Chapter 5 Optimal Queue Management Algorithm for Real-Time Traffic
5.3. Packet-based Systems
In this section, we present two algorithms for packet-based systems. In these algorithms, we break a tie, if exists, arbitrarily. Without loss of generality, we assume that U { , ,...,f f1 2 fK} and
1 2 .... K
.
Again, upon packets arrived, the way to decide if the data buffered in the multiplexer is schedulable is the same as that presented in the previous section. If not, we can obtain the loss amount by using equation (54) and one corresponding queue management is needed if there exists
one j such that Loss nj
0, 1 j K. Algorithm 1 is basically a generalization of the scheme proposed in [11] for systems which handle variable length packets. In this algorithm, t represents the length of the “discarded” packet.Algorithm 1
The second algorithm slightly differs from the first one in the content to be minimized. In this algorithm, t represents the length of the oldest packet of k Queue . Note that it selects, k packet by packet, the queue that minimizes the maximum of normalized running packet loss probability.
5.4. Simulation Results
In this section, we evaluate the transient and steady-state performance of our proposed PL queue management algorithm and the two packet-based algorithms that can be implemented for real systems. We assume that there exist five traffic flows which can be generated by video trace files [54].
We adopt both interactive (parking and lecture camera) and non-interactive (Die Hard III, Mr.
Bean, and Starship Troopers) videos in the simulation. The traffic characteristics and the QoS requirements (including the required delay bound and packet loss probability) are summarized in Tables 5.2.
Table 5.2 Traffic characteristics and QoS requirements of the five flows generated from video trace files.
Traffic flow No. 1 2 3 4 5
Video name Parking Cam Lecture Cam Die Hard III Mr. Bean Starship Troopers Video type Interactive Interactive Non-interactive Non-interactive Non-interactive
Mean data rate (Kbps) 236 58 246 184 202
Peak data rate (Kbps) 1551 686 1632 1513 1453
Mean packet size (bytes) 1182 288 1232 919 1008
Delay bound (ms) 160 160 80 80 80
Packet loss probability 0.01 0.008 0.006 0.004 0.002
To investigate the steady-state performance, the simulation for flows generated video trace files is conducted by repeating the files for 20 times. The length of each time slot is assumed to be 80 ms. The proposed algorithm presented in Chapter 5.3 is referred to as the fluid-flow based algorithm. For performance comparisons, we let the system capacity equal the effective bandwidth under the fluid-flow based algorithm. Note that the effective bandwidth, which is defined as the minimum bandwidth to meet the QoS requirements of all traffic flows, can be found in advance by, say, the bisection method.
Fig. 5.4 shows the evolution of running packet loss probabilities of the five traffic flows. As one can see in Figs. 5.4(a), the steady-state loss probabilities meet the requirements for the fluid-flow based algorithm. The reason is simply because we used the effective bandwidths in both experiments. The loss probabilities are about 2.6 and 2.5 times of the desired upper bounds under the packet based algorithms I and II, respectively. Note that the fluid-flow based algorithm achieves the goal of maintaining the ratios of steady-state packet loss probabilities equal to those of the requested values, which can be seen from the results shown in Table 5.3. In this table, PL mean the steady-state loss probability, which becomes PL,norm after the normalizing it by the loss probability requirement. For the two packet-based algorithms, the PL,norm values of different flows fluctuate slightly due to the constraint of handling packets as data units.
Table 5.3 Steady-state (normalized) packet loss probability for flows generated from video trace files.
Traffic flow No. 1 2 3 4 5
PL algorithm (PL) 0.0100 0.0080 0.0060 0.0040 0.0020
Packet-based algorithm I (PL) 0.0266 0.0213 0.0159 0.0106 0.0053 Packet-based algorithm II (PL) 0.0252 0.0202 0.0151 0.0101 0.0050 PL algorithm (PL,norm) 1.0000 1.0000 1.0000 1.0000 1.0000 Packet-based algorithm I (PL,norm) 2.6582 2.6571 2.6569 2.6572 2.6569 Packet-based algorithm II (PL,norm) 2.5225 2.5205 2.5204 2.5206 2.5204
0 1 2 3 4 5 6 7 8 x 105 0
0.002 0.004 0.006 0.008 0.01 0.012 0.014
Time (slot)
Packet Loss Probability
Our proposed PL algorithm in video trace files
Flow 1 Flow 2 Flow 3 Flow 4 Flow 5
Fig. 5.4 (a)
0 1 2 3 4 5 6 7 8 x 105 0
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
Time (slot)
Packet Loss Probability
Packet-based algorithm I in video trace files
Flow 1 Flow 2 Flow 3 Flow 4 Flow 5
Fig. 5.4 (b)
0 1 2 3 4 5 6 7 8
Fig. 5 4 Sample Path of packet loss probability for video trace files with (a) our proposed PL queue management algorithm (b) Packet-based algorithm I (c) Packet-based algorithm II adopted.
Chapter 6 Conclusions
In this dissertation, we have studied the resource allocation technique for IEEE 802.11e HCCA, OFDMA-based systems and finally extended the results for real-time traffic to a general multiplexing system. The conclusions and future works are drawn below.
In IEEE 802.11e HCCA, we have presented an efficient static TXOP allocation algorithm, a proportional-loss fair service scheduler, and the associated admission control unit to provide QoS guarantee for VBR traffic flows with different packet loss probability and delay bound requirements.
Computer simulations are conducted to evaluate the performance of our proposed scheme. Results show that our proposed scheme is effective in QoS guarantee and, moreover, performs much better than previous works. Our proposed proportional-loss fair service scheduler can also be combined with dynamic TXOP allocation algorithms to provide better QoS support. In real systems, it is likely that there are only a limited number of possible applications. Therefore, one can pre-compute the QoS parameter of each type of application so that admission control can be
performed in real time. An interesting further research topic is to extend the results to different traffic models and other types of wireless networks.
In OFDMA-based systems, we have presented an efficient resource allocation scheme which tries to maximize system throughput while providing QoS support to real-time traffic flows. The basic idea of our proposed scheme is to calculate a dynamic minimum requested bandwidth for each traffic flow and use it as a constraint in an optimization problem which maximizes system throughput. The minimum requested bandwidth is a function of the pre-defined loss probability and the running loss probability. In addition, a user-level PL scheduler is proposed to determine the bandwidth share for multiple real-time flows attached to the same SS. A pre-processor is adopted to maximize the number of real-time flows attached to each SS which meet their QoS requirements, when the resource is not sufficient to provide every flow its minimum requested bandwidth.
Computer simulations were conducted to evaluate the performance of our proposed scheme.
Results show that the running loss probabilities of traffic flows attached to the same SS are effectively controlled to be proportional to their loss probability requirements. Besides, compared with previous designs, our proposed scheme achieves higher throughput while providing QoS support. Although we present our designs for long time average of loss probabilities, the idea can be applied to other measurements such as exponentially weighted moving average. How to design a pre-processor which meets user’s need is an interesting topic which can be further studied.
Evaluation of the impact to user perception of satisfaction for various performance measurements is
another potential further research topic.
Finally, we consider a general multiplexing system. We proposed a PL queue management algorithm for packet discarding. With combined with EDF service scheduler, we show that our proposed queue management algorithm is optimal in the sense that it minimizes the effective bandwidth under generalized space-conserving constraint. Two packet based algorithms were studied for real systems. One of them is a direct extension of a previous scheme which handles fixed-length packets. Another one is designed based on the proposed fluid-flow based algorithm.
Simulations results show that our designed packet based algorithm outperforms the direct extension.
An interesting but challenging further research topic is to develop an efficient queue management algorithm for systems with time-varying service capability.
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Appendix A
Derivations of all equations and
proofs of all lemmas and theorems
Proof of Theorem 3.1
Assume that li j,
n li j,
n for some
,i j . According to equation (20), we have
, ,
a b a b
l n l n for any
a b, U . As a result, it holds that , ,
, ,
, active ,
,
, active ,
,
m
a b a b a b r s a b r s
a bUl n a bUl n a bU l n l n a bU l n Q n
Loss n
.This contradicts equation (21). Therefore, Theorem 3.1 is true.
Proof of Theorem 3.3
It is clear that the solution of the last iteration falls in Case 1. Let M denote the size of U in that iteration. We shall prove that the loss computation algorithm takes at most 2 N M
iterations to find the feasible solution if M N or one iteration if M N. The case of M N is obviously true. We prove the case of M N by mathematical induction. For simplicity, we
use Sub-case i (i1, 2) to represent Sub-case i of Case 4 in this proof.
For N 2, we have M . Since 1 M N , we know that the solution of the first iteration cannot fall in Case 1. By tracing the algorithm, one can see that the number of iterations required to find the feasible solution is equal to 2 2 N M
. Assume that the statement is true forN H and M 1, 2,...,H (Hypothesis I). Consider the case of 1 N H1. If Sub-case 2 is never visited, then the number of iterations required is at most NM 1 2
NM
because at least one queue is removed from Uactive in each iteration before the last one. Assume that Sub-case 2 was visited before the feasible solution is found. If the solution of the first iteration does not fall in Sub-case 2, then the size of U in the second iteration is at most H. According to Hypothesis I, the maximum number of iterations required to find the feasible solution, starting fromiteration 2, is equal to 2 H M
. As a result, the total number of iterations is upper bounded by
2 H M 1 2 NM .
Assume that the solution of the first iteration falls in Sub-case 2. Let V1 i and V2 j with i . Further, let j N k represent the number of queues added to V when iteration 1 2 resumes its execution. The total number of iterations required is at most 1B i k
, 2 j k M
,where B i k
, represents the maximum number of iterations required before iteration 1 resumes its execution and 2 j k M
denotes the upper bound of the number of iterations required to findthe feasible solution for the updated V , according to Hypothesis I. Theorem 3.3 is true if 2
, 2
1B i k ik . We shall prove this by mathematical induction.
By tracing the algorithm one can see that it is true for i2 and k0 or 1. Assume that it is true for i and p k0,1,...,p (Hypothesis II). Consider the case of 1 i . If p 1 Sub-case 2 is not visited again before iteration 1 resumes its execution, then we have B i k
, i k.Note that if k0, then Case 2 is not visited. If k0, then there are 0 to
i k 1
times ofSub-case 1 followed by a Case 2. Since k i 1, we have B i k
, 2 ik
1. Assume that, before Sub-case 1 resumes its execution, Sub-case 2 is visited for the second time in iteration r.This implies the solutions of iterations 2, …, and r all fall in Sub-case 1 and, therefore, at least 1 2
As defined in Chapter 3.3, the running packet loss probability of fi,j, namely, Pi,j[n], can be written as
After substituting the above equation into equation (17), we get
which implies According to equation (18), it holds that
Proof of Lemma 4.2
Let Rn k,
t and Pn k,
t be, respectively, the bandwidth allocated to and the resulting running loss probability of fn k, under our proposed PL scheduler. Further, let Rn k,
t and Pn k,
t be the same variables under some other scheduler. Assume that ,
,1
Assume that there exists a scheduler which can guarantee the loss probability requirements of all the Kn traffic flows. In other words, it holds that Pn k,
t Pn k, 1, 1 k Kn, where Pn k,
t is the loss probability of flow fn k, at the end of the t frame, under the considered scheduler. Let th,
Lemma 4.4 can be easily verified with the calculation results shown in Table 4.1.
Proof of Theorem 4.5
proves Theorem 4.5.
Appendix B
Pseudo codes of the proposed algorithms
Loss computation of the proportional-loss service scheduler Algorithm: Loss computation
l n i j U LossComputation Loss U
10. LossLoss l i j,
n48. end if 49. end for
50. LossComputation Loss V
, 2
51. else
52. for all
,i j V253. li j,
n 0 54. end for 55. exit 56. end if 57. end if 58. end if PL scheduler
25 endwhile
Vita
Yu-Wen Huang (黃郁文) was born in Gangshan District, Kaohsiung City, Taiwan, in 1982.
He received the B.S. and M.S. degree in communication engineering from National Chiao Tung University, Hsinchu, Taiwan, in 2004 and 2006, respectively. Currently, he is pursing his Ph.D.
degree at the same university. His current research interests include resource allocation, power management and communication protocols in wireless networks.
Publication List
Journal Paper (Published or accept)
[J1] T. H. Lee and Y. W. Huang, "Effective Transmission Opportunity Allocation Scheme for Real-Time VBR Traffic Flows with Different Delay Bounds," IET Commun., 2008, Vol.
2, No. 4, pp.598-608
[J2] T. H. Lee and Y. W. Huang, "Resource Allocation Achieving High System Throughput with QoS Support in OFDMA-based Systems," IEEE Trans. on Commun.. (accepted on Nov. 4, 2011)
[J3] T. H. Lee and Y. W. Huang, ”Quality of Service Guarantee for VBR Traffic Flows with
[J3] T. H. Lee and Y. W. Huang, ”Quality of Service Guarantee for VBR Traffic Flows with