Framework for Fair Scheduling Schemes in the Next Generation High-Speed Wireless Links Yoshiaki Ohta, Masato Tsuru, and Yuji Oie Dept. of Computer Science and Electronics, Kyushu Institute of Technology Kawazu 680–4, Iizuka, Fukuoka 820–8502, Japan Fax: +81-948-29-7652 Tel: +81-948-29-7687 E-mail:
[email protected], {tsuru,oie}@cse.kyutech.ac.jp
Abstract— A very significant evolution of mobile telecommunication technologies is the introduction of the high-speed downlink shared channel used by many users to efficiently accommodate packets in networks. In a wireless environment, because of the time-varying channel fluctuations of wireless links, efficient use of the large available bandwidth cannot be achieved without adopting sophisticated channel-stateaware packet scheduling strategies. To cope with this issue, many downlink packet schedulers have been developed and investigated to achieve high throughput and fair share of the link bandwidth. However, handling all situations by simply applying specific schemes is impossible, and, therefore, more than one scheduler may have to be implemented and selectively employed in a base station. Thus, in this paper, we propose a novel framework for downlink packet schedulers to integrate these existing schedulers into a unified form, and evaluate the basic performance by carrying out simulations. Index Terms— HSDPA, Shared Channel, Channel-StateAware Scheduling, Fairness, Resource Management
1. Introduction It is well known that wireless and mobile networks have become widely used for Internet access. Besides the adoption of IP technologies in core networks in the next generation mobile telecommunication systems, the introduction of high-speed shared channels in access networks, which can be used by many users, has accelerated in order to efficiently use the large available radio resources. In particular, the extended wireless access method of WCDMA (Wideband-CDMA) [1] with the high-speed downlink shared channel is referred to as HSDPA (High Speed Downlink Packet Access) [2]–[5], which is expected to achieve higher performance with a peak data rate that is about 10 Mb/s greater than that of 3G W-CDMA systems. In data transmission over wireless links, the link bandwidth dynamically fluctuates because of the dynamics of radio propagation known as fading. Thus, in a fading environment, various technologies to exploit the variance in the channel states is indispensable, including, for example, adaptive modulation and coding schemes (MCS), packet management in link layers, and fast packet scheduling for users sharing the allocated wireless link [5]. In these technologies, considering the link characteristics, only the schedulers can determine the most important pivotal point, i.e., channel-state-aware radio resource allocation. In fact, many sophisticated channel-state-aware schedulers in wireless environments have been developed and investigated [6]–[11]. Of these schedulers, the Proportional Fair (PF) scheduling scheme [7], [8], [11] is the most basic scheduler in terms of fairness and throughput. The objective of the PF scheduler is to provide users with
fair share in throughput which approximately meets a fairness criterion—proportional fairness [12]. Other schedulers, e.g., the Maximum CIR scheduler (Max CIR) that only maximizes system throughput and the Round-Robin (RR) scheduler that fairly allocates time slots for users, are also expected to be fundamental schedulers. However, each scheme has its own characteristics, and it is thus impossible to handle all situations related to radio resource management by simply applying these respective schemes. This causes the problem that more than one scheduler may have to be implemented and selectively employed in a base station. Therefore, we propose a novel framework for downlink packet schedulers to integrate these typical existing schedulers into a unified architecture. We then investigate the basic performance of our framework by simulations. The most important benefit of our study is that our framework expands the flexibility of wireless communications. Our proposed scheduler includes some parameters so that a specific strategy can be easily achieved by adjusting these parameters. Simulation results will show that our scheduler has compounded characteristics of some typical existing schemes and enables operators to flexibly adjust the attributes of wireless communications according to their requirements. 2. Model Description In this section, we describe the model for schedulers over a downlink shared channel in a base station. Next, we show the details of two typical important packet schedulers, the Max CIR scheduler and the PF scheduler. 2.1. Model for Scheduler Fig. 1 shows the model for schedulers in a base station. We assume that the base station serves M users, and selects one transmission user in a slot of some fixed time duration. The packets transmitted from each source are stored in the dedicated transmission buffer equipped for each flow. A scheduler, denoted by S in Fig. 1, computes the metric for user selection, which is defined by M m (n) for user m, where m = 1, 2, · · · , M , in the nth transmission slot. Mm (n) should be defined so that it varies according to the fading process and the user’s service condition. In this system, we assume that the base station knows perfectly the channel conditions of every user by feedback information sent from each destination mobile terminal. By using this information, the feasible rate, i.e., the instantaneous peak rate in a slot, denoted by R m (n), is computed. M m (n) of
3. Proposed Scheduling Scheme
1 2
S
.. .
transmission slot
M transmission buffer Fig. 1.
high-speed wireless link
The model for a scheduler
large values indicates that the channel condition of user m is relatively good. The scheduler selects one user U (n), U (n) = arg
max
m=1,2,··· ,M
Mm (n),
and transmits the packets, the amount of which in a slot is based on link conditions. If more than one user takes the maximum of metric M m (n) in a slot, an appropriate tiebreaking rule is required. In our study, if a tie occurs, the scheduler arbitrarily selects one user at random. 2.2. Maximum CIR Scheduling Scheme The Max CIR scheduler can maximize the overall throughput. In this algorithm, M m (n) is defined by Mm (n) = Rm (n). Thus, the Max CIR scheduler picks a user with the current highest feasible rate. This causes unfairness in resource allocation, and users with continuously bad channel conditions may not be selected in overall transmission slots. 2.3. Proportional Fair Scheduling Scheme The Proportional Fair (PF) scheduling scheme was originally proposed in CDMA 1xEV-DO systems. In the nth transmission slot, Tm (n) denotes the long-term averaged throughput of user m. M m (n) for the PF scheduler is defined by Rm (n) Mm (n) = . Tm (n) In this way, the PF scheduler does not always transmit packets to the users whose channel quality is best, unlike in the Max CIR scheduler, but takes each user’s average throughput T m (n) into account in order to moderate the unfairness arising in the Max CIR scheduler. The throughput of Tm (n) is updated using an exponentially weighted lowpass filter, ⎧ 1 1 ⎪ ⎨ 1− Tm (n) + Rm (n) m = U (n) t t c c Tm (n + 1) = 1 ⎪ ⎩ 1− Tm (n) m = U (n), tc where tc = min {n, c} (n > 1), in which c is a predetermined smoothing coefficient, and T m (1) = minm,n Rm (n)/c for all m, i.e., T m (1) is a small initial value.
The main objective of the proposed scheduling scheme is to integrate existing schedulers into a unified architecture. In addition to using T m (n) and Rm (n), the proposed scheduler uses the long-term channel state of each user m, denoted by Qm (n). Qm (n) is updated using an exponentially weighted moving average, 1 1 Qm (n) + Rm (n + 1). Qm (n + 1) = 1 − td td Qm (n) is the long-term averaged feasible rate, instead of the instantaneous feasible rate, R m (n). Thus, td must be set to a large value. This means that Q m (n) can represent the longrange target throughput. We define t d = min {n, d}, where d is a predetermined smoothing coefficient, and Q m (1) = Rm (1) for all m. The metric for user selection of the proposed scheduler is calculated by using two metrics—the attainment level of user throughput Q m (n)/Tm (n) and the normalized channel condition Rm (n)/Qm (n). Large Qm (n)/Tm (n) indicates the throughput of the corresponding user is decreasing; and large Rm (n)/Qm (n) indicates a better channel condition. By using the above two metrics, the metric M m (n) of our proposed scheduling scheme is defined by Qm (n) Rm (n) q Mm (n) = · Tm (n)p Qm (n) Qm (n)1−q Rm (n)q = , Tm (n)p where p (0 ≤ p ≤ 1) and q (0 ≤ q ≤ 1) are parameters that control, respectively, the impact of the user throughput and the normalized channel condition on the metric. With easy computations, our scheduler can unify the PF scheduler, the Max CIR scheduler, or an approximate RR scheduler, when (p,q) = (1,1), (0,1), or (1,0), respectively. When (p,q) = (1,0), the user throughput roughly converges to some value, while Q m (n)/Tm (n) is kept constant. Thus, we almost achieve the same throughput ratio between users, which is linearly proportional to Q m (n). The RR scheduler performs in the same behavior. Simulation results will show that the above two schedulers are very similar in terms of the throughput and ratio of time-fraction assignments, 1/M . Therefore, when (p,q) = (1,0), we call this scheme the Slot Allocation Fairness (SAF) scheme. The metric Mm (n) is equal to Qm (n) when (p,q) = (0,0). This scheme cannot refer to both the user throughput and the feasible rate in any transmission slots. Thus, this parameter setting should be avoided in our framework. 4. Simulation Model In our simulation study, we assume that the fluctuation of wireless links follows 3GPP HSDPA Release 5. We refer to the minimum possible time interval to change an MCS to another MCS according to link conditions as the TTI (Transmission Time Interval) in a transmission slot. We set the TTI to 2 ms. In consideration of the practical implementation of MCS sets, we only use five allowable MCS sets, which are listed in Table I [2]. As shown in Table II, we suppose that users with smaller user IDs are closer to the base station, and a relatively high MCS frequently appears. In practice, more MCS sets can be used
TABLE I A LLOWABLE MCS SETS AND THEIR INSTANTANEOUS FEASIBLE RATE Total throughput [Mb/s]
Chip Rate = 3.84 Mc/s, SF = 16, TTI = 2 ms, Multi-codes = 15 MCS ID Modulation Code Rate Rm (n) [Mb/s] 1 QPSK 1/4 1.8 2 QPSK 1/2 3.6 3 QPSK 3/4 5.4 4 16QAM 1/2 7.2 5 16QAM 3/4 10.8
c = 1000, d = 1000 8
TABLE II PARAMETERS OF PROBABILITY DISTRIBUTION FUNCTION User ID 1–2 3–4 5–6 7–8 9–10
Min. MCS 2 2 2 1 1
µm 3.00 2.75 2.50 2.25 2.00
Max. MCS 5 5 5 4 4
σm 2/3 2/3 2/3 2/3 2/3
7
6
q q q q q q q q
5
4
= = = = = = = =
0
1.000 0.500 0.100 0.050 0.010 0.005 0.001 0.000 0.2
0.4
0.6
0.8
Fig. 3.
Total throughput p = 1.00, q = 1.000, c = 1000, d = 1000 1e+00
User User User User User
User 1-2 User 3-4 User 5-6 User 7-8 User 9-10
0.7 0.6
Probability
Probability
1e-01
0.8
1
p
1 3 5 7 9
1e-02 1e-03 1e-04
0.5 1e-05
0.4
0
10
20
30
40
50
60
70
80
Interval of slot assignment [slot]
0.3 0.2
Fig. 4.
Probability of time interval of slot assignment (PF)
0.1 0.0 1
2
3
4
5
MCS ID
Fig. 2.
Probability for the MCS selection
in HSDPA [13]. In addition, for simplicity, we assume in this paper that the MCS sets appear according to a normal distribution with average µ m and variance σ m . When Xm denotes the random variable, an MCS is defined by the minimum positive number that exceeds the value of X m . In this case, the probability of the MCS selection is shown in Fig. 2. The scheduler uses R m (n), generated according to this probability, to compute the user-selection metric of Mm (n) during a TTI. From the definition of T m (1), we can set Tm (1) to 1.8/c [Mb/s] for all m. In our simulation, M = 10 users are admitted into our scheduler. The simulation is run for 100,000 time slots, or equivalently, about 200 s of real time. The simulation is performed under an infinite backlog scenario. Thus, the transmission buffer equipped for each flow has infinite backlogs, and we do not consider the transmission errors. The selected user for packet transmission occupies the transmission slot. 5. Simulation Results and Discussions In this section, we evaluate the basic performance of our proposed scheduling algorithms by using the simulation model presented in Section 2. We then show a resource allocation strategy as an example of the parameter settings of our scheduler. 5.1. Total Throughput We investigate the impact of p and q on the total throughput. We set c to 1000 since the recommended value
in HDR systems is 1000 [7]. In addition, because of the simplicity of the parameter settings, we adjust d to 1000. Figure 3 shows the total throughput. From this figure, we find entirely that the total throughput increases with the decrease of p and the increase of q. In our framework, when q = 1, if p is decreasing from 1 to 0, the scheduling characteristics gradually vary from the PF scheduler to the Max CIR scheduler, and thus we can obtain the large total throughput. In addition, when p = 1, if q is increasing from 0 to 1, the scheduling algorithm gradually changes from the SAF scheme to the PF scheme, and so the total throughput increases while the fairness is sacrificed. The characteristics drastically change when p is roughly 0.1 or less for most q. The reason is that the metric of M m (n) comes to Qm (n), resulting in the difficulty in using both feasible rate R m (n) and throughput T m (n). From this result, to keep large total throughput, we must set p to a relatively small value and q to a relatively large value. 5.2. Time Interval of Slot Assignments Figures 4 and 5 show the probability of the time interval of the slot assignment in the PF scheduler and SAF scheduler, respectively. The probability is defined as the probability of the time interval between two contiguous allocated time slots. From these figures, the probability decreases with the increase of the time interval in the PF scheduler; while the probability in the SAF scheduler shows a concave-down function, and the maximum value is shown at the point where the time interval is approximately equivalent to the number of served users, M . This means that the ratio of time-fraction assignments is nearly equal to 1/M for all users, which implies that the characteristics of the SAF scheduler are almost the same as the RR scheduler. In both schemes, the probability functions show almost the
p = 1.00, q = 0.000, c = 1000, d = 1000 User User User User User
Probability
1e-01
p = 1.00, q = 0.000 7.0
1 3 5 7 9
Total throughput [Mb/s]
1e+00
1e-02 1e-03 1e-04 1e-05
ratio ratio ratio ratio ratio
6.5
6.0
5.5
10
20
30
40
50
60
70
80
0
2000
4000
Interval of slot assignment [slot]
Probability of time interval of slot assignment (SAF)
Fig. 7.
8000
10000
Impact of c and d on total throughput (SAF) p = 0.40, q = 0.050, c = 1000, d = 1000 1e+00
PF
7.8
User User User User User
1e-01
Probability
Total throughput [Mb/s]
8.0
6000 c
p = 1.00, q = 1.000
7.6 7.4 7.2
9 7 5 3 1
1e-02 1e-03 1e-04
7.0
1e-05 0
2000
4000
6000
8000
10000
0
c
Fig. 6.
0.2 0.4 0.6 0.8 1.0
5.0 0
Fig. 5.
= = = = =
Impact of c and d on total throughput (PF)
same characteristics among users, and thus the resources are fairly shared. However, the performance of both schedulers shows significant differences in long-term performance: that is, in the PF scheduler, we can see that the case may occur when users cannot get the transmission slot for long-range periods. To capture these results, we can say that the SAF scheduler is a resource fair scheduler, and so it achieves slotallocation fairness and can improve the worst-case behavior in terms of long-term slot allocation. 5.3. Impact of c and d on Total Throughput Figures 6 and 7 show the total throughput as a function of c in the PF scheduler and SAF scheduler. We define the parameter ratio as d/c. This parameter does not affect the performance of the PF scheduler since it does not use Qm (n). From these figures, we can see that the total throughput is not sensitive to the value of c, in particular, in the case when c is set to large values. The reason is that when c is set to large values, the oscillation of each time-averaged user throughput moderates. As a result, the allocation of transmission slots roughly depends only on the rate fluctuations. Thus, in the end, each time-averaged user throughput slowly oscillates around a certain value reflecting the rate fluctuations, and hence the total throughput becomes insensitive to c. From Fig. 6, the total throughput is approximately maximized when c is set to 1000. From Fig. 7, when c is a fixed value in ratio, d affects the total throughput. If we set d to a large value, averaged feasible rate Q m (n) is more smooth than that in the case when d is a small value. As a result, the impact of feasible rate R m (n) on the metric of user selection decreases, and thus the total throughput is decreased.
10
20
30
40
50
60
70
80
Interval of slot assignment [slot]
Fig. 8.
Probability of time interval of slot assignment ((p, q)=(0.4,0.05)) TABLE III T OTAL THROUGHPUT IN INDIVIDUAL SCHEDULER c = 1000, d = 1000 Scheduler Total Throughput [Mb/s] Max CIR 7.860 (p, q) = (0.4,0.05) 7.754 PF 7.705 SAF 5.724 RR 5.702
5.4. Suggestions of Recommended Parameter Settings As stated previously, the proposed scheduler can help operators allocate the wireless communication resource according to their requirements. In the following, some operation guidelines will be given as an example, and we will obtain how to set p and q in order to satisfy the guidelines in our simulation scenario. The guidelines in this paper are as follows: Guideline 1. The scheduler keeps the total throughput equal to that obtained by the PF scheduler. Guideline 2. The scheduler gets high performance compared with the PF scheduler in terms of worst-case behavior of time-slot assignments. Guideline 3. The throughput performance of the individual user follows the strategy: – Users with a relatively good channel condition get larger throughput than that obtained by the PF scheduler. – Users with a relatively bad channel condition get throughput that is not less than in the case when the RR scheduler and the SAF scheduler are adopted. In order to satisfy these guidelines in our simulation scenario, let us first find the recommended values of p and q. According to these guidelines, we can heuristically find the recommended values of p and q. From Fig. 3, the
p = 0.40, q = 0.050, c = 1000, d = 1000
User throughput [Kb/s]
1400
Proposed PF SAF RR
1200 1000 800 600 400 200 0 1
2
3
4
5
6
7
8
9
10
User ID
Fig. 9.
User throughput p = 0.40, q = 0.050
Total throughput [Mb/s]
8.0 7.8 7.6 7.4 ratio ratio ratio ratio ratio
7.2 7.0 0
2000
4000
6000
= = = = =
0.2 0.4 0.6 0.8 1.0 8000
10000
c
Fig. 10.
Impact of c and d on total throughput ((p, q)=(0.4,0.05))
total throughput is roughly maximized for most values of q when p = 0.1. However, when p was equal to 0.1, we could not find the proper values of q to satisfy Guideline 3. We examined a number of (p, q)-pairs in a trial-and-error manner, and finally found (0.4,0.05) as a desired pair. When (p,q) is set to (0.4,0.05), the total throughput of the proposed scheduler is larger than that obtained by the PF scheduler, as shown in Table III. Hence, we can say that the settings satisfy Guideline 1. Figure 8 shows the probability of the time interval of slot assignment when (p,q) is set to (0.4,0.05). We can see from Figs. 4 and 8 that, while the resources cannot be fairly shared among users in Fig. 8, the tail of the distribution is rather short in Fig. 8 in comparison with that in Fig. 4. These results show improvement in the worst-case performance. Guideline 2 is thus satisfied. Figure 9 shows the individual user throughput. The proposed scheduler, in comparison with all the schedulers, achieves the largest throughput for users near the base station. In addition, for users far from the base station, the scheduler provides them with throughout which is approximately equal to that in the case when the SAF scheduler and the RR scheduler are adopted. Thus, we can say that Guideline 3 is satisfied. Finally, Fig. 10 shows the total throughput in some c and d settings. The settings of c and d equal to 1000 almost maximizes the total throughput. In consideration of the adaptive capability to track the unexpected fluctuations of wireless links, we think that the values of (p, q) = (0.4,0.05) are better settings. Furthermore, the throughput degradation in the large d values shown in Fig. 7 does not appear. Thus, the values of c and d equal to 1000 are proper settings.
6. Concluding Remarks In this paper, we proposed a novel framework for fair scheduling schemes in the next generation high-speed wireless links. In future access networks, users can share the high-speed downlink shared channel with dynamic channel fluctuations, which has already brought the development of various channel-state-aware scheduling strategies. We think more flexible communication capability can be provided when these existing schedulers are integrated into a unified form. The proposed scheduler relies on some parameters, and thus various types of strategies can be achieved to satisfy the requirements of network operators. We evaluated basic performance by carrying out simulations. We clarified that the scheduler has compounded characteristics of a few typical existing schemes, and the scheduler showed its effectiveness for radio resource management. To find reference parameter settings, we suggested a resource allocation strategy and showed the scheduler can outperform the PF scheduler in terms of the throughput of users with better channel conditions, while keeping the throughput of users with bad channel conditions not less than that in the RR scheduler. In future work, we will investigate the performance under the TCP/IP environment. Acknowledgment The authors would like to thank NTT DoCoMo, Inc. for many helpful comments, discussions, and suggestions. References [1] F. Adachi, M. Sawahashi, and H. Suda, “Wideband DS-CDMA for next-generation mobile communications systems,” IEEE Communications Magazine, vol. 36, no. 9, pp. 56–69, September 1998. [2] A. Toskala, H. Holma, T. Kolding, F. Frederiksen, and P. Mogensen, WCDMA for UMTS, 2nd ed., H. Holma and A. Toskala, Eds. Chichester, West Susex PO19 8SQ: John Willey & Sons, September 2002. [3] S. Parkval, E. Dahlman, P. Frenger, P. Beming, and M. Person, “The evolution of WCDMA towards higher speed downlink packet data,” in IEEE Vichicular Technology Conference 2001 (Spring), May 2001, pp. 2287–2291. [4] 3GPP, “High Speed Downlink Packet Access (HSDPA); overall description,” 3GPP, Sophia Antipolis, France, Technical Specification 25.308, Version 5.4.0, Release 5, March 2003. [5] 3GPP, “Pyisical layer aspects of UTRA high speed downlink packet access,” 3GPP, Sophia Antipolis, France, Technical Report 25.848, Vergion 4.0.0, Release 4, March 2001. [6] S. Lu, V. Bharghavan, and R. Srikant, “Fair scheduling in wireless packet networks,” IEEE/ACM Transactions on Networking, vol. 7, no. 4, pp. 473–489, August 1999. [7] A. Jalali, R. Padovani, and R. Pankaj, “Data throughput of CDMAHDR a high efficiency-high data rate personal communication wireless system,” in IEEE Vichuliar Technology Conference 2000 (Spring), May 2000, pp. 1854–1858. [8] P. Bender et al., “CDMA/HDR: A bandwidth-efficient high-speed wireless data service for nomadic users,” IEEE Communications Magazine, vol. 38, no. 7, pp. 70–77, July 2000. [9] S. Borst and P. Whiting, “Dynamic rate control algorithms for HDR throughput optimization,” in IEEE INFOCOM 2001, April 2001, pp. 976–985. [10] X. Liu, K. Chong, and N. Shroff, “Opportunistic transmission scheduling with resource sharing constraints in wireless networks,” IEEE Journal on Selected Areas in Communications, vol. 19, no. 10, pp. 2053–2064, October 2001. [11] P. Viswanath, D. Tse, and R. Laroia, “Opportunistic beamforming using dumb antennas,” IEEE Transactions on Information Theory, vol. 48, no. 6, pp. 1277–1294, June 2002. [12] F. Kelly, “Charging and rate control for elastic traffic,” European Transactions on Telecommunications, vol. 8, no. 1, pp. 33–37, January 1997. [13] 3GPP, “Physical layer procedures (FDD),” 3GPP, Sophia Antipolis, France, Technical Specification 25.214, Version 5.4.0, Release 5, March 2003.
