Modeling UMTS discontinuous reception mechanism

Modeling UMTS Discontinuous Reception

Mechanism

Shun-Ren Yang and Yi-Bing Lin, Fellow, IEEE

Abstract—This paper investigates the discontinuous reception

(DRX) mechanism of universal mobile telecommunications system (UMTS). DRX is exercised between the network and a mobile sta-tion (MS) to save the power of the MS. The DRX mechanism is con-trolled by two parameters: the inactivity timer threshold and the DRX cycle. Analytic and simulation models are proposed to study the effects of these two parameters on output measures including the expected queue length, the expected packet waiting time, and the power saving factor. Our study quantitatively shows how to se-lect appropriate inactivity timer and DRX cycle values for various traffic patterns.

Index Terms—Discontinuous reception (DRX), power saving,

universal mobile telecommunications system (UMTS).

I. INTRODUCTION

U

[10] supports mobile multimedia applications with high data transmission rates. Fig. 1 illustrates a simplified UMTS ar-chitecture, which consists of the core network and the UMTS

terrestrial radio access network (UTRAN). The core network

is responsible for switching/routing calls and data connections to the external networks, while the UTRAN handles all radio-re-lated functionalities. The UTRAN consists of radio network

controllers (RNCs) and node Bs (i.e., base stations) that are

con-nected by an asynchronous transfer mode (ATM) network. A

mobile station (MS) communicates with node Bs through the

radio interface based on the WCDMA (Wideband CDMA) tech-nology [10].

In UMTS, MS power consumption is a serious problem for wireless data transmission. The data bandwidth is significantly limited by the battery capacity [15]. Therefore, power saving

Manuscript received June 10, 2003; revised October 3, 2003; accepted November 18, 2003. The editor coordinating the review of this paper and approving it for publication is Z. Zhang. The work of S.-R. Yang was supported by the Mediatek Fellowship and the National Science Council under Contract NSC 93–2213–E-007–112. The work of Y.-B. Lin was supported in part by the National Science Council Excellence Project NSC93–2752–E-0090005–PAE, Chair Professorship of Providence University, IIS/Academia Sinica, FarEas-tone, CCL/ITRI, and by the Lee and MTI Center for Networking Research, National Chiao Tung University.

S.-R. Yang was with the Department of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu, Taiwan 30050, R.O.C. He is now with the Department of Computer Science and Institute of Commu-nications Engineering, National Tsing Hua University, Hsinchu, Taiwan 30050, R.O.C. (e-mail: sryang@cs.nthu.edu.tw).

Y.-B. Lin was with the Department of Computer Science and Information Management, Providence University, Taichung, Taiwan 30050, R.O.C. He is now with the Department of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu, Taiwan 30050, R.O.C. (e-mail: liny@csie.nctu.edu.tw).

Digital Object Identifier 10.1109/TWC.2004.840259

mechanisms are typically exercised to reduce power consump-tion. Most existing wireless mobile networks (including UMTS) employ discontinuous reception (DRX) to conserve the power of MSs. DRX allows an idle MS to power off the radio receiver for a predefined period (called the DRX cycle) instead of con-tinuously listening to the radio channel. In MOBITEX [17], the network periodically transmits a specific SVP6 frame to an-nounce the list of the MSs that have pending packets. All MSs are required to synchronize with every SVP6 frame and wake up immediately before the transmission starts. When some MSs experience high traffic loads, the network may decide to shorten the announcement interval to reduce the frame delay. As a con-sequence, the low traffic MSs will consume extra unnecessary power budget. In CDPD [5], [16], and IEEE 802.11 [11] stan-dards, similar DRX mechanisms are utilized except that an MS is not forced to wake up at every announcement instant. Instead, the MS may choose to omit some announcements to further duce its power consumption. A wake-up MS has to send a re-ceiver ready (RR) frame to inform the network that it is ready to receive the pending frames. However, such RR transmissions may collide with each other if the MSs tend to wake up at the same time. Thus, RR retransmissions are likely to occur and extra power is unnecessarily consumed. UMTS DRX [2], [4] enhances the above mechanisms by allowing an MS to nego-tiate its own DRX cycle length with the network. Therefore, the network is aware of sleep/wake-up scheduling of each MS, and only delivers the paging message when the MS wakes up.

The CDPD DRX mechanism has been investigated through simulation models [16]. In [13], an analytic model was pro-posed to investigate CDPD DRX mechanism. This model does not provide close-form solution. Furthermore, the model was not validated against simulation experiments. This paper inves-tigates the performance of the UMTS DRX with a variant of the

M/G/1 vacation model. We derive the close-form equations for

the output measures and validate the results against simulation. Based on the proposed model, the DRX performance is investi-gated by numerical examples.

II. UMTS DRX MECHANISM

The UMTS DRX mechanism is realized through the radio

re-source control (RRC) finite state machine exercised between the

RNC and the MS [1]. There are two modes in this finite state ma-chine (see Fig. 2). In the RRC Idle mode, the MS is tracked by the core network without involving the UTRAN. When an RRC connection is established between the MS and its serving RNC, the MS enters the RRC Connected mode. This mode consists of four states. If the MS obtains a dedicated traffic channel for the RRC connection, it enters the Cell DCH state. On the

Fig. 1. Simplified UMTS network architecture.

Fig. 2. RRC state diagram.

other hand, if the MS is allocated a common or shared traffic channel (i.e., the channel is shared by several MSs), it enters the Cell FACH state. The data communication activities can only be performed in these two states. In the Cell PCH state, no uplink access is possible, and the MS selects a paging channel (PCH) to monitor paging messages from the RNC. In the above three RRC states, the MS performs location update whenever it moves to a new cell (i.e., the radio coverage of a Node B). If the MS receives packets infrequently, the UTRAN may eliminate the cell update overhead by instructing the MS to move to the

URA PCHstate. In this state, the MS performs location update for every UTRAN registration area (URA) crossing. Details of cell and URA updates can be found in [20].

In the Cell DCH and Cell FACH states, the MS receiver is always turned on to receive packets. These states correspond to the power active mode. In the RRC Idle mode, Cell PCH and URA PCH states, the DRX is exercised to reduce the MS power consumption. These states/mode correspond to the power

saving mode. The MS receiver activities are described in terms

of three periods.

The busy period: During packet transmission (i.e., the

“server” is “busy”), the UMTS core network sends the packets to an MS through the RNC and Node B. The incoming packets are first stored in the RNC buffer before they are delivered to the MS. Since the MS is in the power active mode, the RNC processor immediately transmits packets in the first in–first out (FIFO) order. Due to high error-rate and low bit-rate nature of radio transmission, the

stop-and-wait hybrid automatic repeat reQuest

(SAW-Hy-brid ARQ) flow control algorithm [3] is exercised between the Node B and the MS to guarantee successful radio packet delivery. The SAW-Hybrid ARQ algorithm works as follows. When the Node B sends a packet to the MS, it waits for a positive acknowledgment (ack) from the MS before it can transmit the next packet. The Node B may receive negative acknowledgments (naks) from the MS,

which indicate that some errors have occurred (e.g., the transmitted packet is damaged). In this case, the Node B re-transmits the packet until an ack is received.

The inactivity period: If the RNC buffer becomes empty,

the RNC inactivity timer is activated. If any packet arrives at the RNC before the inactivity timer expires, the timer is stopped. The RNC processor starts to transmit packets, and another busy period begins. Note that the MS is in the power active mode in both the busy and inactivity periods, where the MS receiver is turned off.

The sleep period: If no packet arrives before the inactivity

timer expires, the MS enters the power saving mode and the MS receiver is turned off. The MS sleep period contains at least one DRX cycles. At the end of a DRX cycle, the MS wakes up to listen to the PCH. If some packets have arrived at the RNC during the last DRX cycle (i.e., the paging indicator for this MS is set), the MS starts to receive packets and the sleep period terminates. Otherwise, the MS returns to sleep until the end of the next DRX cycle. In the power saving mode, the RNC processor will not transmit any packets to the MS.

Based on the above description, we propose an analytic model for the UMTS DRX mechanism. As illustrated in Fig. 1, the UMTS core network sends the packets to an MS through the RNC and Node B. We assume that packet arrivals to the RNC form a Poisson stream with rate . The RNC processor sends the packets to the Node B through an ATM link. The Node B then forward the packets to the MS by the WCDMA radio link. Compared with WCDMA radio transmission, ATM is much faster and more reliable. Therefore the ATM transmission delay is ignored in our analytic model, and the RNC and the Node B are treated as a FIFO server. Let denote the time interval be-tween when a packet is transmitted by the RNC processor and when the corresponding ack is received by the RNC processor. Let be the threshold of the RNC inactivity timer, and be the MS sleep period. The UMTS DRX is modeled as a variant of

the M/G/1 queue with multiple vacations [19], where repre-sents the service time (the period between when a packet is sent from the UTRAN to the MS and when the UTRAN receives the ack from the MS), and corresponds to the server vacations. Our model is different from the existing M/G/1 vacation model due to the introduction of the inactivity timer threshold . In our model, the server can not enter vacation mode immediately after the queue is empty. The following output measures are de-rived:

1) mean queue length: the expected number of packets buffered in the UTRAN, including the one in delivery and those waiting in the RNC buffer;

2) mean packet waiting time: the expected waiting time of a packet in the RNC buffer before it is transmitted to the MS;

3) power saving factor: the probability that the MS re-ceiver is turned off when exercising the UMTS DRX mechanism; this factor indicates the percentage of power saving in the DRX (compared with the case where DRX is not exercised).

III. QUEUELENGTH ANDPACKETWAITINGTIME

This section derives the generating function for the queue length distribution and the Laplace Transform for the packet waiting time. Denote as the queue length of the RNC buffer immediately after the th packet completes service and departs (i.e., at the time when the th ack is received by the RNC pro-cessor). implies that the RNC buffer is empty after the th packet has been received by the MS. In this case, the RNC inactivity timer is activated. Suppose that packets arrive at the RNC before the inactivity timer expires. If , the MS enters the power saving mode. Let be the number of packets that arrive during the sleep period. The probability mass

func-tions for and are denoted as (where

) and (where ),

respectively. Let be the number of packets that arrive during the service time of the st packet. The relationship

between , and can be expressed as

for for for

(1)

The above equation indicates that is independent of for , and the sequence of the random variables

constitutes a Markov chain [18]. Let be the queue length in the steady state. The steady state distribution for this Markov chain is defined as

for

which can be solved by using and the balance equations

(2)

where is the state transition probability.

Denote for and . Based on (1),

is expressed as (3), shown at the bottom of the page. Substituting (3) into (2), is expressed as

(4)

Let be the generating function for the

distribution. From (4), we have

(5)

Let be the probability generating function for (the probability that packets arrive during a packet ser-vice time ). These packet arrivals form a Poisson process with rate , which is independent of . Suppose that the distribu-tion has the Laplace Transform , mean and variance

. From [7, Th. 4.2], we have (6) for for for (3)

Let be the generating function for the distribution. From (6), (5) is rewritten as

(7) By rearranging the terms in (7), we obtain

(8)

Let . Since , we derive from (8)

as

(9) where . Substituting (9) into (8), we have

(10) The Laplace Transform for the packet waiting time is derived as follows. Following the FIFO scheduling policy, the RNC queue length seen by a departing packet is precisely the number of packets that arrived during the response time of the packet, where

(11) Let be the Laplace Transform of . Similar to the deriva-tion of (in [7, Th. 4.2]),

(12) Since the service time for a packet does not depend on the time it spends in the RNC buffer, and are independent. From (11) and the convolution property of the Laplace Transform, we have

(13)

From (10), (12), and (13), we have

(14) Assume that the length of each DRX cycle in a sleep pe-riod is independent and identically distributed with mean , variance , and the Laplace Transform . From [21]

(15) and

(16) Assume that the inactivity timer threshold has the density function , mean , variance , and Laplace Transform

. From the Poisson distribution

(17) Substituting (15), (16), and (17) into (10) and (14), we obtain (18) and (19), as shown at the bottom of the page.

From (18) and (19), the expected number of packets and the mean packet waiting time are expressed as

(20) and (21) (18) and (19)

Fig. 3. Regeneration cycles for MS activities.

IV. POWERSAVINGFACTOR

This section derives the power saving factor . We draw the timing diagram of MS receiver activities in Fig. 3. In this figure, the MS receiver activities are characterized by a regenerative

process [18], where a regeneration cycle consists of an inactivity

period , a sleep period , and a busy period . We note that at the end of every DRX cycle, the MS must wake up for a short period so that it can listen to the paging information from the network. Therefore, the “power saving” period in a DRX cycle is . Suppose that there are DRX cycles in a sleep period. From [18, Th. 3.7.1]

the receiver is turned off at time (22)

, and are derived as follows. In Fig. 3, is the time interval between when the RNC inactivity timer is activated and when the next packet arrives. Thus, . If the next packet arrives before the inactivity timer expires (i.e., ), then , and the next busy period follows (see the st cycle in Fig. 3). Otherwise, (the next packet arrives after the inactivity timer has expired; i.e., ) , and the next sleep period follows as illustrated in the th cycle in Fig. 3. From the memoryless property of Poisson process [18], is exponentially distributed with rate

. Therefore

(23) is derived as follows. If , then and packets arrive during the period. Let be the Laplace Transform of . From [7, Th. 4.2]

(24)

From (15) and (24), we have

(25) From (25), the mean sleep period is

(26) Note that with probability . From (26), we have

(27) Substitute (17) into (27) to yield

(28) The expected value is derived as follows. Since a period consists of DRX cycles , from Wald’s theorem [18], we have

(29) Substitute (28) into (29) to yield

(30) We derive as follows. If (with probability ), and is exactly the same as the busy period of an

M/G/1 queue. From [7]

(31)

where . If (with probability ), , and

packets arrive during the period. In this case, is the sum of periods. From Wald’s theorem, we have

TABLE I

COMPARISON OF THEANALYTIC ANDSIMULATIONRESULTS(V = 10= ; t = 60E[t ]; t = 5E[t ],AND = 0:1E[t ])

Fig. 4. Effects of and t (V = (1= ); t = 5E[t ];  = 0:1E[t ]). (a) E[L]. (b) E[t ] (unit: E[t ]). (c) P .

Substitute (31) and (16) into (32) to yield

(33)

From (31) and (33), we have

(34)

Substitute (17) into (34) to yield

(35) From (23), (28), (30), and (35), (22) is rewritten as

(36)

V. NUMERICALEXAMPLES

Our analytic model has been validated against a discrete event simulation model. This simulation model is similar to the one we developed in [14], and the details are omitted. For demonstration

purpose, we assume to have a Gamma distribution with mean , variance , and the Laplace Transform

where

The Gamma distribution is often used in mobile telecommuni-cations network modeling [6], [8], [9]. It has been shown that the distribution of any positive random variable can be approx-imated by a mixture of Gamma distributions (see [12, Lemma 3.9]). One may also measure the periods in a real UMTS net-work, and the measured data can be approximated by a Gamma distribution as the input to our models. Table I compares the analytic and simulation results. We consider fixed and .

In this table, , and

. The table indicates that the errors between the an-alytic and simulation models are less than 0.05% in most cases. Based on the analytic model, we investigate the DRX perfor-mance.

Figs. 4–6 plot the , and curves. In these fig-ures, has the Gamma distribution with variance , and and are fixed. The parameter settings are described in the captions of the figures.

Effects of : Fig. 4(a) indicates that the mean queue length

increases as increases. For is

insignificantly affected by the change of . When ap-proaches , the resulting queueing system becomes un-stable, and grows without bound. Fig. 4(b) plots the mean packet waiting time normalized by the mean

Fig. 5. Effects oft and  (V = (1= );  = 0:1 ). (a) E[L]. (b) E[t ] (unit: E[t ]). (c) P .

Fig. 6. Effects ofV ( = 0:1E[t ]). (a) E[L]. (b) E[t ] (unit: E[t ]). (c) P .

packet service time . The “ ” curve shows intuitive result that for an M/G/1 queue, is an increasing func-tion of . For DRX, curves decrease and then in-crease as increases. This phenomenon is explained as

follows. For is affected by the power

saving mode operation. Specifically, when approaches 0, the MS is always in the power saving mode. From (21), every arrival packet is expected to wait for

(37)

In Fig. 4(b), . From (37),

, which is the value we observe in the figure. As increases, it is more likely that the MS is in the power active mode when packets arrive. In this case, more packets are processed without experiencing the sleep periods, and

decreases as increases. On the other hand, if approaches , the packet traffic load exceeds the transmis-sion capability, and increases as increases. Fig. 4(c) shows the intuitive result that the power saving factor

is a decreasing function of .

Effects of : Fig. 4 indicates that by increasing the in-activity timer threshold , and decrease. When , the MS never enters the power saving mode, and the system is the same as an M/G/1 queue. When

is small (e.g., ), the inactivity timer al-ways expires before the next packet arrives. Therefore, the output measures are insignificantly affected by the change of .

Effects of : Fig. 5 indicates that , and are increasing functions of . We observe that when is small [e.g., for the dashed curves in Figs. 5(a) and (b)], decreasing will not improve the and performance. On the other hand, when is large [e.g., for the dashed curves in Fig. 5(c)], increasing will not improve the performance. Therefore, for (i.e., the dashed curves),

should be selected in the range .

Effects of : It is clear that and are not affected by . Fig. 5(c) illustrates the impact of on . When is large, (the cost of wakeup) is a small portion of a DRX cycle, which only has insignificant impact on . When is large and is small, the MS receiver is almost always turned on and . In this case, the impact is also insignificant. When both and are small, is significantly increased as decreases.

Effects of : Fig. 6 illustrates that and are in-creasing functions of the variance of the packet trans-mission delay . This effect is well known in queueing systems. On the other hand, is not affected by . There-fore, the effect of can be ignored when tuning the DRX parameters for power saving.

VI. CONCLUSION

This paper investigated the UMTS DRX mechanism for MS power saving. The DRX mechanism is controlled by two param-eters: the inactivity timer threshold and the DRX cycle . We proposed a variant M/G/1 queueing model with vacations to study the effects of and on output measures including the expected queue length, the expected packet waiting time, and the power saving factor. Our analytic model is different from the existing M/G/1 vacation model due to the introduction of (and therefore, the server can not enter the vacation mode immediately after the queue is empty). The analytic approach was validated against the simulation experiments. Several nu-merical examples were presented to quantitatively show how to select appropriate and values for various traffic patterns. Our study indicated that with proper parameter settings, UMTS DRX can effectively reduce the MS power consumption.

ACKNOWLEDGMENT

The authors would like to thank the three anonymous re-viewers. Their valuable comments have significantly enhanced the quality of this paper.

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Shun-Ren Yang received the BSCSIE, MSCSIE, and

Ph.D. degrees from National Chiao Tung University (NCTU), Hsinchu, Taiwan, R.O.C., in 1998, 1999, and 2004, respectively.

Since August 2004, he has been with the Depart-ment of Computer Science and Institute of Commu-nications Engineering, National Tsing Hua Univer-sity, Taiwan. His current research interests include design and analysis of personal communications ser-vices networks, computer telephony integration, mo-bile computing, and performance modeling.

Yi-Bing Lin (M’95–SM’95–F’03) received the

B.S.E.E. degree from National Cheng Kung Univer-sity, Tainan, Taiwan, R.O.C., in 1983, and the Ph.D. degree in computer science from the University of Washington, Seattle, in 1990.

From 1990 to 1995, he was with the Applied Research Area at Bell Communications Research (Bellcore), Morristown, NJ. In 1995, he was ap-pointed as a Professor of Department of Computer Science and Information Engineering (CSIE), Na-tional Chiao Tung University (NCTU). In 1996, he was appointed Deputy Director of Microelectronics and Information Systems Research Center, NCTU. During 1997–1999, he was elected as Chairman of CSIE, NCTU. He is an Adjunct Research Fellow of Academia Sinica, and is Chair Professor at Providence University, Taichung, Taiwan, R.O.C. He serves as a consultant to many telecommunications companies, including FarEasTone and Chung Hwa Telecom. His current research interests include design and analysis of personal communications services network, mobile computing, distributed simulation, and performance modeling. He has published over 150 journal articles and more than 200 conference papers. He is coauthor of the book Wireless and Mobile Network Architecture (New York: Wiley, 2001).

Dr. Lin is a Senior Technical Editor ofIEEENETWORK, an Editor ofIEEE TRANSACTIONS ONWIRELESSCOMMUNICATIONS, an Associate Editor ofIEEE TRANSACTIONS ONVEHICULAR TECHNOLOGY, an Associate Editor of IEEE COMMUNICATIONS SURVEY ANDTUTORIALS, an Editor of IEEE PERSONAL COMMUNICATIONS MAGAZINE, an Editor of Computer Networks, an Area Editor of ACM Mobile Computing and Communication Review, a columnist of

ACM Simulation Digest, an Editor of International Journal of Communications Systems, an Editor of ACM/Baltzer Wireless Networks, an Editor of Computer Simulation Modeling and Analysis, an Editor of Journal of Information Science and Engineering, Program Chair for the 8th Workshop on Distributed

and Parallel Simulation, General Chair for the 9th Workshop on Distributed and Parallel Simulation. Program Chair for the 2nd International Mobile Computing Conference, Guest Editor for the ACM/Baltzer MONET special issue on Personal Communications, a Guest Editor forIEEETRANSACTIONS ONCOMPUTERSspecial issue on Mobile Computing, a Guest Editor forIEEE TRANSACTIONS ON COMPUTERS special issue on Wireless Internet, and a Guest Editor forIEEECOMMUNICATIONSMAGAZINEspecial issue on Active, Programmable, and Mobile Code Networking. He received the 1998, 2000, and 2002 Outstanding Research Awards from the National Science Council, R.O.C., and the 1998 Outstanding Youth Electrical Engineer Award from the Chinese Institute of Electrical Engineering (CIEE), R.O.C. He also received the NCTU Outstanding Teaching Award in 2002. He is a ACM Fellow.