Part I 8
5. Conclusions
The characteristics of time-varying channel capacity and location-dependent error exhibited in
wireless communications make packet scheduling be a challenge. We proposed the LWTP scheduler to provide the proportional delay differentiation for the wireless environment with the following goals: 1) to provide proportional delay differentiation; 2) to offer low queueing delay; and 3) to conquer the HOL blocking problem.
Simulations are conducted to investigate the effects of the traffic load, mean channel capacity, variance of channel capacity, and number of mobile hosts on the delay ratios and delay improvement. From the simulation results, LWTP is examined to deal with location-dependent channel capacity well and does provide more accurate (or at least no worse) proportional delay differentiation than WWTP does under different circumstances. Moreover, LWTP is able to reduce the average queueing delay, compared with WWTP, and thus provide better service performance.
Our future works include developing a wireless proportional scheduler to provide both delay and loss differentiation, and adapting the LWTP scheduler in a CDMA environment where a base station will transmit multiple packets concurrently.
References
1. Wang, Z.: Integrated Services: Internet QoS: Architectures and Mechanisms for Quality of Service, Morgan Kaufmann Publishers, pp.15-78, 2001.
2. Blake, S., Black, D., Carlson, M., Davies, E., Wang, Z., Weiss, W.: An Architecture for Differentiated Services, IETF RFC 2475, Dec. 1998.
3. Dovrolis, C., Ramanathan, P.: A Case for Relative Differentiated Services and the Proportional Differentiation Model, IEEE Network, Sep. 1999.
4. Nichols, K., Jacobson, V., Poduri, K.: Expedited Forwarding PHB Group, IETF RFC 2598, June 1999.
5. Clark, D., Fang, W.: Explicit Allocation of Best Effort Packet Delivery Service, IEEE ACM Transactions on Networking, Vol. 6, pp.362-373, Aug. 1998.
6. Dovrolis, C., Stiliadis, D., Ramanathan, P.: Proportional Differentiated Services: Delay Differentiation and Packet Scheduling, ACM SIGCOMM 1999.
7. Dovrolis, C., Ramanathan, P.: Proportional Differentiated Services, Part II: Loss Rate Differentiation and Packet Dropping, Proc. IWQoS 2000, Pittsburgh PA, June 2000.
8. Bodamer, S.: A New Scheduling Mechanism to Provide Relative Differentiation for Real-Time IP Traffic, Proc. IEEE GLOBECOM 2000, San Francisco, CA, pp. 646-650, Nov. 2000.
9. Striegel, A., Manimaran, G.: Packet Scheduling with Delay and Loss Differentiation, Computer Communications, vol. 25, no. 1, pp.21-31, Jan. 2002.
10. Cao, Y., Li, V. O. K.: Scheduling Algorithms in Broad-Band Wireless Networks, IEEE Proceedings of The IEEE, Vol. 89, No.1, pp.76-87, Jan. 2001.
11. Kleinrock, L.: Queueing Systems, Volume 2: Computer Applications, Wiley-Interscience, 1976.
12. Dovrolis, C., Stiliadis, D., Ramanathan, P.: Proportional Differentiated Services: Delay Differentiation and Packet Scheduling, IEEE/ACM Transactions in Networking, Feb.
2002.
13. Saito, H., Lukovszki, C., Moldovan, I.: Local Optimal Proportional Differentiation Scheduler for Relative Differentiated Services, Proc. IEEE ICCCN, Nov. 2000.
14. Leung, M. K. H., Lui, J. C. S., Yau, D. K. Y.: Adaptive Proportional Delay Differentiated Services: Characterization and Performance Evaluation, IEEE/ACM Transactions on Networking, 2001.
15. Jeong, M. R., Kakami K., Morikawa H., Aoyama T.: Wireless Scheduler Providing Relative Delay Differentiation, Proc. The Third International Symposium on Wireless Personal Multimedia Communications (WPMC'00), Bangkok, Thailand, pp.1067-1072, Nov. 2000.
Part II: Proportional Throughput Differentiation
1 Introduction
Fair scheduling draws a lot of attention constantly and be a major issue of wireless scheduling.
Some representatives are idealized wireless fair queueing (IWFQ) [1], channel independent fair queueing (CIFQ) [2], server-based fair approach (SBFA) [3], and channel state dependent packet scheduling (CSDPS) [4].
In [5], Cao et al. defined the fairness in the wireless network as effort fair or outcome fair.
Effort fair means that the allocation of throughput to each flow is fair, regardless of the actual amount of data successfully delivered by the flow, while outcome fair means that the actual received throughput of each flow is fair. Ng et al. specify that the any wireless fair scheduling algorithm should have the following properties: 1) delay bound and throughput guarantees; 2) long-term fairness; 3) short-term fairness; and 4) graceful degradation [2].
Many fair scheduling methods employ different compensation models to achieve the fairness among all flows in a wireless network. However, all methods have one thing in common, i.e., the wireless channel is assumed to be either “Good” or “Bad”. When a flow experiences channel error (corresponding to “Bad” state), it gives up this service opportunity and yields to other flows with a good channel state. The original flow will be compensated once its destined channel changes into “Good” state and the flow receiving the additional services will give back excess service later. In practical, a wireless channel has multiple states, which makes current methods not that realistic. Thus, in this report, we propose a novel fair queueing algorithm to provide high performance and better fairness in the wireless network with a multi-state channel. Our proposed algorithm considers the channel capacity and the degree of lagging, and achieves the following goals: 1) providing outcome fair, 2) offering lower delay, and 3) reducing computational complexity.
2 Background
2.1 Fair Scheduling Model
In the wireless network, a base station is responsible for packet scheduling on a downlink link.
Assume that each flow has a dedicated queue in a base station, and the base station is aware of each packet arrival time at all downlink flows. Also assume that the base station has full knowledge of channel state. Under this model, most wireless fair queueing algorithms consist of two operations as follows:
z Flow queue operation: tags each arrival packet.
z Scheduler operation: transmits the HOL packet of flow i to mobile host i and updates parameters.
2.2 Idealized Weighted Fair Queueing (IWFQ)
IWFQ is derived from the fluid fair queueing (FFQ) [6] algorithm. IWFQ maintains an error-free model,Sr, for reference. By comparing the real system, S, to Sr, a flow that has received more service, less service, and equal service are called a leading flow, a lagging flow, and a satisfied flow, respectively. IWFQ works as follows.
1) Flow queue operation
When the n-th packet of flow i, pin, arrives, it is tagged with two parameters, start time S p( in) and finish time f p( in), defined as follows:
( ) m ax { [ ( )], ( 1)} ;
( ) ( ) /
n n n
i i i
n n n
i i i i
S p v A p F p
F p S p l r
= −
= + (1) wherel is the size of this packet,in v A p[ ( in)] is virtual time derived from the error-free model,
ri is service weight of flow i, and A p is its arrival time. ( )in 2) Scheduler operation
The scheduler chooses the HOL packet with the smallest finish time to serve. If the chosen packet can not be served because it encounters the “Bad” channel, the scheduler continually finds another HOL packet which has the next smallest finish time until it finds a packet with the “Good” channel.
IWFQ can satisfy long-term fairness and throughput bound, but it has some limitations, which have been pointed out in [7].
2.3 Channel-Condition Independent Fair Queueing (CIFQ)
CIFQ uses start-time fair queueing (SFQ) [7] as its error-free model, that is, Sr = SSFQr . SFQ is an approximation of WFQ and operates as follows:
1) Flow queue operation
When the n-th packet of flow i, pin, arrives, it is tagged with two parameters: start time ( )S p and finish time (in F pin), as in eq. (1). CIFQ is associated with an additional variable, lagi, to record the difference between the throughputs that flow i should receive in the error-free model and it has received in the real system.
2) Scheduler operation
The scheduler selects the HOL packet of flow i with the smallest v ini Sr, and really transmits the corresponding packet in S unless one of the following situations occurs.
z Flow i experienced channel error.
z Flow i is leading and during the current leading period (time elapsed since the flow starts to lead), the flow has received more than a fraction α of the normalized service it should have received.
In either case, flow i gives up the service and the lagging flow j has a opportunity to receive this service to compensate its lag. In this case, the scheduler updates vi and cj. If no lagging flow can receive service because of experiencing error-prone channel, the service is distributed to each non-lagging flow j in proportion to its service weight. In this case, the scheduler updatesv and fi j. If all flows experience error-prone channel, the scheduler will selects a flow j with the maximum j
j
lag
r to receive the forced compensation with an infinitesimally dummy packet, and then update .v i
2.4 Exponential Rule
Shakkottai et al. proposed a scheduling algorithm called the exponential rule in High Data Rate (HDR) [8]. This algorithm supports a mixture of real-time and non- real-time data in
CDMA/HDR. Each flow computes a value according to following equation:
=
∑
= is the rate corresponding to the mean fading level of user i, and ( )u t is the capacity of channel i at time t, andi W t to be the amount of time the HOL i( ) packet of channel i has spent at the base station. The value ofa determines the tradeoff i between reducing delays and being fair.The rule selecting a HOL packet to transmit is combined with channel capacity and waiting time threshold. The scheduler selects flow i with the maximum fi to be served.
3 Exponential-rule Fair Queueing
Previous methods have an impractical assumption: the channel only stays in two states (good or bad). If some flows are in a “not so good” channel state (i.e. 1% ~ 99% errors) during a long period, they can not receive any service until exiting from error channel state. Meanwhile, some flows with error-free channel will take over these services. During this period, the amounts of services that each flow receives are unfair. Thus the previous methods only achieve a poor fairness and lower throughput guarantee in the wireless network with a multi-state channel.
EFQ not only wants to get high throughput but also distributes service fairly among active flows in the wireless network with a multi-state channel. The detailed algorithm of EFQ is described in the following subsection.
3.1 Algorithm Description
EFQ maintains an error-free system S for comparing with the real system S and also r
r r .
S =SSFQ When the n-th packet of flow i, p arrives at the queue, it is stamped with two in, tags, start time and finish time, as in eq. (1).
Except for virtual time parameters, each flow i is also associated with an additional
parameter lagi to record the difference between the service that flow i should receive inSSFQr and the service it has received in S.
In order to select an applicable flow to transmit at any time in S, EFQ uses an additional parameter, Expi, to perceive how good the channel i is and how lag the flow i is. The result, Expi, is got from the following formula:
threshold lag
lag i
i
i
e rate service
Exp = _ ⋅ _ (3)
where lag_threshold is the lagging or leading bound. In order to get high throughput in the wireless network with a multi-state channel, the scheduler should select the flow i with the maximal service rate of flow i. However, if the scheduler always selects the flow with the maximal service rate to transmit, it will ignore the lagging and leading bound of each flow, that is, some flows with high service rates always receive excess service and some ones with low service rates receive insufficient service during a long period. Thus bandwidth resource can not be fairly distributed to flows and lagging flows may violate delay bound. EFQ considers a lagging term which is calculated as lag threshold
lagi
e _ to restrict the degree of lagging or leading.
When a lagging flow i does not receive any service during a long period, lagi will become much larger than lag_threshold and the value of the lagging term will increase rapidly. Even though the service rate of this flow is low, Expi increases after multiplying the lagging term, and then causes this lagging flow get transmission opportunity. Similarly, the negative value of lagj means that flow j has received additional services. EFQ will not select this flow because Expj is very small in this case. The algorithm of EFQ is plotted in Fig. 1.
Fig. 1. The algorithm of EFQ.
4 Evaluation and Discussion
We evaluate EFQ to demonstrate its achieved fairness and delay by conducting some experiments. The wireless channel is modeled by a multi-state Markov process, which has five states with the default value of capacity varying among 100%, 75%, 50%, 25%, and 0%. The infinitesimal generator for this Markov process is set as:
HOL
i i j
HOL
j j j
lag lag l lag lag l
= +
= −
H O L j
i i
i
v v l
= + r
2 3 4
where r is the state transition rate to other states and pi is the probability of state i being translated to its neighbor states when the transition occurs. The value of pi can be calculated by letting the sum of each row be equal to zero. The default value of r is 0.2. For simplify, the packet size is fixed at 0.5 Kbytes and full channel capacity is 120 Kbps. There are four flows, and the packet arrival process in each flow follows a Poisson process and its mean arrival rateλ= packets/sec. 3
In addition, we use a performance metric ∆ to evaluate whether our proposed algorithm satisfies fairness. The∆ is defined as follows:
z Fairness index∆i( )τ : The coefficient of variation (CoV) of flow’s throughput in the ith time intervalτ.
In the following sections, we first show the fairness and delay of EFQ and the difference between EFQ and CIFQ on short-term observation. Then, we compare the throughput and delay between the EFQ and CIFQ with different parameters, packet arrival rate, channel capacity rate and channel state distribution. Finally, we show the results when using various access criteria in CIFQ. For the sake of stability, all simulations are run 20 hours and useτ =15000 p-units to divide simulation time, where p-unit is the packet transmission time at full link capacity, i.e., 1/30 sec. In each experiment, we measure the∆i( )τ of each timescale, and the fairness, ,∆ is obtained as follow:
1 ( )
where N is the total number of time intervalτ in simulation time. The default values of flow
parameters are as follows:
Table 1. Parameters of four flows.
Flow Type Weight Arrival rate lag threshold_ α (CIFQ)
1 Poisson 0.25 3 pkts/sec 1000 or 10000 0.5 2 Poisson 0.25 3 pkts/sec 1000 or 10000 0.5 3 Poisson 0.25 3 pkts/sec 1000 or 10000 0.5 4 Poisson 0.25 3 pkts/sec 1000 or 10000 0.5
In CIFQ, a flow can receive service only when it has perfect channel state or a flow cannot receive service only when it has zero channel capacity. Applying this concept, two models used in the environment with a multi-state channel is
z CIFQ_A: a flow which has only perfect channel can receive service.
z CIFQ_B: a flow which has zero channel capacity can not receive service.
4.1 The behavior of EFQ and CIFQ
In this simulation, EFQ_1000 and CIFQ_A last for 360 seconds and the four flows are observed. As shown in figure 2(a), the amount of throughput that each flow receives is close regardless of the channel state of each flow at any time. When flow 2 experiences higher channel error during the time interval [0, 10], it does not receive any service and then its lag increases rapidly. The value of Exp becomes huge and EFQ will select flow 2 to serve. 2 From figure 2(b), when a long time passes, the average delay of four flows will be stable and equal. Although some of flows experience high channel error and do not receive service during a time interval, it will get back lost service later. From figure 3(a), the difference of the received service of each flow in CIFQ is much larger than EFQ_1000. Because each flow which only experiences an error-free channel can receive service in CIFQ_A, thus some flows may receive much service and some ones may not receive any service. Similarly, according to the above reason, the packets of CIFQ_A will wait a longer time to transmit that of EFQ_1000, as shown in figure 3(b).
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 60 120 180 240 300 360
Time (s)
Throughput (Mb)
Flow 1 Flow 2 Flow 3 Flow 4
(a)Throughput
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0 60 120 180 240 300 360
Time (s)
Average delay (s) Flow 1
Flow 2 Flow 3 Flow 4
(b) Average Delay
Fig. 2. Throughput and average delay of four flows in EFQ_1000.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 60 120 180 240 300 360
Time (s)
Throughput (Mb) Flow 1Flow 2
Flow 3 Flow 4
(a)Throughput
0 5 10 15 20 25 30 35 40 45
0 60 120 180 240 300 360
Time (s)
Average delay (s)
Flow 1 Flow 2 Flow 3 Flow 4
(b) Average Delay
Fig. 3. Throughput and average delay of four flows in CIFQ_A.
4.2 Short Timescale
In this section, we observe the behavior of flows under different timescales using five time intervals ,τ i.e. 300, 3000, 6000, 15000, and 30000 p-units. Figure 4(a) and 4(b) show five percentiles, 5%, 25%, 50%, 75%, and 95%, of the fairness, ,∆ and average delay, respectively.
From figure 4, EFQ has narrower range than CIFQ under short timescales, while they have similar fairness range under long timescales. This is because CIFQ does not consider how good state of the channel, and have not enough time to fairly serve each flow under short timescales. EFQ considers the lag of each flow according to lagging term, thus it has the better fairness. Also EFQ considers the channel state of each flow, thus its average delay is stable and lower than that of CIFQ, shown in figure 5.
Fig. 4. The fairness under various short timescales.
Fig. 5. The average delay under various short timescales.
4.3 Packet Arrival Rate
We observe the influence of different packet arrival rate on fairness and average delay, under the environment that the packet arrival rateλ is varied from 1 to 6 packets/sec. Figure 6(a) shows that the fairness achieved by EFQ and CIFQ are satisfactory at light traffic load. As the packet arrival rate increases, EFQ achieves fairer throughput allocation to active flows than CIFQ. The reason is described in the following:
z In CIFQ_A, when the packet arrival rate increases, many packets of a flow wait for transmission in its queue until the channel state becomes perfect. When only a flow is in perfect channel during a period, it receives much service but others do not receive any service. Thus the fairness is bad.
z In CIFQ_B, when the channel is not in pure bad, the scheduler selects a flow with
low service rate, transmitting this kind of packet spends much time. In high traffic rate, the packets of other flows wait much time to transmit than those in low traffic rate. Thus the queueing delay becomes large.
From figure 6(a), there is an interaction between two curves of EFQ at 4 pkts/sec arrival rate. At the small arrival rate, EFQ_1000 is fairer than EFQ_10000. When the scheduler spends much time to transmit the HOL packet of flow with low capacity channel, the degree of average delay increasing in high traffic load is larger than in low traffic load. Thus EFQ_1000 is unfair than EFQ_10000 in high packet arrival rate. Figure 6(b) reveals that EFQ have lower average delay than CIFQ. When arrival rates are greater than 4 pkts/sec and 5 pkts/sec in CIF_A and CIF_B, the system can not reach stationary status. We also see that in EFQ a flow with a larger lag threshod it has a longer waiting time. Figure 6(c) shows that the mean _ , used capacities of various scheduling algorithm at various arrival rates. CIFQ obviously uses the low service capacity when packet arrival rate is high.
0 0.04 0.08 0.12 0.16
0 1 2 3 4 5 6 7
Arrival rate (pkt/sec)
Fairness
EFQ_1000 EFQ_10000 CIFQ_A CIFQ_B
(a)Fairness
0 10 20 30 40 50 60 70
0 1 2 3 4 5 6 7
Arrival rate (pkt/sec)
Av erag e d elay (s)
EFQ_1000 EFQ_10000 CIFQ_A CIFQ_B
(b)Average delay
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 1 2 3 4 5 6 7
Arrival rate (pkt/sec)
Mean service capacity
EFQ_1000 EFQ_10000 CIFQ_A CIFQ_B
(c)Mean service capacity
Fig. 6. Fairness, average delay, and mean service capacity under various packet arrival rates.
4.4 Channel Transition Rate
We adjust the channel transition rate to observe its effect on fairness and average delay. The larger this value, the less frequent the channel transition.
0 0.05 0.1 0.15 0.2 0.25
0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1
channel transition rate
Fairness
EFQ_1000 EFQ_10000 CIFQ_A CIFQ_B
(a) Fairness
0 20 40 60 80 100 120 140
0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1
channel transition rate
Average delay (s)
EFQ_1000 EFQ_10000 CIFQ_A CIFQ_B
(b) Average delay
Fig. 7. Fairness and average delay under different channel transition rate.
Figure 7(a) shows that when the channel transition rate is small, the fairness is poor in CIFQ.
For CIFQ_A, if changing channel state does not occur frequently, a flow encountering purely-bad channel soon recoveries to the channel state with some capacities, and now it can be selected by the scheduler to receive service. Although CIFQ_B allows flow with poor channel state to receive service, it does not consider the difference of transmitting between a flow with a better channel and a flow with a worse channel state. If channel state is unchanged continually, their difference in received service becomes larger. Figure 7(b) shows that the
For CIFQ_A, if changing channel state does not occur frequently, a flow encountering purely-bad channel soon recoveries to the channel state with some capacities, and now it can be selected by the scheduler to receive service. Although CIFQ_B allows flow with poor channel state to receive service, it does not consider the difference of transmitting between a flow with a better channel and a flow with a worse channel state. If channel state is unchanged continually, their difference in received service becomes larger. Figure 7(b) shows that the