (4) and (5), we ﬁnally at an arbitrary time (k = 0, 1, ..., K). To derive Qk by d a obtain PB as follows: using πj , we let πj be the probability that an arriving packet ﬁnds j packets in the system, (j = 0, 1, ..., K). E[B] From the PASTA (Poisson Arrivals See Time Average) PB = 1 − . (6) λE[X]E[C] property, To consider two performance measures PB and P C si- a πj = Q j , 0 ≤ j ≤ K. (7) multaneously, we propose a new combined performance measure P Ce , called the power consumption per unit Since the state changes only by unit steps, by Burke’s time per eﬀective arrival and deﬁned by theorem [12], a d PC πj = (1 − QK )πj , 0 ≤ j ≤ K − 1. (8) P Ce = . λ(1 − PB ) Therefore, combining equations (7) and (8), we obtain Note that P Ce is the average actual power consumption d Qj = (1 − QK )πj , 0 ≤ j ≤ K − 1, (9) to transmit a packet. Note that QK is the blocking probability. So, by equa- 6.2 The average packet response delay tion (6) QK is, in fact, given as E[B] In this subsection, we propose the average packet re- QK = 1 − . λE[X]E[C] sponse delay deﬁned by the sum of queueing delay in the buﬀer and transmission delay from the BS to Then using equation (9) and Theorem 5 we can obtain the MS. To do this, ﬁrst, we obtain the distribution {Qj | 0 ≤ j ≤ K}. Let Le and D be the number of pack- of the number of backlogged packets in the system ets in the system at an arbitrary time and the response (called the queue length) immediately after a service delay of an arbitrary packet in the system, respectively. completion by applying the embedded Markov chain Then the expectation E[Le ] is given by method. Second, we derive the queue length distribu- K tion at an arbitrary time. We consider a set of embed- E[Le ] = kQk (10) ded Markov points which are those points in time when k=0 PARK and HWANG: AN EFFICIENT POWER SAVING MECHANISM FOR DELAY-GUARANTEED SERVICES IN IEEE 802.16E 7 Then, from Little’s formula, the average packet re- E[X]=2, K=10, T0=2 sponse delay E[D] is derived as follows: 35 I =64(Num) A IA=64(Sim) 1 30 E[D] = E[Le ]. (11) I =32(Num) Average Packet Response Delay ( E[D] ) A λ(1 − QK ) IA=32(Sim) 25 I =16(Num) A I =16(Sim) 6.3 The Procedure to get the optimal sleep-mode op- A IA=8(Num) 20 eration I =8(Sim) A 15 For simulation studies, we develop a MATLAB code to simulate the system. The simulation condition is as 10 follows. Since the sleep-mode operation is performed between one BS and one MS and we consider downlink 5 transmission, one BS and one MS are considered in our simulation. We assume an ideal wireless channel model 0 and generate 3×105 frames for each simulation. We also 4 8 16 32 64 128 256 T max assume that the time to transmit the control messages E[X]=2, K=10, T0=2 is zero. Here, the control messages are MOB SLP- 900 REQ, MOB SLP-RSP, and MOB TRF-IND. Since the I =64(Num) A IA=64(Sim) purpose of the standardized sleep-mode operation in Power consumption per effective arrival ( PCe ) 800 I =32(Num) IEEE 802.16e is to save the power consumption for low- 700 A IA=32(Sim) rate traﬃc environment, we use the expected interar- I =16(Num) A rival time IA (= 1/λ) = 8, 16, 32, 64 frames. For all ex- 600 I =16(Sim) A amples in this subsection, otherwise mentioned, we as- 500 IA=8(Num) I =8(Sim) sume that the service time of a packet has the geometric A distribution with mean E[X] = 2, and the system size 400 K is 10. Note that the choice of E[X] = 2 and K = 10 300 is an example. The system size K is not a critical pa- rameter in our model due to the fact that the packet 200 blocking probability is very low in low-rate traﬃc envi- 100 ronment. We can choose any other values of E[X] and K in our analysis. We follow the guidelines of IEEE 0 4 8 16 32 64 128 256 T 802.16e standard for the initial sleep window T0 , the max ﬁnal sleep window Tmax , and the listening interval L. Fig. 2 E[D] and P Ce for diﬀerent IA and Tmax The length L of a listening interval is ﬁxed. We assume that the length of L is equal to 1. Since there is no gen- eral information of the actual parameters for the power by simulation, the results obtained by our analysis and consumption units, we use ES : EL : EW = 1 : 10 : 10 the expected interarrival time (= 1/λ) of the packets and Eon−switch : Eof f −switch = 30 : 20, as given (in frame), respectively. As seen from the ﬁgure, our in [5, 10, 17–19]. analytic results are well matched with the simulation In this subsection, we ﬁrst propose a procedure to results, which partially veriﬁes the validity of our anal- get the optimal value of Tmax for the delay-guaranteed ysis. From the ﬁgure, we also see that the value of Tmax services. That is, for given mean service time E[X], aﬀects E[D] and P Ce for each ﬁxed value of IA , and system size K and the initial sleep interval T0 we show the eﬀect of Tmax on E[D] and P Ce becomes more sig- how to get the optimal value of Tmax based on two per- niﬁcant as IA increases. The reason for this is that, as formance measures – the power consumption per unit IA decreases, it occurs more frequently that the sleep- time per eﬀective arrival in subsection 6.1 and the av- mode period is terminated before the length of a va- erage packet response delay in subsection 6.2. Then, cation period reaches the maximum possible value (re- by investigating the results, we show how to determine lated with Tmax ). the optimal values of T0 and Tmax for a given delay re- Another observation from Fig. 2 is that, in most quirement to minimize the power consumption per unit cases except IA = 64 frame, when Tmax is greater than time per eﬀective arrival. 128, Tmax does not aﬀect E[D] and P Ce any more. In Fig. 2, we change the value of Tmax and the This result is in accordance with previously known re- packet arrival rate λ, and plot the resulting value of sults in [11,21]. That is, when the value IA is small (the E[D] and P Ce for given mean service time E[X], sys- high-rate traﬃc environment in this case), the param- tem size K and the initial sleep interval T0 . In the ﬁg- eter Tmax does not aﬀect the system performance sig- ure, ‘Sim’, ‘Num’ and ‘IA ’ denotes the results obtained niﬁcantly. However, since the sleep-mode operation is IEICE TRANS. COMMUN., VOL.Exx–??, NO.xx XXXX 200x 8 Table 1 Optimal value of Tmax given delay requirement E[X]=2, K=10 (T0 =2) 40 PP IA T =4, I =64 0 A PP T0=4, IA=32 delay PP 64 32 16 8 35 T =4, I =16 requirement PP Average Packet Response Delay ( E[D] ) 0 A P 30 T0=4, IA=8 T =16, I =64 10 frames 16 16 16 1024 0 A T =16, I =32 25 0 A T0=16, IA=16 15 frames 16 32 1024 1024 T =16, I =8 20 0 A 20 frames 32 1024 1024 1024 15 25 frames 64 1024 1024 1024 10 30 frames 128 1024 1024 1024 5 0 8 16 32 64 128 256 considered to save the power consumption for low-rate T max traﬃc environment (under which the eﬀect of Tmax is E[X]=2, K=10 signiﬁcant), ﬁnding a suitable value of Tmax is impor- 600 T =4, I =64 0 A tant for low-rate traﬃc environment. T0=4, IA=32 Power consumption per effective arrival ( PCe ) To get the optimal value of Tmax , ﬁrst note that 500 T =4, I =16 0 A the average packet response delay E[D] increases and T0=4, IA=8 T =16, I =64 the power consumption per unit time per eﬀective ar- 400 0 A T =16, I =32 rival P Ce decreases as we change the value of Tmax . 0 A T0=16, IA=16 This implies that we can not improve E[D] and P Ce 300 T =16, I =8 0 A simultaneously. Hence, we assume that a certain level of delay requirement is given. Then we consider the following twofold procedure. In the ﬁrst step, for given 200 mean service time E[X], system size K, initial sleep in- terval T0 and interarrival time IA , we select the values 100 of Tmax with which the value of E[D] is lower than the delay requirement. In the second step, among the se- 0 8 16 32 64 128 256 lected values of Tmax , we then choose the optimal value T max of Tmax which minimizes the value of P Ce . In all pro- Fig. 3 The eﬀect of T0 cedures in this subsection, we assume the value of Tmax is of the form 2M T0 for simplicity. Using Fig. 2 and the twofold procedure, we can choose the optimal value of Tmax as follows when the cordingly the number of packets stored in the buﬀer other parameters are given as E[X] = 2, K = 10 and during the sleep intervals increases. This results in T0 = 2. For instance, assume that the delay require- the increase in E[D]. On the contrary, as T0 increases, ment is 15 frames and IA = 32 frames. Then, from the the MS has longer sleep-mode periods and switches its delay requirement we can ﬁrst select Tmax = 4, 8, 16, 32 mode less frequently. Noting that the power consump- because they result in the average packet response de- tion units Eon−switch and Eof f −switch are greater than lay lower than the delay requirement. Among these the power consumption units ES , EW and EL in sleep- selected values of Tmax , we check the corresponding val- mode, wake-mode and listening intervals, the less the ues of P Ce from Fig. 2 and ﬁnally choose Tmax = 32 MS switches its mode, the less it consumes its power. as the optimal value which minimizes P Ce . For other Thus, P Ce decreases. The optimal values of Tmax for values of delay requirement and interarrival times, we various values of T0 are summarized in Table 2 and can perform the same procedure to obtain the optimal 3. In Table 3, the notation * means that the optimal value of Tmax and the results are summarized in Table value of Tmax does not exist. This can happen since 1. Note that the maximum length of Tmax is ﬁxed and the value of T0 is relatively large compared with the equal to 1024 [3], so we do not consider values greater delay requirement. That is, if T0 is large, then the than 1024 for Tmax to obtain Table 1. length of sleep-mode period is large. So, the average In Fig. 3, we change the value of T0 and plot packet response delay is large and accordingly the de- the resulting value of E[D] and P Ce . From the ﬁg- lay requirement is violated for any value of Tmax in this ure, we see that, as T0 increases, E[D] increases and case. P Ce decreases. The reason for this is as follows. As Finally, using the above procedure for each given T0 increases, the sleep intervals become longer and ac- T0 and other parameters, we can determine the opti- PARK and HWANG: AN EFFICIENT POWER SAVING MECHANISM FOR DELAY-GUARANTEED SERVICES IN IEEE 802.16E 9 Table 2 Optimal value of Tmax given delay requirement Table 4 Optimal values of T0 and Tmax (IA = 64 and delay (T0 =4) requirement=15 frames) PP IA P delay PP 64 32 16 8 (T0 , Tmax ) P Ce P requirement PPP (2, 16) 394.3040 10 frames 8 16 16 1024 (3, 24) 321.8611 15 frames 16 32 1024 1024 (4, 16) 354.7521 20 frames 32 1024 1024 1024 (5, 20) 312.7799 25 frames 64 1024 1024 1024 (6, 24) 283.7988 30 frames 64 1024 1024 1024 (7, 14) 349.4597 Table 3 Optimal value of Tmax given delay requirement (8, 16) 320.6569 (T0 =16) PP (9, 18) 297.8579 PP IA delay PP 64 32 16 8 (10, 20) 279.3499 requirement PP P (11, 22) 264.0157 10 frames * * * * (12, 24) 251.0954 15 frames * * 32 1024 (13, *) - 20 frames 32 32 1024 1024 (14, *) - 25 frames 32 1024 1024 1024 (15, *) - 30 frames 64 1024 1024 1024 (16, *) - mal values of T0 and Tmax that minimize the power consumption per unit time per eﬀective arrival P Ce . that satisﬁes a given delay requirement and minimizes For instance, assume that the delay requirement is 15 the power consumption per unit time per eﬀective ar- frames and the interarrival time IA is 64 frames. In rival. this case, we compute the optimal value of Tmax and the corresponding value of P Ce for each value of T0 , and References the results are given in Table 4. Then, obviously the optimal values of (T0 , Tmax ) are (12, 24) because they [1] IEEE Standard for Local and metropolitan area networks Part 16: Air Interface for Fixed Broadband Wireless Access minimize P Ce . From this result, we see that a relatively Systems, IEEE Standard 802.16, 2004. large value of T0 would minimize the power consump- [2] C. Eklund, R. B. Marks, K.L. Stanwood, and S. Wang, tion per unit time per eﬀective arrival for low-rate traf- “IEEE standard 802.16: A technical overview of the wire- ﬁc environment. For another delay requirements and lessMAN air interface for broadband wireless access”, IEEE traﬃc conditions, we use the same procedure to deter- Communications Magazine, vol.40, no.6, pp.98-107, June 2002. mine the optimal values of T0 and Tmax . [3] Part 16: Air Interface for Fixed and Mobile Broad- band Wireless Access Systems, Amendment for Physical 7. Conclusions and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands, IEEE Standard In this paper, we model and analyze the sleep-mode op- 802.16e, 2006. eration in IEEE 802.16e WMAN using the M/GI/1/K [4] Dinh Thi Thuy Nga, Min-Gon Kim, and Minho Kang, “Delay-guaranteed Energy Saving Algorithm for the Delay- queueing system with multiple vacations, exhaustive sensitive Applications in IEEE 802.16e Systems”, IEEE services and setup times. We analyze the wake-mode Trans. Consumer Electron., vol.53, no.4, pp.1339-1347, period as well as the sleep-mode period together. We Nov. 2007. also consider the power consumption for switching the [5] Yang Xiao, “Energy saving mechanism in the IEEE 802.16e mode. Based on the analysis, we consider two perfor- wireless MAN”, IEEE Communications Letters, vol.9, no.7, pp.595-597, July 2005. mance measures – the power consumption per unit time [6] Jun-Bae Seo, Seung-Que Lee, Nam-Hoon Park, Hyong- per eﬀective arrival and the average packet response Woo Lee, and Choong-Ho Cho, “Performance analysis of delay. By considering these two performance measures sleep mode operation in IEEE802.16e”, Vehicular Technol- together, we obtain the optimal sleep-mode operation ogy Conference, vol.2, no.26-29, pp.1169-1173, Sept. 2004. IEICE TRANS. COMMUN., VOL.Exx–??, NO.xx XXXX 200x 10 [7] Jaehyuk Jang, Kwanghun Han, and Sunghyun Choi, “Adaptive Power Saving Strategies for IEEE 802.16e Mo- Appendices bile Broadband Wireless Access”, Asia-Paciﬁc Conference on Communications, pp.1-5, Aug. 2006. [8] Min-Gon KIM, JungYul CHOI, Bokrae JUNG, and Minho A.1. Derivation of E[V ] KANG, “Adaptive Power Management Mechanism Consid- ering Remaining Energy in IEEE 802.16e”, IEICE Trans. Commun., vol.E90-B, no.9, pp.2621-2624, Sep. 2007. ∞ [9] Min-Gon Kim, Minho Kang, and Jung Yul Choi, “Per- formance Evaluation of the Sleep Mode Operation in the E[V ] = Sj Pr[V = Sj ] IEEE 802.16e MAC”, International Conference on Ad- j=0 vanced Communication Technology, vol.1, pp.602-605, Feb. ∞ 2007. = S0 (1 − e−λS0 ) + Sj e−λSj−1 (1 − e−λvj ) [10] Fangmin Xu, Wei Zhong, and Zheng Zhou, “A Novel Adap- j=1 tive Energy Saving Mode in IEEE 802.16E System”, Mili- ∞ tary Communications conference, pp.1-6, Oct. 2006. [11] Guojun Dong, Chengjun Zheng, Hongxia Zhang, and = S0 (1 − e−λS0 ) + (Sj e−λSj−1 − Sj e−λSj ) Jufern Dai, “Power saving class I sleep mode in IEEE j=1 802.16e system”, Advanced Communication Technology, ∞ vol.3, pp.1487-1491, Feb. 2007. = S0 + e−λSj−1 (Sj − Sj−1 ) [12] Hideaki Takagi, Queueing Analysis: A Foundation of Per- j=1 formance Evaluation, Volume 1:Vacation and priority Sys- M tems, Amsterdam: North Holland, 1991. [13] Tony T. Lee, “M/G/1/N queue with vacation time and = S0 + e−λSj−1 (Sj − Sj−1 ) exhaustive service discipline”, Operation Research, vol.32, j=1 no.4, pp.774-784, 1984. ∞ [14] Hideaki Takagi, Queueing Analysis: A Foundation of Per- + e−λSj−1 (Sj − Sj−1 ) formance Evaluation, Volume 2:Finite systems, Amster- j=M +1 dam: North Holland, 1993. [15] Leonard Kleinrock, Queueing systems, volume1: Theory. M ∞ New York: John Wileys & Sons, 1975. = S0 + e−λSj−1 vj + e−λSj−1 vM [16] Louis W. Miller, “A note on the busy period of an M/G/1 j=1 j=M +1 ﬁnite queue”, Operation Research, vol.23, no.6, pp.1179- M 1182, Nov. 1975. [17] Yang Xiao, Haizhon Li, Yi Pan, Kui Wu, and Jie Li, = S0 + e−λSj−1 vj “On optimizing energy consumption for mobile handsets”, j=1 −λSM IEEE Transactions on Vehicular Technology, vol.53, no.6, +e vM 1 + e−λvM + (e−λvM )2 + · · · pp.1927-1941, Nov. 2004. [18] Ying-Wen Bai, and Ching-Ho Lai, “A bitmap scaling and M vM rotation design for SH1 low power CPU”, Proceedings of = S0 + e−λSj−1 vj + e−λSM . the 2nd ACM international workshop on Modeling, analy- j=1 1 − e−λvM sis and simulation of wireless and mobile systems MSWiM, pp.101-106, 1999. [19] Ching-Long Su, Chi-Ying Tsui, and Alvin M Despain, “Sav- ing power in the control path of embedded processors”, IEEE Design and Test of Computers, vol.11, no.4, pp.24-31, 1994. [20] J. Banks, J. S. Carson II, B. L. Nelson, and D. M. Nicol Discrete-Event System Simulation, 3rd Edition, Prentice Hall, 2001. [21] Yunju Park, and Gang Uk Hwang, “Performance Modelling and Analysis of the Sleep-Mode in IEEE802.16e WMAN”, IEEE 65th Vehicular Technology Conference, pp.2801-2806, April, 2007. [22] Andreas Frey, and Yoshitaka Takahashi, “Explicit Solutions for the M/GI/1/N Finite Capacity Queues With and With- out Vacation Time”, Proc. 15th International Teletraﬃc Congress, pp.507-516, June 1997. [23] Hideaki Takagi, “Analysis of a Finite Capacity M/G/1 Queue with Resume Level”, Performance Evaluation, vol.5, no.3, pp.197-203, 1985. PARK and HWANG: AN EFFICIENT POWER SAVING MECHANISM FOR DELAY-GUARANTEED SERVICES IN IEEE 802.16E 11 A.2. Derivation of E[NI ] A.4. Proof of Theorem 2 For 1 ≤ j ≤ K − 1, K−2 ∞ Pr[NS = j] = Pr[NS = j|NV = i]Pr[NV = i] i=1 E[NI ] = jPr[V = Sj−1 ] j j=1 = Pr[AS = j − i]Pr[NV = i]. ∞ −λS0 −λSj−2 −λvj−1 i=1 = (1 − e )+ je (1 − e ) j j=2 (λS)j−i e−λS = × ∞ i=1 (j − i)! = (1 − e−λS0 ) + (je−λSj−2 − je−λSj−1 ) M i (λvM ) −λvM (λvn )i e−λSn e j=2 + i! e−λSM . ∞ n=0 i! 1 − e−λvM = 1+ e−λSj Similarly as in the proof of Theorem 1, we get Pr[NS = j=0 K]. M ∞ −λSj = 1+ e + e−λSj j=0 j=M +1 A.5. Proof of Theorem 4 M = 1+ e−λSj j=0 K +e−λSM e−λvM + (e−λvM )2 + · · · E[B] = E[B|NS = j]Pr[NS = j] M e−λvM j=1 = 1+ e−λSj + e−λSM K−1 j=0 1 − e−λvM = E[B|NS = j]Pr[NS = j] j=1 +E[B|NS = K]Pr[NS = K] K−1 A.3. Proof of Theorem 1 = E[B(j)]Pr[NS = j] j=1 For 1 ≤ i ≤ K − 1, + (E[X] + E[B(K − 1)]) Pr[NS = K] ∞ K−1 K−1 Pr[NV = i] = Pr[NV = i|NI = n]Pr[NI = n] = E[Bi ]Pr[NS = j] n=0 j=1 i=K−j = Pr[NV = i|NI = 0]Pr[NI = 0] K−1 M + E[X] + E[Bi ] Pr[NS = K] + Pr[NV = i|NI = n]Pr[NI = n] i=1 n=1 ∞ + Pr[NV = i|NI = n]Pr[NI = n] n=M +1 A.6. Proof of Theorem 5 (λv0 )i −λv0 e = i! (1 − e−λv0 ) d Let πj be the steady state probability that j packets are 1 − e−λv0 M (λvn )i −λvn left in the system immediately after service completion e + i! e−λSn−1 (1 − e−λvn ) (0 ≤ j ≤ K − 1). Let Ln be the number of packets 1 − e−λvn n=1 left behind in the system immediately after the n-th (λvM )i −λvM d e ∞ Markov point (n = 1, 2, ...). Then the πj is represented + i! e−λ(SM +kvM ) (1 − e−λvM ) as follows: 1 − e−λvM k=0 d M (λvn ) e i −λSn (λvM )i −λvM e πj = lim Pr[Ln = j], 0 ≤ j ≤ K − 1. = + i! e−λSM . n→∞ n=0 i! 1 − e−λvM Let pij and ak be the one step transition probability in the Markov chain and the probability that k packets K−1 We have Pr[NV = K] = 1 − i=1 Pr[NV = i]. arrive during a service time, respectively. Then pij and IEICE TRANS. COMMUN., VOL.Exx–??, NO.xx XXXX 200x 12 d ak are represented as follows: with K unknowns {πj | 0 ≤ j ≤ K − 1}. An eﬃcient d ∆ algorithm for computing {πj | 0 ≤ j ≤ K − 1} can be pi,j = Pr[Ln+1 = j|Ln = i] given in terms of ∞ ∆ (λx)k −λx d ak = e dF (x) k = 0, 1, .... ∆ πj 0 k! πj = 0 ≤ j ≤ K − 1. (20) d π0 Then the one step transition probability pij is derived as follows: This πj is called an upper Hessenberg matrix [12,22,23]. j+1 It is easy to see from equation (18) that {πj | 0 ≤ j ≤ P0,j = aj−k+1 Pr[NS = k], 0 ≤ j ≤ K − 2, K − 1} can be recursively computed as follows. For k=1 0≤j ≤K −2 (12) K ∞ π0 = 1 d P0,K−1 = al Pr[NS = k], j = K − 1, (13) πj k=1 l=K−k πj = d π0 d j+1 j+1 d π0 k=1 aj−k+1 Pr[NS = k] + i=1 πi aj−i+1 Pi,j = aj−i+1 , 1 ≤ i ≤ K − 1, i − 1 ≤ j ≤ K − 2, = π0d (14) j+1 j+1 ∞ = aj−k+1 Pr[NS = k] + πi aj−i+1 Pi,K−1 = al , 1 ≤ i ≤ K − 1, j = K − 1, (15) k=1 i=1 l=K−i j+1 j Pij = 0, otherwise. = aj−k+1 Pr[NS = k] + πi aj−i+1 + πj+1 a0 . k=1 i=1 Note here that NS is the number of backlogged packets at the beginning of a busy period. Also, the balance Thus, for 0 ≤ j ≤ K − 2, equations for the steady state probabilities are given by 1 j j+1 πj+1 = π − π aj−i+1 − aj−k+1 Pr[NS = k] . (21) K−1 a0 j i=1 i k=1 d d πj = πi pi,j , 0 ≤ j ≤ K − 1, i=0 From equations (17) and (20), we have j+1 1 d πi pi,j , 0 ≤ j ≤ K − 2, d π0 = . (22) K−1 πj i=0 j=0 = K−1 (16) d πi pi,j , j = K − 1, Hence, using equation (20), (21) and (22), we can get d i=0 {πj | 0 ≤ j ≤ K − 1}. K−1 d πj = 1. (17) j=0 Then, for 0 ≤ j ≤ K − 2, by substituting (12) and (14) into (16), we have j+1 j+1 d d d πj = π0 aj−k+1 Pr[NS = k] + πi aj−i+1 . (18) k=1 i=1 Similarly, for j = K − 1, by substituting (13) and (15) into (16), we have K ∞ d d πK−1 = π0 al Pr[NS = k] k=1 l=K−k K−1 ∞ d + πi al (19) i=1 l=K−i Note that equation (19) is redundant, and that equa- tions (17) and (18) provide K independent equations PARK and HWANG: AN EFFICIENT POWER SAVING MECHANISM FOR DELAY-GUARANTEED SERVICES IN IEEE 802.16E 13 Yunju Park received the B.S. de- gree in Mathematics from Kyungpook National University in 2002 and the M.S. degree in Mathematics from Korea Ad- vanced Institute of Science and Technol- ogy (KAIST), Daejeon, Korea, in 2004. She is currently working toward the Ph.D. degree in the Department of Mathemati- cal Sciences at KAIST. Her research in- terests include IEEE 802.16e and the power saving and performance modelling of wireless networks. Gang Uk Hwang received the B.Sc., M.Sc., and Ph. D. degrees in Mathemat- ics (Applied Probability) from Korea Ad- vanced Institute of Science and Technol- ogy (KAIST), Daejeon, Korea, in 1991, 1993 and 1997, respectively. From Febru- ary 1997 to March 2000, he was with Electronics and Telecommunications Re- search Institute (ETRI), Daejeon, Korea. From March 2000 to February 2002, he was a visiting scholar at the Department of Computer Sciences and Electrical Engineering in University of Missouri - Kansas City. Since March 2002, he has been with the Department of Mathematical Sciences and Telecommunica- tion Engineering Program at KAIST, where he is an Associate Professor. His research interests include teletraﬃc theory, perfor- mance evaluation of communication systems, quality of service provisioning for wired/wireless networks and cross-layer design for wireless networks.