MSDU-based ARQ Scheme for IP-Level Performance Maximization Youngkyu Choi*, Sunghyun Choi*, and Seokhyun Yoon+ *
School of Electrical & Computer Engineering, Seoul National University, Seoul 151-744, Korea School of Electrical, Electronics & Computer Engineering, Dankook University, Seoul 140-714, Korea Email: *
[email protected], *
[email protected], and
[email protected]
+
Abstract-Automatic Repeat reQuest (ARQ) is one of the effective techniques against the transmission error at the medium access control (MAC) layer. An erroneous MAC protocol data unit (MPDU) can be typically retransmitted within a given limit. In order to improve the IP-level performance, which directly affects the user-perceived qualityof-service (QoS), we propose a different ARQ strategy, called ‘MSDU-based’ scheme, with simple and minor modification from the existing ARQ concept. We evaluate the analytical IPlevel performance of both the conventional and proposed scheme.
I. INTRODUCTION In recent years, the broad-band Internet experience drives the demand for the wireless access to the IP network everywhere even in the mobile environments. In order to respond to this fashion, new wireless systems are emerging [1][2]. One of the most difficult aspects in building wireless IP network is how to guarantee the reliable communication over the unreliable wireless medium. In order to overcome the imperfection of the wireless medium, numerous technologies, e.g., channel coding, and diversity techniques, have been developed both in the academy and industry. Automatic Repeat reQuest (ARQ) [4] has been widely employed due mainly to its simplicity. ARQ technique is classified into various types, e.g., stop-and-wait ARQ, cumulative acknowledgement ARQ, and selective repeat ARQ, depending on the use of transmission window, or the difference of the acknowledgement protocol, etc. [4]. There have been numerous efforts related with the ARQ in the literature [5][6][7]. Some researchers attempted to analyze the performance of ARQ in their specific system, and others attempted to optimize ARQ with other specific techniques, e.g., modulation, channel coding, and duplexing. Even though it may compromise the average delay resulting from the multiple transmissions of the same information, its remarkable contribution in terms of reducing the error probability makes it an indispensable part of many practical systems. There is a physical layer version of ARQ, the hybrid ARQ (HARQ) which improves the probability of successful reception at the physical layer (PHY), by combining the recently received signal with the previous one [8][9]. In contrast to HARQ, ARQ is often used at the medium access control (MAC) layer independent of the PHY layer.
Since the unit of transmission is a MAC Protocol Data Unit (MPDU) in the MAC’s perspective, the unit of retransmission is also an MPDU. Since typical ARQ schemes limit the maximum retransmission number1 to each MPDU, if an MPDU can not be successfully transmitted until the maximum limit is reached, then that MPDU is discarded by the MAC. The size of payload within an MPDU is often much less than that of the IP datagram. This observation is generally reasonable, especially for the mobile wireless IP network since the time width of a transmission unit should be designed as short as possible in order to mitigate the severe channel fading due to the mobility. Inevitably, an IP datagram should be fragmented into multiple MPDUs. Surely, there is an exceptional example, wireless LAN (WLAN), where the whole IP datagram with over 2k bytes may be transmitted without any fragmentation although it supports the fragmentation functionality at the MAC. Finally, all fragments from the original IP datagram should be transferred error free for the successful reassembly at the receiver-side MAC. Otherwise, the final delivery failure of a single MPDU (after retransmissions) makes the successful deliveries of other MPDUs useless if we do not consider the additional coding scheme above the MAC layer [10][11]. We argue that the user-perceived quality-of-service (QoS) is directly affected by the performance measure at the IP level, indirectly to that of the link layer or physical layer assuming that the wireless part is the bottleneck along the end-to-end path. Accordingly, we propose a new ARQ strategy which offers the enhanced IP level performance compared to the conventional ARQ strategy. Moreover, the proposed scheme can be used together with various ARQ structures, e.g., stop and wait, cumulative ACK, and selective repeat ARQ, since the idea is independent of either the acknowledgement protocol or sliding-window management. The rest of this paper is organized as follows: Section II describes our proposed scheme with implementation issues, and then analytical results in terms of the error probability and delay at the IP layer are presented and discussed in Section III. Finally, this paper concludes with Section IV. II. THE PROPOSED ARQ STRATEGY Before presenting our approach, we should mention that the IP datagram will be regarded as MAC Service Data Unit 1
This research was in part supported by University IT Research Center (ITRC) and Samsung Electronics.
Note that some technologies such as IEEE 802.16 [3] employ the maximum life time instead of the maximum retransmission number. The idea presented in this paper can be also easily applied to such systems.
(MSDU) by the MAC. In practical systems, an intermediate layer, e.g., IEEE 802.2 logical link control (LLC), between IP and the MAC layer may attach its own header to the IP datagram, and then forward it to the MAC. Since a transmission failure is often due to the channel error from temporary deep channel fading, it might increase the probability of successful transmission of the IP packet to retransmit an erroneous MPDU up to a given fixed limit instead of discarding it. Let us consider the retransmission opportunity as a form of system resource. We can interpret the conventional ARQ to allocate an equal amount of resource, i.e., precisely equal opportunity, to each MPDU. However, an MPDU transmitted under a good channel status does not need the excessive resource any more, while other MPDUs under a poor channel status may require more resources. Therefore, we can figure out the equal resource allocation via the conventional ARQ strategy is not optimal given the total sum of resources available to the MSDU. Our proposed ARQ strategy is sharing the total retransmission opportunities among the MPDUs derived from the same MSDU. This concept is similar to the resource management in the CDMA network, where the power is the main resource. In such a system, more transmit power is allocated to the user in poor channel in order to maintain the required signal quality. For the purpose of distinguishing between the proposed scheme and the conventional one, let us refer the proposed strategy to as ‘MSDU-based’ ARQ scheme, and the conventional strategy to as ‘MPDU-based’ ARQ scheme. The operational procedure for ‘MSDU-based’ ARQ scheme can be described as follows: 1) When it begins to transmit a sequence of MPDUs divided from the new MSDU, initialize the retransmission counter, Cmsdu , to a predefined limit. 2)
For each MPDU transmission attempt, decrease Cmsdu by 1. 3) An erroneous MPDU could be retransmitted only if Cmsdu is not zero. 4) If Cmsdu becomes zero, all the pending MPDUs from the same MSDU are discarded. In fact, we can detect earlier whether attempting to transmit the rest of MPDUs is meaningful at step 3 before reaching to step 4. That is, if the number of pending MPDUs to be transmitted is larger than the remaining resource, Cmsdu , the failure of the MSDU is inevitable. Therefore, we can declare the transmission failure of the IP datagram without wasting the air resource. In order to supplement this capability, the step 3) can be modified as 3') The erroneous MPDU can be retransmitted only if the number of remaining MPDUs is fewer than or equal to Cmsdu . Let’s denote this modified ‘MSDU-based’ scheme as ‘MSDU w/early drop’. The modified scheme is expected to
reduce the average delay without compromising other performances, i.e., goodput, and MSDU drop ratio. Similarly, we can define the ‘MPDU w/early drop’ scheme, which discards the pending MPDUs belonging to the same MSDU whenever it fails first to deliver a single MPDU in spite of retransmissions. For the implementation issue, our proposed scheme requires that the MAC should be able to recognize which MSDU a group of MPDUs were generated from. For the ‘MSDU w/early drop’ scheme, the MAC needs the additional information about the total number of MPDUs belonging to a complete IP datagram. In other words, the MAC needs to know the information of the IP layer. These constraints are not impossible to satisfy because such information is also required to reassembly the fragmented payloads at the receiver. At this point, we argue that our proposed scheme, ‘MSDU-based’ ARQ, does not require any complex MAC structure or additional information. III. PERFORMANCE ANALYSIS For analytical simplicity, we consider a time-slotted system where a single MPDU is transmitted during a fixed time slot. We assume an IP datagram is fragmented into N MPDUs, and a transmission failure occurs with given probability, p , at each time slot. Here, we ignore the error or delay invoked from the acknowledgement message. That is to say, the transmitter can know if its transmission is successful or not immediately after a transmission. Let us consider that the ‘MPDU-based’ ARQ scheme allows an MPDU to be transmitted up to M times including the initial trial as well as the subsequent (M-1) retransmissions. For fair comparison, the maximum retransmission limit of M’=NM is allowed for an MSDU in the ‘MSDU-based’ scheme. Actually, M in the ‘MSDU-based’ scheme may not be necessarily an integer as long as M’ is an integer. In Section III-A, we present the error probability of an IP datagram, and the average IP delay in terms of M, N, and p. Additionally, when a target IP-level error probability is given, the energy consumption of a transmitter is analyzed in Section III-B. The numerical results for the analysis are presented in Section III-C.
A.
Analysis of IP-Level Performance Measures
We first derive the IP datagram transmission failure probability for both schemes. The successful transmission probability of a single MPDU within a given transmission limit, M, can be represented by 1-pM since the transmission failure occurs independently at each time slot. Accordingly, the probability Pfail of an IP datagram transmission failure in the ‘MPDU-based’ ARQ scheme is given by (1) Pfail , MPDU ( N ) = 1 − (1 − p M ) N . Let us denote the probability of successful transmission of N MPDUs after i time-slots by PN(i). This probability in the ‘MSDU-based’ ARQ scheme can be represented by
⎛ i −1 ⎞ N i−N (2) PN (i ) = ⎜ ⎟ (1 − p ) p , (i ≥ N ) , − N 1 ⎝ ⎠ which is a well known equation of the negative binomial distribution [12]. For i < N , PN (i) is naturally zero. Then,
When an N by ( NM ) table is given with P1 (i ) = S (i) , we can obtain any PN (i ) using Eq. (5) with iterative manner. Therefore, the average IP packet delay in the ‘MPDU-based’ scheme can be obtained as NM
∑ i ⋅ P (i )
Pfail in the ‘MSDU-based’ scheme can be determined by
⎛ i −1 ⎞ N i− N (3) Pfail , MSDU ( N ) = 1 − ∑ PN (i ) = 1 − ∑ ⎜ ⎟ (1 − p) p i=N i = N ⎝ N − 1⎠ Next, we compute the average delay of IP datagram. Let us denote the average IP packet delay as D . This can be obtained as the expectation of total time slots used to transmit an IP datagram conditioned on the successful delivery. Therefore, D can be written by NM
NM
D = E{number of time slots | IP successful delivery}=
∑i ⋅ P i=N
N
(i )
1 − Pfail ( N )
.
We need to get PN (i ) for ‘MPDU-based’ scheme in order to compute D while PN (i ) for the ‘MSDU-based’ scheme is already shown at Eq. (2). When the transfer of an IP datagram with N MPDUs is successfully completed at the ith time slot, there exist many possible combinations of the number of time slots consumed to transmit each MPDU successfully. We denote the combination as N dimensionaltuple, n = (n1 , n2 , " , nN ) , where n j , (1 ≤ n j ≤ M ) represents
the number of slots used to deliver the j-th MPDU, and the tuple space satisfying
N
DMPDU ( N , p )= i = N M N . (1 − p )
NM
∑
N j =1
n j = i as Ai . It is similar to the
set partitioning problem with constraint that the number of elements belonging to a partition is between 1 and M. Therefore, the cardinality of Ai , i.e., the number of elements
⎛ i −1 ⎞ of Ai can be roughly upper-bounded by ⎜ ⎟ . Since i ⎝ N − 1⎠ can have the value of NM , the number of combinations can be enormous. When we define a probability mass function, n −1 S (n j ) as p j (1 − p ), (1 ≤ n j ≤ M ) , PN (i) can be computed as N
∑
∏ S (n ) .
n=(n1 , n2 ,", nN )∈ Ai j =1
j
(4)
Eq. (4) can not be solved in closed-form. However, we find the form of Eq. (4) is much similar to the target problem of the Buzen’s algorithm, which is used to analyze the state probability in the closed-queuing network [13]. Buzen’s algorithm is a kind of computationally efficient tabular method. If it takes k time slots to transmit N-th MPDU, PN (i ) can be expressed in terms of S ( k ) , and PN −1 (i − k ) , i.e., M
PN (i ) = ∑ S (k ) PN −1 (i − k ) . k =1
(5)
(6)
On the other hand, D for the ‘MSDU-based’ scheme can be obtained using Eqs. (2) and (3) easily as NM ⎛i ⎞ N ∑ ⎜ ⎟ pi i=N N . (7) DMSDU ( N , p ) = NM ⎝ ⎠ ⎛ i −1 ⎞ i ∑ ⎜ ⎟p i = N ⎝ N − 1⎠ B.
Analysis of Energy Consumption
When the transmission error probability, i.e., p, is given, two different schemes achieve different delivery failure probabilities of IP datagram. As shown in the graphs in Section III-C, the ‘MSDU-based’ scheme always results in lower error probability of IP datagram over the ‘MPDUbased’ scheme. Changing the view-point, if a target delivery failure probability of IP datagram is given from IP layer and the total transmission opportunities, i.e., NM, are fixed, the transmission power in the ‘MSDU-based’ scheme can be reduced. That is, two schemes require different transmission error probability to accomplish the same IP-level performance. Let us denote the target delivery failure probability of IP datagram as ξ target and required transmission error probabilities of each scheme satisfying Eqs. (1) and (3) as pMPDU and pMSDU, respectively. Therefore, pMPDU and pMSDU satisfy the following equations.
ξ target = 1 − (1 − ( pMPDU )M ) N NM ⎛ i −1 ⎞ N i−N = 1− ∑⎜ ⎟ (1 − pMSDU ) ( pMSDU ) i = N ⎝ N − 1⎠
For the purpose of computing the energy consumption, we should know the average transmission time, T , which can be obtained as T = E{number of time slots} = D ⋅ (1 − ξ target ) +
(8)
E{number of time slots | IP unsuccessful delivery} ⋅ ξ target .
Note that when either ‘MPDU-based’ or ‘MSDU-based’ scheme is determined, the second term in Eq. (8) depends on the use of the ‘early drop’ functionality, while the first term, i.e., D , does not. Accordingly, four different T can be determined as
1
N
TMPDU = DMPDU ( N , pMPDU ) ⋅ (1 − ξ target ) + ξ target ⋅ ∑ ( M ⋅ i + i =1
N
TMPDU / ED ( pMPDU )=DMPDU ( N , pMPDU ) ⋅ (1 − ξ target ) + ξ target ⋅ ∑ ( M + i =1
DMPDU (i − 1, pMPDU )) ⋅ p
(1 − p
M i −1 MPDU
)
TMSDU ( pMSDU ) = DMSDU ( N , pMSDU ) ⋅ (1 − ξ target ) + NM ⋅ ξ target
Error Prob. of IP datagram
⎛N⎞ M M DMPDU ( N − i, pMPDU )) ⋅ ⎜ ⎟ ( pMPDU )i (1 − pMPDU ) N −i ⎝i ⎠
M MPDU
N=5 N=10 N=15 N=20 N=25 N=30
0.1
0.01
1E-3
1E-4
MPDU-based MSDU-based
1E-5
1E-6 0.1
TMSDU / ED ( pMSDU ) = DMSDU ( N , pMSDU ) ⋅ (1 − ξ target ) + ⎛ NM − i ⎞ N −i NM − N +1 ⎟(1 − pMSDU ) pMSDU . ⎝ N −i ⎠
N
ξ target ⋅ ∑ ( NM − (i − 1)) ⋅ ⎜ i =1
Finally, the energy consumption of a transmitter can be represented, respectively, as EMPDU = TMPDU ( pMPDU )WMPDU , where pMPDU = δ (WMPDU ) EMPDU / ED = TMPDU / ED ( pMPDU )WMPDU , EMSDU = TMSDU ( pMSDU )WMSDU , where pMSDU = δ (WMSDU )
(9)
EMSDU / ED = TMSDU / ED ( pMSDU )WMSDU , where W represents the transmission power, and δ (W ) denotes the error probability of an MPDU at the receiver’s perspective. Further, we assume δ (W ) can be modeled as [14]
W < Wth ⎧ 1, , (10) ⎩exp(− B (W − Wth )), W ≥ Wth where B is a parameter determining the declining ratio of error curve, which is related with the diversity order achieved via various physical layer techniques, and Wth depends on the distance of the receiver from the transmitter.
δ (W ) = ⎨
C.
Numerical Results
Firstly, M is increased from 1 to 6 with N=30. In Fig. 1, we observe that the ‘MSDU-based’ scheme reduces the error probability of IP datagram more rapidly as M increases. It is interesting that the ‘MSDU-based’ scheme with M=2 outperforms the ‘MPDU-based’ scheme with M=6. Straightforwardly, this fact shows the effectiveness of our proposed scheme.
Fig. 2. Error probability of IP datagram vs. error probability p of MPDU, M=3 At this time, N is increased from 5 to 30 while M is fixed to 3. In Fig. 2, the curves are shown grouped according to the scheme. It is also observed that the ‘MSDU-based’ scheme is better than ‘MPDU-based’ scheme at all ranges of N, i.e., the size of IP datagram. Another interesting observation is that a longer IP datagram shows lower error probability in the ‘MSDU-based’ scheme for a given transmission error probability, i.e., p, while a shorter IP datagram shows a lower error probability in the ‘MPDUbased’ scheme. Note that the statistical multiplexing gain from the ‘MSDU-based’ scheme increases as N increases. Therefore, the difference in the error probability of IP datagram between ‘MSDU-based’ and ‘MPDU-based’ scheme gets bigger as N becomes larger. Considering that a few of long IP packets dominate the overall utilization of the current IP network [15], the property favorable for long IP packet is believed to be useful. Secondly, Fig. 3 shows the error probability of IP datagram as well as the average packet delay of successfully received IP datagram when M=3 and N=10. Each point represents two IP-level performances simultaneously given transmission error probability, p, which can be interpreted as the channel quality. As the channel quality becomes worse, i.e., higher p, more time slots are commonly consumed to deliver an IP datagram due to increased retransmissions. However, the ‘MSDU-based’ scheme is shown to achieve substantial gain in terms of IP datagram error probability over the ‘MPDU-based’ scheme.
1
0.01
M=1 M=2 M=3 M=4 M=5 M=6
1E-3
1E-4
1E-5
MPDU-based MSDU-based
1E-6
Error Prob. of IP datagram
0.25
0.1
Error Prob. of IP datagram
1
p
0.20
MPDU-based MSDU-based 0.15
p=0.3 0.10
0.05
10.0 0.1
1
p
Fig. 1. Error probability of IP datagram vs. Error probability p of MPDU, N=30
p=0.2
p=0.05
p=0.1
0.00
p=0.001, 0.01
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.0
14.5
Average IP packet delay (slots)
Fig. 3. Error probability of IP datagram vs. average IP packet delay, when M=3, N=10
The packet delivery delay of the ‘MSDU-based’ scheme is observed to take larger values than the ‘MPDU-based’ scheme. Based on this fact, one may say that the ‘MSDUbased’ scheme is worse than the ‘MPDU-based’ scheme with respect to the average delay. However, we should be careful for this since the goal of ARQ should be to minimize the error probability of IP datagram by fully utilizing the available resources, not to minimize the average delivery delay, when the transmission opportunities, i.e., NM are allowed to an MSDU. Note that NM basically represents the allowed worst case delay. In this context, the fact that the ‘MPDU-based’ scheme provides a worse IP datagram error probability and a better delay performance is not desirable at all. 1.4
MPDU-based w/ED MSDU-based MSDU-based w/ED
Normalized energy consumption
1.3 1.2 1.1 1.0 0.9
ξtarget=0.01
0.8
ξtarget=0.001 0.7
ξtarget=0.0001
0.6 1
2
3
4
5
6
7
W th
Fig. 4. Energy consumption normalized by ‘MPDU-based’ scheme, when M=3, N=10, and B=1 Finally, Fig. 4 shows the energy consumption computed by Eq. (9) and normalized by the value of the ‘MPDUbased’ scheme. When a target IP error probability is given, we find whether the transmission energy can be reduced via our proposed scheme depends on a parameter of error model, Wth. That is, if Wth is higher than the threshold, the total transmission time is the dominant factor so that the ‘MSDUbased’ scheme consumes more energy. Otherwise, the reduced transmission power becomes the dominant factor so that the ‘MSDU-based’ scheme consumes less energy. Due to this reason, for the purpose of practically meaningful result, it is important to insert the typical values to Wth even though the trend of the performance is just envisioned in this paper. However, the trends can be interpreted in terms of the distance since Wth is surely related with the distance from the transmitter. Additionally, the threshold depends on the target IP error probability. As the IP layer requires more strict error performance, it is more advantageous for the link layer to use the ‘MSDU-based’ scheme. Each scheme with ‘Early Drop’ functionality can reduce the energy further, especially when the target requirement is not strict. IV. CONCLUDING REMARKS In this paper, we proposed a new ARQ strategy in order to enhance the IP-level performance, which is directly related to the user’s satisfaction. Since our proposed scheme simply
changes the objective of resource allocation from MPDU to MSDU, i.e., IP datagram, it does not require any complex algorithm or protocols. In spite of the simplicity of the proposed approach, we observed that the IP-level error performance is dramatically improved from the analytical result. Additionally, the performance trends in terms of the energy consumption were also studied. REFERENCES [1] TTAS.KO-06.0064, Air and Network Interface Specifications for 2.3GHz band Portable Internet Service, Standard, TTA, June 2004. [2] IEEE 802.16e/D5-2004, Draft Supplement to Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems – Amendment for Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed Bands, September 2004. [3] IEEE 802.16d/D5-2004, Draft Revision to Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems, May 2004. [4] Dimitri Bertsekas, and Robert Gallager, Data Networks, 2ed, Prentice Hall, 1992. [5] M. Naijoh et al., “ARQ schemes with adaptive modulation/TDMA/TDD systems for wireless multimedia communication services,” in Proc. of IEEE PIMRC, vol. 2, pp. 709-713, September 1997. [6] H. Li et al., “Automatic repeat request (ARQ) mechanism in HYPERLAN/2,” in Proc. of IEEE VTC, vol. 3, pp. 2093-2097, May 2000. [7] V. Iyengar et al., “Comparison of ARQ protocols for asynchronous data transmission over Rayleigh fading channels,” in Proc. of IEEE Globecom, vol. 3, pp. 1703-1707, December 1993. [8] D. Chase, “Code combining: A maximum-likelihood decoding approach for combining an arbitrary number of noisy packets,” IEEE Trans. on comm., vol. 33, no. 5, pp. 385-393, May 1985. [9] S. Lin, and P.S. Yu, “A hybrid ARQ scheme with parity retransmission for error control of satellite channels,” IEEE Trans. on comm., vol. 30, no. 7, pp. 1701-1719, 1982. [10] Luis Muñoz et al., “Optimizing Internet Flows over IEEE 802.11b Wireless Local Area Networks: A PerformanceEnhancing Proxy Based on Forward Error Correction,” IEEE Communications, vol. 39, no. 12, pp. 60–67, December 2001. [11] Marta García et al., “Design, Implementation and Evaluation of an Adaptive Forward Error Correction Scheme over WLAN,” in Proc. of WPMC, October 2003. [12] A. L. Garcia, Probability and Random Processes for Electrical Engineering, pp. 100-101, 2ed, Addison-Wesley, 1994. [13] J. P. Buzen, “Computational algorithms for closed queueing networks with exponential servers,” Commun. ACM, vol. 16, no. 9, pp. 527-531, September 1973. [14] Qingwen Liu et al., “Cross-Layer Combining of Adaptive Modulation and Coding with Truncated ARQ over Wireless Links,” IEEE Trans. on wireless comm., vol. 3, no. 5, September 2004. [15] Y. Joo et al., “TCP/IP Traffic Dynamics and Network Performance: A Lesson in Workload Modeling, Flow Control, and Trace-Driven Simulations,” ACM Computer Comm. Review, April 2001.
