Dimensioning the packet loss burstiness over wireless channels: a novel metric, its analysis and application

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1 WIREESS COMMUNICATIONS AND MOBIE COMPUTING Wirel. Commun. Mo. Comut. (22) Pulished online in Wiley Online irary (wileyonlinelirary.com). DOI:.2/wcm.2262 RESEARCH ARTICE Dimensioning the acket loss urstiness over wireless channels: a novel metric, its analysis and alication Fangqin iu *, Tom H. uan 2, Xuemin (Sherman) Shen 2 and Chuang in Deartment of Comuter Science and Technology, Tsinghua University, Beijing, 84, China 2 Deartment of Electrical and Comuter Engineering, University of Waterloo, Waterloo, Ontario, N2 3G, Canada ABSTRACT The acket loss urstiness over wireless channels is commonly acknowledged as a key imacting factor on the erformance of networking rotocols. An accurate evaluation of the acket loss urstiness, which reveals the characteristics and erformance of the wireless channels, is crucial to the design of wireless systems and the quality-of-service rovisioning to end users. In this aer, a simle yet accurate analytical framework is develoed to dimension the acket loss urstiness over generic wireless channels. In secific, we first roose a novel and effective metric to characterize the acket loss urstiness, which is shown to e more comact, effective, and accurate than the metrics roosed in existing literature for the same urose. With this metric, we then develo an analytical framework and derive the closed-form solutions of the acket loss erformance, including the acket loss rate and the loss-urst/loss-ga length distriutions. astly, as an examle to show how the derived results can e alied to the design of wireless systems, we aly the analytical results to devise an adative acketization scheme. The roosed acketization scheme adatively adjusts the acket length of transmissions ased on the rediction of the acket loss rate and loss-urst/loss-ga lengths of the wireless channel. Via extensive simulations, we show that with the roosed acketization scheme, the channel throughut can e enhanced y more than % than the traditional scheme. Coyright 22 John Wiley & Sons, td. KEYWORDS wireless channels; acket loss urstiness; correlation analysis *Corresondence Fangqin iu, Deartment of Comuter Science and Technology, Tsinghua University, Beijing, 84, China. fqliu@csnet.cs.tsinghua.edu.cn. INTRODUCTION Packet losses over wireless channels tyically have strong correlations and occur in a ursty fashion. As the acket loss erformance directly affects the effectiveness and efficiency of communications, the acket loss urstiness has a significant imact on the erformance of on-to rotocols in wireless networks [ 3]. For examle, as reorted in [4], the automatic reeat-request (ARQ) rotocol erforms much worse over links with urst acket losses than it does over links of indeendent acket losses. Because of its imortance, an extensive ody of research has een develoed in the ast decades to evaluate the acket loss urstiness in wireless channels. To dimension the acket loss urstiness, the foremost issue is to devise the aroriate metrics, which can accurately characterize the urstiness. In [5], the Allan deviation [6] of acket recetion rate (PRR) is used to measure the urstiness of acket losses in 82. mesh networks. With this metric, the acket-loss-urst length can e evaluated to imrove the design of retransmission algorithms in wireless networks. In [7], a metric ˇ is roosed ased on the concet of conditional roaility delivery function (CPDF) for measuring the urstiness in wireless sensor networks. Such a metric is then used to devise an oortune transmission algorithm to oost the PRR. In this work, we roose a new metric to characterize PRR, which distinguishes from the existing metrics in the following two asects. First, the existing metrics are tyically derived emirically through exeriments using network datasets. As such, their effectiveness and efficiencies need to e validated efore they can e alied in real-world scenarios. Our roosed metric is a theoretical and generic metric, which is alicale to general settings. Therefore, it is suitale for theoretical analysis to rovide comrehensive insights on the features of wireless channels. Second, our roosed metric can e easily used to design and otimize the communication rotocols. In this aer, we show an examle y develoing an Coyright 22 John Wiley & Sons, td.

2 Packet loss urstiness over wireless channels F. iu et al. analytical framework ased on the roosed metric to accurately evaluate and redict the acket loss erformance, such as the acket loss rate and the distriutions of the loss-urst/loss-ga lengths (defined as a maximumlength sequence of consecutive corruted/correct ackets). With the accurate evaluation of acket loss erformance, we show that the otimal communication rotocols can e devised according to the timely changing characteristics of wireless channels. To summarize, our major contriutions are threefold. First, we develo a new aroach, namely acket transmission segmentation, to investigate on the correlations of acket losses mathematically, and roose a new and efficient metric to measure the acket loss urstiness. We show that this metric is more effective and accurate to gauge the urstiness of wireless channels than revious metrics when the channel is with intensive transmission errors or low acket loss urstiness. Second, we show how to utilize the newly roosed metric to derive the acket loss erformance. The closed-form solutions for the acket loss rate and loss-urst/loss-ga length distriutions are develoed accordingly. Via extensive simulations, we show the accuracy of the develoed analysis in different scenarios of wireless channels. To the est of our knowledge, this work reresents the first research to derive the closed-form solutions for the acket loss erformance in ursty wireless channels. Notaly, the analytical results ridge the channel conditions to the resultant acket loss erformance using a simle yet accurate exression, which aves the way for the evaluation, design, and otimization of communication rotocols. Third, we demonstrate the erformance gain rought y alying the derived analytical results in rotocol designs. Using the it error erformance as the inut to the roosed analytical framework, we redict the acket loss rate and loss-urst/loss-ga lengths. We then aly the rediction method to devise an enhanced acketization scheme. Using simulations, we show that the roosed analytical framework can work much faster than existing aroaches to characterize the acket loss erformance and the roosed acketization scheme can oost the channel throughut y more than % with guaranteed transmission delay and failure roaility than the traditional scheme. The remainder of this aer is organized as follows: Section 2 investigates on the correlations of acket losses and develos the metric. Section 3 derives the acket loss erformance, including the average acket loss rate and the loss-urst/loss-ga length distriutions. Section 4 designs a rediction mechanism and alies it to a acketization scheme. Section 5 reviews the metrics roosed in revious work to measure the acket loss urstiness. Finally, Section 6 concludes this aer. 2. MEASURING PACKET OSS BURSTINESS In this section, We first analyze the correlations of acket losses. With this analysis, we then introduce a new metric q good ad hg hg h g h h Figure. Transition diagram for the GE model. called the average correlation length of acket loss rate to characterize the acket loss urstiness in wireless channels. h 2.. Correlation analysis of acket losses It has een shown that the Gilert Elliott (GE) model can cature the it error statistics with sufficient accuracy in Rayleigh fading channels [8,9], and the GE channel, referring to the wireless channel where the it errors can e descried y the GE model, is the most oular ursty channel used in existing literature. In this aer, we also focus on the GE channel. As shown in Figure, the GE channel has two states: good and ad. The state changes from ad to good with roaility and from good to ad with roaility q. h g and h are the it error roailities in state good and state ad, resectively. Previous works evaluate the acket losses tyically y enumerating the cominations of the it states (it is in good or ad channel conditions) in a acket. As a acket tyically consists of hundreds or thousands of its, it is difficult to evaluate the acket losses efficiently and accurately using such a method. In what follows, we introduce a novel and much more efficient method, namely acket transmission segmentation, to analyze the acket loss erformance. () B-run and G-run: Considering a communication session where multile ackets are transmitted in the unit of its over the wireless channel, we define a B-run as a maximum-length run (or sequence) of consecutive its in the ad state and a G-run as a maximum-length run of consecutive its in Although the GE model can cature the it error statistics with sufficient accuracy in Rayleigh fading channels, its effectiveness and accuracy in evaluating the acket error erformance still remain an oen rolem. In [], we have derived the acket loss rate in the simlified Gilert channel (i.e., h g D and h D ) and on the assumtion of >q. In this aer, our analysis is over the general GE channel and without the assumtion. Moreover, we extend the work to study the correlation length of acket losses and the loss-urst/loss-ga lengths. Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

3 F. iu et al. Packet loss urstiness over wireless channels Figure 2. Transmission segments over a wireless channel. Tale I. Notations used in the aer. Transition roaility from the ad state to the good state in the GE model. q Transition roaility from the good state to the ad state in the GE model. h g Bit error roaility in the good state of the GE model. h Bit error roaility in the ad state of the GE model. The acket length in terms of its. X n (or X) The B-run length in segment n. Y n (or Y ) The G-run length in segment n. R n (or R) The nth residual length. Z n (or Z) The sum of a G-run length and a adjacent B-run length in segment n. A n (or A) The remainder of Y n minus R n. C The correlation length of the acket loss rate. PR The average acket loss rate of the communication session. E n (or E) The length of the nth loss ga. F n (or F) The length of the nth loss urst. M n (or M) A n mod (or A mod ). the good state. The communication session is hence comosed of the iterative B-runs and G-runs, as shown in Figure 2. et X and Y denote the lengths of a randomly selected B-run and G-run, resectively. As indicated in [], in the GE model, oth X and Y are indeendent and identically distriuted (IID) random variales and geometrically distriuted with the roaility mass functions (PMFs) Pr.X D k/ D. / k and Pr.Y D k/ D q. q/ k, resectively. Tale I summarizes the rimary notations used in this aer. (2) Residual length: We divide the whole transmission session into multile segments for analysis on the asis of the residual length of ackets. The residual length of a acket is defined as the length (in the unit of its) from the it immediately after the last B-run in a acket to the end of the acket. et R n, where n D ; 2; : : :, denote the nth residual length during the communication session, as shown in Figure 2. R n varies within Œ;,whereis the acket length. The adjacent its ahead of and after a B-run (res. G-run) are in the good state (res. the ad state). R n equals to when the last it of the acket is in the ad state and the following it is in the good state. (3) Packet transmission segmentation: We define segment n (n D ; 2; : : :) as the length from the it right after R n to the last it of R n (R is the start of the communication session), as shown in Figure 2. Aarently, the segmentation does not reak any single acket, and each segment can e divided into two arts: in Part I, all the its in the acket are in the good state; whereas in Part II, the acket must contain at least it in the ad state. We first resent the roerties of segmentations to reveal the correlations of acket losses. emma. R n and R n are indeendent, and R n has the following roaility distriution. Pr.R n D k/ D. q/ kc q. / kc. q/.. q/ / q q. /.. / / ;k2 Œ; / Proof. Denote the sum of a G-run length and an adjacent B-run length in segment n y a new random variale Z n, that is, Z n D Y n C X n. Z n is memoryless as X n and Y n are oth memoryless. Intuitively, R n and R n are indeendent according to the memoryless roerty of Z n.see Aendix A for the detailed roof. () Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

4 Packet loss urstiness over wireless channels F. iu et al. et A n denote the ortion that Y n minus R n,asshown in Figure 2. From emma, we have emma 2 as follows. emma 2. X n, Y n, and A n are indeendent of A n, and A n has the roaility distriution as where f.a;x/ is the numer of error ackets in segment n when A n D a and X n D x. As oth A n and X n are indeendent of A n and X n, N n is indeendent of N n. Similarly, N e;n is also indeendent of N e;n ecause f.a;x/is only related to A n, 8Pr.A n D k/ D ˆ<. q/ k q 2. /... /. q// /. q/.. q/ / q q. /.. / / q q C. q/.. q/2 / 2 q ; k 2 Œ; /; q ˆ: 2. / 2 k... /. q// Ck /. q/.. q/ / q q. /.. / / q q C. q/2 k.. q/ 2.Ck / / 2 q ;k2œ2 ; (2) Proof. Intuitively, X n is indeendent of R n as X n and Y n are oth memoryless. X n and A n are then indeendent ecause X n is also indeendent of Y n and A n D Y n R n. More strictly, we can derive Pr.A n D a/ D Pr.A n D ajx n D x/ similarly as in Aendix A to rove that X n is indeendent of A n (the derivation is omitted here ecause of the sace limit). ikewise, we can also rove that Y n and A n are indeendent of A n. The PMF of A n can e derived from the PMFs of Y n and R n. For simlicity, in this aer, we do not consider the error-recovery (e.g, ARQ) or error-resilient (e.g, forward error correction (FEC) codes) mechanisms. In other words, once a it error occurs in a acket, the acket will e corruted. Then, from emma 2, we otain the following theorem. Theorem. The average acket loss rate in segment.n / is indeendent of that in segment n. X n,andy n. Then, the length of a segment and the numer of error ackets in a segment are oth indeendent. As a result, Theorem holds. From Theorem, we know that the correlations of acket losses only last for a segment Average correlation length of acket loss rate The correlation length of acket loss rate, denoted as C, is defined as the minimum interval to guarantee that the average acket loss rates are indeendent in different intervals. From Theorem, we know that the average acket loss rates in different segments are indeendent. Thus, the correlation length of acket loss rate (in the unit of ackets) equals to the numer of ackets in a segment. From here onwards, for simlicity we remove the suscrit n of notations in Tale l I. The PMF m of C is then derived as Pr.C D k/ D Pr ACX D k. From the PMFs of X and A, we can derive that.kc/ 2 X Pr.C D k/ xdk k x X ad2 k X C xd k x X ad.k /C x A Pr.A D a/ Pr.X D x/; k (5) Proof.etN n and N e;n denote the total numer of ackets and the numer of error ackets in segment n, resectively. The average acket loss rate in segment n thus equals to N e;n N n. According to the definitions of R n and segment n, the length of segment n minus.a n C X n / is no longer than, son n can e derived as X X x C a N n D Pr.X n D x/pr.a n D a/ xd ad2 (3) As shown in Figure 2, N e;n can e derived as N e;n D X X xd ad2 Pr.X n D x/pr.a n D a/f.a; x/ (4) From Equation (5), we can otain the average correlation length of acket loss rate, that is, EŒC (the closed-form solutions for Pr.C D k/ and EŒC are reresented in [2]). EŒC is the metric that we roose to measure the acket loss urstiness. The larger EŒC is, the longer the correlations of acket losses stay, indicating that the wireless channel is more ursty. If EŒC D, the acket losses are memoryless Comarisons to other metrics In revious literature, a variety of metrics have een roosed to measure the acket loss urstiness, including the metric [3], the Allan deviation of PRR [5], and the Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

5 F. iu et al. Packet loss urstiness over wireless channels metric ˇ [7]. This section comares our roosed metric with the existing metrics. If the acket errors can e descried y the GE model in wireless networks, the metric [3] is calculated as D./ q./ (6) where./ and q./ are the roailities of the state transiting from good to ad and from ad to good in the GE model, resectively. The suerscrit./ denotes that it is the acket-level quantity. The larger is, the more ursty the channel is. The formula of the Allan deviation of PRR [5], denoted as D,is v u D D t nx.r i r i / 2n 2 (7) 2 where r i is the PRR in interval i. In the cases of different time scales, we can otain different Allan deviations. For the case that the interval lengths are aroximately equal to the acket-loss-urst length, the PRRs of different intervals deviate a lot, and accordingly, the Allan deviation is large. For the case of smaller intervals, the PRRs of adjacent intervals change slowly, making the Allan deviation small. In the case of large intervals, the PRRs of different intervals tend to e the long-term average, and the Allan deviation is small. The metric ˇ [7] is calculated from CPDFs. The CPDF, denoted as C.n/, is the roaility that the next acket will succeed given n consecutive acket successes (for n > ) or failures (for n<). The formula of ˇ is ˇ D KW.I/ KW.E/ KW.I/ where KW./ is the Kantorovich Wasserstein (KW) distance [4] from the CPDF of the ideal ursty link. E is the CPDF of the link in question, and I is the CPDF of an indeendent link with the same average PRR. An ideal ursty link has a ˇ D, and a link with indeendent acket losses has a ˇ D. Negativeˇ values are ermitted, and this haens when there is a negative correlation in acket losses; that is, the next acket is more likely to e corruted when more ackets are received, and the next acket is more likely to e delivered successfully when more ackets are corruted. Figure 3 comares the inverse of our metric EŒC to revious metrics and ˇ in different wireless channels. We set h g D, h D, and the other arameters in Figure 3(a) (c) resectively as follows: D 4 ;q D 5 4 ; 2 Œ2; 2 ; 2 Œ 4 ; 3 ; q D 5 4 ; D 8; and D 4 ;q 2 Œ 4 ; 3 ; D 8. We use the GE model to model the acket errors In the ideal ursty link, C.n/D if n<and C.n/D if n>. (8) and calculate./ and q./ to otain **. In Figure 3(a), we see that the acket loss urstiness decreases when increases, and the urstiness is vanished when is long enough. This matches with our intuitive understanding. Figure 3() shows that the urstiness also decreases when or q increases. This is ecause in the GE model, the memory will fade away with or q increasing (i.e., C q aroaches to ) ecause the memory will disaear when D q. In Figure 3(), the values of are close to almost all the time, whereas the variation of EŒC is more ovious, imlying that our metric EŒC can reveal the urstiness more effectively than when the acket loss urstinessislow. In Figure 3(a), ˇ decreases monotonically with increasing when is small. However, when is large, we have ˇ<and we cannot oserve any atterns that ˇ follows. This is ecause more transmission errors would e encountered when increasing the acket length, and intensive transmissions errors would cause the negative correlations in acket losses. In addition, the metric ˇ cannot reveal the acket loss urstiness when ˇ<as that when ˇ (we can get that from the calculation of ˇ). In Figure 3() and (c), we also show the negative ˇ values in different and q, and we cannot find the attern of ˇ values either. Therefore, our metric EŒC can characterize the acket loss urstiness more effectively than ˇ when the transmission errors are severe. Figure 4 shows the Allan deviation of PRR (D) in different time scales (in the unit of ackets) and with different average correlation lengths of acket loss rate (EŒC )and different average loss-urst lengths (EŒF ). The four cominations of EŒC and EŒF values are otained with the settings of,q, and, resectively: D 6 ;q D 5 ; D 8; D 5 ;q D 5 ; D 8; D 5 ;q D 4 ; D 8; and D 6 ;q D 4 ; D 8. We can see that the Allan deviation of PRR is maximized when the time scale is near the average loss-urst length, indicating that we can otain the average loss-urst length aroximately y analyzing the Allan deviations of PRR in different time scales. However, the average loss-urst length is not a good metric to measure the acket loss urstiness ecause it cannot tell whether the wireless channel is of urst losses or indeendent losses. In addition, we cannot otain EŒC or other clues to characterize the acket loss urstiness from the Allan deviations. Therefore, the Allan deviation of PRR is not suitale to measure the acket loss urstiness. 3. COSED-FORM SOUTIONS FOR PACKET OSS PERFORMANCE This section derives the acket loss erformance, including the average acket loss rate and the loss-urst/loss-ga **In Section 3.2.2, we demonstrate that the acket errors also follow the GE model if the it errors can e catured y the GE model, and derive the closed-form solutions for./ and q./. Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

6 Packet loss urstiness over wireless channels F. iu et al. Metrics /E[C] μ β x 4 (a). Metrics.5.5 /E[C] μ β x 4 (). Metrics /E[C] μ β q x 4 (c) q. Figure 3. Comarisons of,, andˇ with different,, andq. EŒC D E[C]=37.5,E[F]=3 E[C]=24.9,E[F]=4.5 E[C]=3.9,E[F]=2.5 E[C]=26.4,E[F]= Time scale (acket) Figure 4. Allan Deviation of PRR (D) with different EŒC and EŒF. length distriutions ased on our correlation analysis and the metric C roosed earlier. 3.. Average acket loss rate et PR denote the average acket loss rate in the communication session. It equals to the average acket loss rate in a single segment ecause the length of a segment is just the correlation length of acket loss rate C. As shown in Figure 2, each segment can e divided into two arts. f.a; x/ and f 2.a; x/ are denoted as the numers of error ackets in Part I and Part II, resectively. Then, f.a;x/in Equation (4) equals to f.a; x/ C f 2.a; x/. For a acket, n is denoted as the numer of its in the ad state, then the acket loss roaility is. h g / n. h / n. Therefore, f.a; x/ D a c.. h g/ /. In the last acket of Part II, denote the length of the its after the first B-run as s, asshownin Figure 2. The numer of its in the ad state in s cannot e derived easily ecause the numer of B-runs cannot e determined. In the calculation of f 2.a; x/,weusetheaverage numer of its in the ad state, that is, s q Cq,asan aroximation. Then y denoting that a D q a C r a and x D q x C r x.łeqq x ;q a I r x ;r a </, we otain f 2.a; x/dh d r a C x C max e 2. h g / r a. h / r a ; d r a C x e 2.. h / / C. h g / n. h / n ; n < ; where H.n/D ; n ; and n can e derived as 8 r ˆ< x C q Cq. r a r x /; r x C r a ; q x D ; n D Cq.r a C r x /; r x C r a ; q x ; ˆ: Cq.2 r a r x /; r x C r a >;q x The three comonents in Equation (9) are the numer of ackets that contain the its of the first G-run in a segment, the numer of ackets that are totally located in the B-run, and the numer of ackets that contain the its of s, resectively. Then, we derive the closed-form exression of PR. The exression is omitted here as it is lengthy. See [2] for the details. When the wireless channel is not in a very ad condition, the eriod of good channel state is usually longer than the eriod of ad channel state; that is, is larger than q. This aroximation will not affect the accuracy of PR too much ecause it only exists in the last acket of a segment and s is usually not long. The simulation results in Section 3.3. also validate that. q a (res. q x ) is the quotient of a (res. x) dividedy and r a (res. r x ) is the remainder. (9) Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

7 F. iu et al. Packet loss urstiness over wireless channels Then, we have. / and can otain a simlified. q/ exression for PR accordingly as PR D. q / PR t 2. q/ t. / q. h / t 2 t 3. h g /. PR / () where PR is the acket loss rate when h g D and h D,and. q/. q/ PR D. q/ q. q/. / t D. h / q Cq. h g / Cq C. h g / Cq h t 2 D C.q /. h g h / q Cq t 3 D. q/h g. /h C q 3.2. oss-urst/loss-ga length distriutions () We first study the loss-urst/loss-ga length distriutions in the simlified Gilert channel, which is a secial case of the GE channel when h g D and h D In the simlified Gilert channel. From emma 2, we have Theorem 2 as follows. Theorem 2. In the simlified Gilert channel, oth the loss-ga length and the loss-urst length are IID, and the loss-ga length is indeendent of the loss-urst length. Proof. In the simlified Gilert channel, the its are errorfree in the good stateandarealwayserrorinthead state. Therefore, as shown in Figure 2, for a segment, in j k An Part I, ackets are transmitted correctly, whereas l m in Part II, Mn CX n ackets are corruted, where M n equals to A n mod, that is, the remainder of A n divided y. According to the definition of a segment, aarently, a loss ga never crosses multile segments ecause a segment always ends with an error acket, and a loss urst may cross different segments when all the ackets in a segment are corruted. For examle, as shown in Figure 2, the ackets in segment.n C / are all corruted. With these oservations, we derive the roof as follows. et E i and F i denote the lengths of the ith loss ga and the ith loss urst, resectively. Assuming that E i is in segment n, thepmfofe i is thus Pr.E i D k/ D Pr An D k k (2) As different loss gas are within searate segments and A n is IID, the loss-ga length is IID. Assume that F i crosses m.m / segments (starting from segment n to segment n C m ); denote the numer of error ackets in segment n as N e;n.n e;n /, and denote y C D N e;n C N e;nc C :::CN e;ncm D k W N e;ncj. j<m/ ; 8 < m [ MnCj C X W ncj : j D 9 D N e;ncj A [ m A ncj <A [ =.A ncm / ; j D The roaility that F i D k equals to the roaility that there are k ackets in the m segments. The PMF of F i can then e derived y Pr l Mn CX n kx X Pr.F i D k/ D Pr.W / k (3) md C m [ A ncj <A in W indicates that the error j D ackets san to m consecutive segments, and.a ncm / in W indicates that the loss urst terminates after m segments. Aarently, different loss ursts will aear in searate segments, and A n, X n,andm n are all IID. Therefore, the loss-urst length isnl also IID. m o et W D W Mn CX n D N e;n fa ncm g. From (2), we have Mn C X n Pr.W je i D k / D Pr D N e;n je i D k Pr.W / Pr.A ncm / (4) ItcaneeasilyrovedthatPr.M l n Dm mje i D k / D Pr.M n D m/. As a result, Pr Mn CX n D N e;n je i D k D m D N e;n, which imlies that E i is indeendent of F i. As F i sans from segment n to segment.n C m /, E ic would aear in segment.n C m/. Consequently, Pr.E ic D k/ D Pr j AnCm k D k. Similarly, we can rove that F i is indeendent of E ic. Therefore, Theorem 2 holds: oth the loss-ga length and the loss-urst length are IID, and the loss-ga length is indeendent of the loss-urst length. For simlicity of notation, we remove the suscrit i in the remaining analysis of this section. From Equations (2) Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

8 Packet loss urstiness over wireless channels F. iu et al. and (3), we have the PMFs of the loss-ga length and the loss-urst length aroximately as where Pr.E D k/ D.. q/ /.. q/ / k ; k ; Pr.F D k/ D. q/.. q/ /.. / / q. q/.. q/ /.. / k (5) / q ; k The detailed derivation is given in Aendix B. Therefore, in the simlified Gilert channel, the lossga length and the loss-urst length follow geometric distriutions with arameters. q/ and. q/.. q/ /.. / / q, resectively. With the loss-urst/loss-ga length distriutions, we can develo a model to characterize the acket losses in the simlified Gilert channel. et n denote the status of the nth acket transmitted, where n D if the nth acket is corruted and n D if the acket is correctly transmitted. From Theorem 2, we know that in the simlified Gilert channel, oth the loss-ga length and the loss-urst length are IID, and the loss-ga length is indeendent of the loss-urst length. Therefore, we have that Pr.E i C / Pr. nc D j n D / D ; Pr.E i/ (6) Pr.E D i/ Pr. nc D j n D / D Pr.E i/ where i refers to that there are i consecutive correct ackets efore the.n C /th acket, and Pr.F D j/ Pr. nc D j n D / D Pr.F j/ ; (7) Pr.F j C / Pr. nc D j n D / D Pr.F j/ where j refers to that there are j consecutive corruted ackets efore the.n C /th acket. By sustituting Equation (5) into Equations (6) and (7), we have Pr. nc D j n D / D. q/ ; Pr. nc D j n D / D. q/ ; Pr. nc D j n D / D. q/.. q/ /.. / / ; q Pr. nc D j n D / D. q/.. q/ /.. / / q (8) Therefore, we develo a simlified Gilert model for acket losses in the simlified Gilert channel with the transition roaility matrix etween the good./ state and the ad./ state as! q./ q./././ (9)./ D Pr. nc D j n D /; q./ D Pr. nc D j n D / (2) The acket loss roaility in the good./ state, denoted y h./ g,is, and the acket loss roaility in the ad./ state, denoted y h./,is In the GE channel. The loss-urst/loss-ga length distriutions in the general GE channel cannot e derived so easily as in the simlified Gilert channel. In this section, we first develo a model to characterize the acket losses in the GE channel ased on the model in the simlified Gilert channel, and then derive the loss-urst/loss-ga length distriutions. We now extend the aforementioned acket-level simlified Gilert model to the GE channel. In the GE channel, the transition roaility matrix etween the good./ state and the ad./ state remains the same as that in the simlified Gilert channel, whereas the acket loss roaility in the good./ state (h./ g ) is nonzero and equals to.. h g / /. The acket losses in the ad./ state is no longer indeendent, and the acket loss roaility deends on the numer of error its in a acket. In that case, to develo a recise model for acket losses according to these different loss roailities, we need to add a multitude of new states, and the correlations etween these states are strong ecause of the ig numer of its in a acket and the correlation etween the states of two adjacent its in the GE channel. Here, in the ad./ state, we use the average acket loss rate as the acket loss roaility (h./ ) and construct a first-order Markov model (i.e., a GE model) in the GE channel aroximately. According to the GE model, the average acket loss rate equals to h./ g./ Ch./ q./. Recall that in Section 3.,./ Cq./ we have derived the average acket loss rate (PR)inthe communication session, then PR D h./ g./ Ch./ q./../ Cq./ Given the knowledge of PR, h./ g,./,andq./,we can derive h./ y PR../ Cq./ / h./ g./. q./ The simlified Gilert model is a secial case of the GE model. As indicated in [5], the simlified Gilert model is of renewal nature; that is, oth the loss-urst length and the loss-ga length are indeendently distriuted. The loss-urst length and the loss-ga length are then derived to e geometric distriutions with arameters q./ and./, resectively. Yet, the GE model is non-renewale, and the loss-urst/loss-ga length distriutions are difficult Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

9 F. iu et al. Packet loss urstiness over wireless channels to derive. In [5], Pimentel and Blake gave a recursive solution for them using the enumeration theory. In the GE channel, we then can use such recursive solution to calculate the loss-urst/loss-ga length distriutions. In what follows, we discuss on the values of h./ g and h./ on the asis of the tyical values of, q, h g,andh. As indicated in [6], with vehicle seeds to e 5 km/h, modulation frequency f D 9 MHz, and Rayleigh fading enveloe D db, we have q D 9:3. With edestrian seeds to e 2 km/h, the same modulation frequency, and D 2 db, we have q D 99:4. h g is usually set to 5,andh is set to :. In Figure 5, h./ is lot- ted with h g D 5, h D :, and different q and as () q D 3 and D 5, and(2)q D 5 and D, resectively. We see that if is small, h./ equals to. Meanwhile, h g makes h./ g aroach to, which imlies that the GE model for acket losses degrades to the simlified Gilert model when is small. eing small means that the channel is in ad condition as is the average eriod length of ad channel state. In addition to that, the GE model will e memoryless if aroaches to as we have./ q./ in Equation (9). This matches the analysis in Section 2.3: using the average correlation length of the acket loss rate, we demonstrate that the correlation etween acket losses decreases when increasing. In summary, the GE model for the acket losses will regress to the simlified Gilert model when the GE channel regresses to the simlified Gilert channel or the channel is in ad condition, and the GE model will e memoryless when the channel is in good condition s This section demonstrates the accuracy of the derived closed-form models for the average acket loss rate and the loss-urst/loss-ga length distriutions in different settings. Packet error roaility in state B () (h () ) q=.,=5 q=.,= Figure 5. The acket loss roaility in the ad./ state (h./ ) with the increase of Average acket loss rate. Figure 6 shows the effects of,, andq on the acket loss rate when h g D 5 6 and h D :9. The arameters, q, and, in Figure 6(a) (c) are, resectively, D 5 6 ;q D 6 ; 2 Œ2; 7 ; 2 Œ 7 ; 5 ; q D 6 ; D 8; and D 5 6, q 2 Œ 7 ; 5, D 8. We oserve that the average acket loss rate increases with increasing, indicating that increasing the acket length would incur more transmission errors; and the average acket loss rate increases monotonically with decreasing or q increasing as the channel condition ecomes worse in this case. and 2 refer to the derived analysis without simlification and with the simlification in Equation (), resectively. It can e seen that our results without simlification are accurate for different,, and q. In Figure 6() and 6(c), the results with the simlification in Equation () are inaccurate when is close to or smaller than q, and they match the simulations well when >q. This indicates that Equation () is accurate enough Sim. result Sim. result.8 2 Sim. result.8 PR PR PR x 4 (a) x 7 x 6 () q x 7 q x 6 (c) q. Figure 6. Packet loss rate (PR) with the increases of,, andq. Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

10 Packet loss urstiness over wireless channels F. iu et al. to redict the acket loss rate of the wireless channel in good channel condition oss-urst/loss-ga lengths. In this exeriment, we evaluate the loss-urst/loss-ga length distriutions and the average loss-urst/loss-ga lengths y changing in the range of Π4 ; :9 and setting other arameters as q D 7 4 ; D ; h g D 5 ;h D :5. Figure 7 shows the PMFs of the loss-urst length with different. From Figure 7(a) (d), we can see that our results are slightly inaccurate when D 4 and with accetale accuracy when D 3. The results accurately match the simulations when D 5 3.However, the accuracy slightly decreases when D :9. The ga etween the simulations and analysis mainly attriutes to the aroximation we have made to calculate Pr.E D / in the analysis of the loss-urst length distriution (see Aendix B for details). Figure 8 shows the PMFs of the loss-ga length. The accuracy of the loss-ga length is not sensitive to, and our results are accurate for all. Figure 9 shows the effects of on the average lossurst/loss-ga lengths. The results for oth the average loss-urst and the average loss-ga length are accurate for all. In summary, our results matches the simulations very well, and there exist a slight error when the roaility of loss-urst length equals to. 4. PROTOCO IMPROVEMENTS To know the acket loss rate and the loss-urst/loss-ga lengths is key for the evaluation or otimization of communication rotocols and algorithms. For examle, the acket loss rate is an imortant metric to design FEC codes, ARQ, and adative acketization schemes [7 9]; the loss-urst/loss-ga lengths can e alied to the design of the retransmission time and the route rotocols [7]. The existing methods to redict the acket loss rate and the loss-urst/loss-ga lengths, however, are often comlicate yet not accurate enough PMF.2.5 PMF...5 =..5 = oss urst ength oss urst ength (a) = 4. () = PMF PMF =.5.2. = oss urst ength (c) = oss urst ength (d) =.9. Figure 7. The roaility mass function (PMF) of the loss-urst length with different. Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

11 F. iu et al. Packet loss urstiness over wireless channels PMF.4.3 PMF.4.3 PMF =.. =..5 = oss ga ength oss ga ength oss ga ength (a) = 4. () = 3. (c) =.9. Figure 8. The roaility mass function (PMF) of the loss-ga length with different Average oss urst ength Average oss ga ength (a) The average loss-urst length. () The average loss-ga length. Figure 9. The average loss-urst/loss-ga lengths with the increase of. In the revious sections, we have derived the closedform exressions of the average acket loss rate and the average loss-urst/loss-ga lengths. On the asis of the results, in what follows, we roose an analytical method to redict the acket loss rate and the loss-urst/loss-ga lengths in wireless networks, and design a transmission-delay-constrained and failureroaility-constrained acketization scheme accordingly as an examle to showcase the imlementation of the analytical models. 4.. Prediction of channel erformance As indicated in [6], with a secific digital modulation scheme and knowing the arameters of the channel fading model, such as the maximum Doler frequency and the fading enveloe, we can derive the arameters of the it-level GE model, that is,, q, h g,andh (Phase I). In this aer, we ridge the it-level GE model with the acket loss rate in Section 3. and the loss-urst/loss-ga lengths in Section 3.2 (Phase II). By comining the two hases, we can derive the acket loss erformance given the arameters of the channel fading model. The comutation comlexity of this rediction method is constant as the comutation comlexities of the two hases are oth constant. In addition, our udate interval is adated to the dynamics of the fading model arameters, and it is longer than the udate interval in revious work, which tyically udates the acket loss erformance after the delivery of each acket [7,8]. Therefore, our rediction method is faster and can e used for the evaluation and otimization of wireless communications more conveniently than revious work Alication for acketization design et t d and f denote the exected transmission delay and failure roaility, resectively. Our goal is to maximize the ayload of transmission with ounded delay and failure roaility, mathematically, ot W (2) maximize s:t:; t d T d ; f P f Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

12 Packet loss urstiness over wireless channels F. iu et al. where T d and P f denote the uer ounds of transmission delay and failure roaility, resectively. Given the arameters of the channel fading model, we first derive the it-level arameters (i.e.,, q, h g,andh ), then derive the acket loss rate PR. Comining with the maximum retransmission numer m and the channel caacity andwidth B, the transmission delay and failure roaility of ackets are functions of the acket length as t d D mx.i C /. PR. j //PR. j / i ; B (22) id mx f D. PR. j //PR. j / i : (23) id By sustituting Equations (22) and (23), ot can e otimally solved. The acket length is udated corresondingly at each interval T on the asis of ot. Here, the interval T is adated to the dynamics of the fading model arameters. Most revious work [7,8] to design acketization schemes assumes that the it errors are IID for simlicity, and then to derive the acket loss rate, denoted as PR IID,yPR IID D. /,where is the it error roaility. The acketization scheme [7,8], which uses PR IID to redict the acket loss rate and udates the acket length after the delivery of each acket, is called the IID-ased scheme. In what follows, we comare our solution of ot with the IID-ased scheme using simulations. In the simulation, a node sends ackets to a ase station. We set T d D 2 ms, P f D 3, the modulation frequency f D 9 MHz, and the Rayleigh fading enveloe D 2 db. The moving seed of the node varies etween 2 and 5 km/h. The rotocol header (MAC+PHY header) size is 46 its. We define the effective throughut of wireless channels as the transmission rate of ayloads. From Figure, we can see that the effective throughut of the roosed scheme is more than % higher comared with the IID-ased scheme. Figure shows the PMFs of the transmission delay and the failure roaility. As we can see, the results of oth the schemes can meet the transmission-delay ound (2 ms) and the transmissionfailure-roaility ound (:). Most transmission failure roailities from the schemes are much smaller than the ound, indicating that the main restriction on acket length is the delay ound in this simulation. Moreover, using our scheme the average transmission delay is more close to 2 ms comared with that achieved y using the IID-ased scheme, and the distriutions of transmission failure roaility of the two schemes are very similar. In summary, y alying our rediction mechanism, the roosed acketization scheme can meet the requirements of the delay or acket-loss-sensitive services, and achieve a etter alance among transmission delay, failure roaility, and effective throughut to imrove the service erformance. Effective throughut (ks) I.I.D. ased scheme Our scheme 2.% 22.% Bandwidth (ks) Figure. The throughut comarison of two acketization schemes. PMF Transmission delay (ms) I.I.D. ased scheme Our scheme.5. Transmission failure roaility Figure. The PMFs of transmission delay and failure roaility. 5. REATED WORK The henomenon of acket loss urstiness in wireless channels has een oserved in many early works, and how to measure the acket loss urstiness and address the urstiness in rotocol designs are intensively ursued. The tyical mathematical metrics for descriing the inter-correlations of a sequence, such as the autocorrelation and CPDF, can e used to measure the acket loss urstiness. However, the autocorrelation is inconvenient to hel design rotocols ecause it does not distinguish the loss gas from the loss ursts. The CPDF is more informative and owerful than the autocorrelation, ut cannot e directly alied for rotocol designs ecause of its comlexity. Consequently, some metrics to guide rotocol Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

13 F. iu et al. Packet loss urstiness over wireless channels designs are develoed on the asis of CPDF, such as ˇ and descried next. Aguayo et al. [5] oserve the acket loss urstiness in a 82. mesh network and use the Allan deviation [6] of PRR over different time scales to measure the urstiness of acket losses. The Allan deviation is large when the time interval is near the acket-loss-urst length, and it is small for other time intervals. Then, the Allan deviation is an indirectly metric through which we can otain the acket-loss-urst length aroximately. The acket-lossurst length is very helful for network designs, while it is not so owerful to reresent the acket loss urstiness, ecause it is hard to distinguish the wireless channel with urst losses from the wireless channel with indeendent acket losses through their loss-urst lengths. Srinivasan et al. [7] studied the ursty losses in various wireless sensor networks and roosed a metric ˇ that uses the concet of CPDF for measuring the urstiness. By analyzing the different values of ˇ in different time intervals, we can find the smallest time interval with which the urstiness of acket losses is minimized. Then, we can ause for this smallest time interval to send the next acket after encountering a transmission failure. Such algorithm can reak the acket loss correlations, and it is called oortune transmission, which can reduce the average transmission cost y 5%. Actually, the average acket-loss-urst length can also e used to design this algorithm instead of the smallest time interval otained from the metric ˇ. All the aforementioned metrics are emirical; that is, they are more suitale to e derived from real network measurements. There are also some works for modeling acket losses using theoretical models, and such models could e extended to measure the acket loss urstiness. In the GE model [,2], which is a oular model for wireless channels, the metric is roosed to reveal the urstiness [3]. The larger the is, the more ursty the wireless channel is. The metric is also an effective metric to reveal the channel caacity, and it can e used to imrove the channel caacity. Our roosed metric, average correlation length of acket loss rate, is also derived from the theoretical model. It, however, is more effective to reresent the acket loss urstiness than revious metrics, and it rovides a new means for the evaluation or otimization of communication rotocols and algorithms, that is, to derive the closed-form solutions on the acket loss rate and the loss-urst/loss-ga length distriutions. 6. CONCUSION In this aer, we have develoed a new metric called average correlation length of acket loss rate to dimension the acket loss urstiness in a generic GE wireless channel. We have derived the closed-form analytical models for the acket loss erformance, including the average acket loss rate and the loss-urst/loss-ga length distriutions. These derived results can hel to evaluate or otimize wireless communications conveniently. We have taken a acketization scheme as an examle to show the imrovements. In the future work, we will study the urstiness of the acket losses caused y on-to rotocols, such as MAC rotocols and FEC schemes. APPENDIX A: PROOF OF EMMA In segment n, denote the length of the first air of G-run and B-run as P n, and the length of the left airs of G-runs and B-runs as Q n. Assume that there are C.C / ackets, as shown in Figure 2. We then otain Equation (A) on the asis of the definitions of R n and segment n. R n C C D R n C Q n C P n ; P n >.C / C R n ; P nc >R n (A) Denote the sum of a G-run length and an adjacent B-run length in segment n as Z n. Then, from Equation (A) and the distriution of Z n, we can derive the distriutions of P n and Q n as in Equation (A2). Pr.Zn D z/;.c / C j C z C C j r 2 D; Pr.P n D z/ D ; else; Pr.D Zn D z/ ; z D C C j r P Pr.Q n D z/ D n ; ; else (A2) where R n D r, R n D j,andd is the numer of airs of G-runs and B-runs in Q n. Thus, Pr.R n D rjr n D j/is derived y X C D. r /=2 X DD C Cj r 2D X zd.c /Cj C Pr.Z n D z/ Pr.D Z n D C C j r z/pr.z nc >r/ (A3) Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

14 Packet loss urstiness over wireless channels On the asis of Equation (A3), we use mathematical induction to rove that the PMF of R n is as Equation (). (I) We show that the PMF of R is as Equation (). Pr.R n D r/ can e calculated as X j D Pr.R n D rjr n D j/pr.r n D j/ (A4) By denoting that R D j (j can e any value etween and ), we have Pr.R D j/ D. Comining with Equation (A3), we can then derive the PMF of R as Equation (). (II) Assuming that the PMF of R n can e derived y Equation () and sustituting Equation (A3) into Equation (A4), we can derive the PMF of R n as Equation (). Comining I and II, we conclude that the PMF of R n.n D ; ; 2 : : :/ is given y Equation (). Moreover, we otain Pr.R n D r/ D Pr.R n D rjr n D j/from Equation (A3); thus, R n and R n are indeendent. APPENDIX B: DERIVATION OF THE OSS-BURST/OSS-GAP ENGTH DISTRIBUTIONS From Equation (2), the PMF of E can e otained as Pr.E D k/ D.. q/ / k.. q/ / Denoting y W j.k/ D o <,wehave nl MnCj CX ncj k (B) m D k;a ncj F. iu et al. l m / MnCj CX /. Therefore, Pr.W j.k// D Pr. ncj D k/pr.a ncj </. m [ MnCj C X In ncj D N e;ncj A is j D the sum of m indeendent variales following the geometric distriution with arameter. /.Thisis a negative inomial distriution, and the roaility function is f.m;k/ D.k /Š.k m/š.m /Š.. / / m.. / / k m. m k/. From Equation (3), F is then derived y Pr.F D k/ kx D f.m; k/.pr.a < // m. Pr.A < // md D.Pr.A < /.. / / C. / / k..pr.a < /.. / /C. / // k where Pr.A < / D X ad2 Pr.A D a/. ACKNOWEDGEMENTS (B4) This work is suorted in art y the National Basic Research Program of China (Nos. 2CB3285 and 29CB3255) and the National Natural Science Foundation of China (Nos , 6782, , 6738, and 672). 8 ˆ< Pr.W j.k// D ˆ: X a X X a C A Pr.A ncj D a/ Pr.X ncj D x/ k D ; ad2 xd a ad xd X k a X Pr.A ncj D a/ Pr.X ncj D x/ k > ad2 xd.k /C a (B2) The value of Pr.W j.// is a izarre oint. For ease of comutation, it is necessary to ignore the difference etween the exressions of Pr.W j.k// when k D and k>in Equation (B2) and make an aroximation that Pr.W j.k// is calculated y X k a X Pr.A ncj Da/ Pr.X ncj Dx/.k/ ad2 xd.k /C a (B3) The accuracy of this aroximation is investigated in Pr.W Section After normalization, j.k// is derived Pr.A ncj </ as.. l / / k.m. / /. Similarly, we can derive MnCj CX Pr. ncj D k/ D.. / / k.. REFERENCES. Gandikota V, Tamma B, Murthy C. Adative FECased acket loss resilience scheme for suorting voice communication over ad hoc wireless networks. IEEE Transactions on Moile Comuting 28; 7(): Kamer W, Nemethova O, Svooda P, Ru M. ink error analysis and modeling for video streaming crosslayer design in moile communication networks. ETRI Journal 27; 29(5): Alizai M, andsiedel O, ink J, G Rotz S, Wehrle K. Bursty traffic over ursty links, In Proceedings of ACM Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

15 F. iu et al. Packet loss urstiness over wireless channels Conference on Emedded Networked Sensor Systems (SenSys), Berkeley, CA, USA, ACM, 29; Aggarwal R, Schniter P, Koksal C. Rate adatation via link-layer feedack for goodut maximization over a time-varying channel. IEEE Transactions on Wireless Communications 29; 8(8): Aguayo D, Bicket J, Biswas S, Judd G, Morris R. inklevel measurements from an 82. mesh network. ACM SIGCOMM Comuter Communication Review 24; 34(4): Allan D. Time and frequency (time-domain) characterization, estimation, and rediction of recision clocks and oscillators. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 987; 34(6): Srinivasan K, Kazandjieva M, Agarwal S, evis P. The ˇ-factor: measuring wireless link urstiness, In Proceedings of ACM Conference on Emedded Networked Sensor Systems (SenSys), Raleigh, NC, USA, ACM, 28; Wang H, Chang P. On verifying the first-order markovian assumtion for a rayleigh fading channel miodel. IEEE Transactions on Vehicular Technology 996; 45(2): Zorzi M, Rao R, Milstein. On the accuracy of a first-order markov model for data transmission on fading channels, In Proceedings of IEEE International Conference on Universal Personal Communications (ICUPC), Tokyo, Jaan, IEEE, 995; iu F, Fan Y, Shen X, in C, Zeng R. An analytical model to study the acket loss urstiness over wireless channels, In Gloecom 2, 2 IEEE Gloal Telecommunications Conference, IEEE, 2; 5.. Elliott E. Estimates of error rates for codes on urstnoise channels. Bell Systems Technical Journal 963; 42(9): [Online]. Availale from: htt://qos.cs.tsinghua.edu. cn/~fqliu/calculation.rar [Accessed on 22]. 3. Mushkin M, Bar-David I. Caacity and coding for the Gilert Elliot channels. IEEE Transactions on Information Theory 989; 35(6): Runer Y, Tomasi C, Guias. A metric for distriutions with alications to image dataases, In Proceedings of IEEE International Conference on Comuter Vision (ICCV), Bomay, India, IEEE, 998; Pimentel C, Blake I. Enumeration of Markov chains and urst error statistics for finite state channel models. IEEE Transactions on Vehicular Technology 999; 48(2): ettieri P, Fragouli C, Srivastava M. ow ower error control for wireless links, In Annual International Conference on Moile Comuting and Networking (MoiCom), Budaest, Hungary, ACM, 997; Setton E, Yoo T, Zhu X, Goldsmith A, Girod B. Cross-layer design of ad hoc networks for realtime video streaming. IEEE Wireless Communications 25; 2(4): van der Schaar M, Turaga D. Cross-layer acketization and retransmission strategies for delay-sensitive wireless multimedia transmission. IEEE Transactions on Multimedia 27; 9(): Cai, Shen X, Mark J. Multimedia services in wireless internet: modeling and analysis. John Wiley & Sons, 29; Gilert E. Caacity of a urst-noise channel. Bell Systems Technical Journal 96; 39(9): AUTHORS BIOGRAPHIES Fangqin iu is in her final year of comleting the dissertation research for her doctoral degree in Comuter Science and Technology Deartment from Tsinghua University (China), where she received her BSc degree in 26. Her research area is erformance evaluation and transmission design of multimedia services in wireless networks. Tom H. uan received the BE degree in Xi an Jiaotong University, China, in 24 and the MPhil degree in electronic engineering from the Hong Kong University of Science and Technology, Kowloon, Hong Kong in 27. He is now ursuing the PhD degree at the University of Waterloo, ON, Canada. His current research interests focus on wired and wireless multimedia streaming, QoS routing in multiho wireless networks, eer-to-eer streaming and vehicular network design. Xuemin (Sherman) Shen received the BSc(982) degree from Dalian Maritime University, China, and the MSc (987) and PhD degrees (99) from Rutgers University, NJ, USA, all in electrical engineering. He is a Professor and University Research Chair, Deartment of Electrical and Comuter Engineering, University of Waterloo, Canada. Dr. Shen s research focuses on moility and resource management in interconnected wireless/wired networks, UWB wireless communications networks, wireless network security, wireless ody area networks, and vehicular Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm

16 Packet loss urstiness over wireless channels F. iu et al. ad hoc and sensor networks. He is a co-author of three ooks and has ulished more than 4 aers and ook chaters in wireless communications and networks, control, and filtering. Dr. Shen served as the Tutorial Chair for IEEE ICC 8, the Technical Program Committee Chair for IEEE Gloecom 7, the General Co- Chair for Chinacom 7, and QShine 6, the Founding Chair for IEEE Communications Society Technical Committee on P2P Communications and Networking. He also serves as the Editor-in-Chief for Peer-to-Peer Networking and Alication; Associate Editor for IEEE Transactions on Vehicular Technology; KICS/IEEE Journal of Communications and Networks, Comuter Networks; ACM/Wireless Networks; and Wireless Communications and Moile Comuting (Wiley), etc. He has also served as Guest Editor for IEEE JSAC, IEEE Wireless Communications, IEEE Communications Magazine, and ACM Moile Networks and Alications, etc. Dr. Shen received the Excellent Graduate Suervision Award in 26, and the Outstanding Performance Award in 24 and 28 from the University of Waterloo, the Premier s Research Excellence Award (PREA) in 23 from the Province of Ontario, Canada, and the Distinguished Performance Award in 22 and 27 from the Faculty of Engineering, University of Waterloo. Dr. Shen is a registered Professional Engineer of Ontario, Canada, an IEEE Fellow, and a Distinguished ecturer of IEEE Communications Society. Chuang in is a rofessor of the Deartment of Comuter Science and Technology, Tsinghua University, Beijing, China. He is a Honorary Visiting Professor, University of Bradford, UK. He received the Ph.D. degree in Comuter Science from the Tsinghua University in 994. His current research interests include comuter networks, erformance evaluation, network security analysis, and Petri net theory and its alications. He has ulished more than 3 aers in research journals and IEEE conference roceedings in these areas and has ulished four ooks. Professor in is a senior memer of the IEEE and the Chinese Delegate in TC6 of IFIP. He serves as the Technical Program Vice Chair, the th IEEE Worksho on Future Trends of Distriuted Comuting Systems (FTDCS 24); the General Chair, ACM SIGCOMM Asia worksho 25 and the 2 IEEE International Worksho on Quality of Service (IWQoS 2); the Associate Editor, IEEE Transactions on Vehicular Technology; the Area Editor, Journal of Comuter Networks; and the Area Editor, Journal of Parallel and Distriuted Comuting. Wirel. Commun. Mo. Comut. (22) 22 John Wiley & Sons, td. DOI:.2/wcm