Aggregated Priority Queueing as an Efficient ...

Aggregated Priority Queueing as an Efficient Queueing Mechanism to Overcome Effects of Self-Similarity C. Watagodakumbura, A. Jennings and R. Harris

N. Shenoy

School of Electrical and Computer Engineering RMIT University Melbourne, Australia

Department of Information Technology Rochester Institute of Technology New York, USA

{[email protected], [email protected], [email protected]}

Abstract - Differentiated Services (DiffServ) architecture is based on aggregation of traffic and, unlike the Integrated Services (IntServ) the resources are not reserved on a per flow basis. One of the current research issues is the provision of Quality of Service (QoS) guarantees to real time traffic in the DiffServ environment. The idea here is to achieve these guarantees without per flow resource allocation while safeguarding the best effort traffic from extremely high delays. The self-similar nature of Internet traffic that results in burstiness and very high delays has been identified in the recent past. The problem at hand is, what packet-scheduling scheme can be used to minimise delay to reasonable limits and the levels of control to be applied on the aggregated traffic to achieve such limits. We propose a class based aggregated Priority Queue with Lower Real time Traffic Utilisation (PQ-LRTU) as a packetscheduling scheme that is capable of providing statistical delay guarantees for DiffServ networks. Since only a real time traffic utilization threshold is maintained at the entrance to the network to control traffic, it provides a simple mechanism. Overall queue efficiency is achieved by using different levels of delay tolerable lower priority traffic. Keywords—priority queueing, traffic aggregation, self-similar Traffic, quality of service, Differentiated Services Architecture

1. Introduction A scalable solution for supporting QoS in the rapidly expanding Internet is sought through a Differentiated Services (DiffServ) framework [1]. Unlike in Integrated Services (IntServ) where each traffic micro flow is treated separately, DiffServ treats traffic in aggregation [2]. The aim is to achieve scalability and better bandwidth utilisation. One of the related research issues is the provision of QoS and the type of guarantee that network operators can provide to end users. IntServ provides deterministic guarantees through resource allocation and admission control at the expense of simplicity, scalability and possibly the utilisation. In a broader sense, the challenge that DiffServ faces is to meet all these requirements while providing reasonable QoS guarantees to end users. The

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need for identifying proper queueing systems along with scheduling schemes is still an open research issue of great importance. The discovery of self-similarity or fractal-like behaviour of data network traffic has initiated many new research directions in the area of traffic engineering [3]-[11]. That is, the traffic possesses similar statistical properties in a wide range of time scales such as milliseconds, seconds, minutes, hours, days etc., unlike that found in conventional short-range-dependent traffic models. Beyond its statistical significance, self-similarity has a considerable impact on queueing performance [7]. Expedited Forwarding (EF) is defined in relation to the DiffServ framework as the transmission of packets with minimum delay [12]. One main requirement in EF servicing is that the packet service rate is always greater than or equal to the arrival rate. The same requirements apply for the transmission of real time packets related to applications such as voice and video-conferencing. In the presence of self-similar traffic, how to satisfy the above condition is a matter of conjecture, as the traffic could be bursty in a wide range of time scales. That is, the queues could grow faster than its service rate, a possible cause for extremely high delays. Weighted Fair Queueing (WFQ) [13]-[15] and Priority Queueing (PQ) are two possible scheduling schemes for a DiffServ framework. In the PQ scheme the real time packets can be serviced with highest priority. As expected, PQ has better one-way delay and instantaneous packet delay variation (IPDV) outcomes compared to WFQ for real time data [16]. In this paper, we study the effects of aggregated self-similar traffic on delay of a PQ discipline, which only uses a real time traffic utilization threshold at the entrance of the network to control traffic, and compare them with the results of traditional Markovian traffic models. We identify a class based aggregated priority queue with a lower real time utilisation (PQ-LRTU) model as a candidate scheduling scheme for DiffServ networks

serving real time traffic, that also maintains a better overall queue efficiency in the presence of self-similar traffic. Section II of this paper describes some related work carried out in this area. Section III and IV describe the proposed PQLRTU mechanism and how self-similar traffic is generated, respectively. The basis on which the simulations were carried out is explained in section V while results obtained from simulations are given in section VI. We discuss the results in section VII before concluding the paper with a summary in section VIII.

where W is the average wait time in the buffer and average service time.

P{D > d } ≤

1−α d exp(−24( 2 ) ) α σ ρ 2π 1

for

α≥

d

σ ρ

N

D = ∑ ixp i + x i =0

Mean delay D of a general queueing discipline is given by

D =W + S

(2)

(4)

i =0

Now consider the mean delay calculated from a slowly decreasing (or nearly constant) pi function at fairly large N values, in the order of hundreds or more D (as in a heavy tail distribution); gets extremely large as N gets larger. This is demonstrated in the following equation. N  M D = x ∑ ip i + pc ∑ i + 1 i = M +1   i =0

(5)

That is,

p ( M + N + 1)( N − M )  M D = x ∑ ip i + c + 1 2  i =0 

(6)

where pc is a constant probability value and M and N are very large. The summation term from i = M+1 to i = N has a greater impact on mean delay as M and N get larger.

(

(1)

3. PQ-LRTU Mechanism

(3)

N

D = x (∑ ipi + 1)

Further (5) can be written as

Fractal Point Processes (FPPs) were used to model selfsimilar traffic in [9] in a parsimonious and computationally efficient manner. Using this framework the fractal characteristics such as long-range dependence, slowly decaying variance and 1/f noise were completely characterised by three fundamental parameters: mean arrival rate, Hurst Parameter and fractal onset time. Based on [9] different fractal traffic models were constructed and their statistical properties were studied in [10]. Some of these are of the ON-OFF type and implemented in OPNET as traffic generators. We use these ON-OFF sources as self-similar traffic generators for our simulations.

is the

Let the instantaneous queue size, the number of packets waiting to be served at the time of the arrival of a packet be denoted by i and, the probability that the queue-size is equal to i is pi. Then for constant service time x and maximum queuesize of N for the period of time, the mean delay is given by

2. Related work Edge-to-edge delay bound for priority traffic of a network using aggregate priority FIFO scheduling is calculated in [17]. It has been found that delay bound is valid only for reasonably small utilization values. In a similar study of deterministic guarantees for aggregated real time traffic in [18], it is again revealed that such approaches result in a very low utilization level. In both of these studies a token bucket traffic controller is used at the entrance to the network. This leads to packet loss especially when bursty self-similar traffic is served. To overcome the problem of a very low utilization level possible in a deterministic guarantees approach, it is pointed out in [19] the importance of using a statistical guarantees approach for real time traffic in an aggregated priority queueing environment. A much higher utilization level is calculated as achievable from this approach. An expression for delay violation probability for an aggregated static priority scheduler is derived. That is, probability that delay at a static priority scheduler exceeds d, in the case of single real time class of traffic, is given by

S

)

D = x De + D p +1 where

D

(7)

is the delay component composed of

e

exponential decay portion of queue-size distribution whereas

D

p

is the component composed of the

power-law decay portion. From the viewpoint of the queueing performance the level of utilisation and H have similar effects: the higher the utilisation or H, the larger the maximum queue-size. As seen from (6) and Figure 1, when the queue-size becomes larger the resulting mean queue delay increases exponentially. H depends on the traffic stream or the source whereas utilisation of aggregated traffic depends on the number of flows aggregated and the arrival rate of each flow. That is, the H is a traffic flow attribute whereas the real time utilisation level is an attribute that the network operator has control of. Therefore, it is possible to control the queue-size, in effect the mean queue

4. Generation of self-similar traffic The traffic was generated from a Fractal-Modulated Poisson Point Process (FMPP), which falls under the category of Doubly-Stochastic Poisson Process (DSPP). The FMPP we used was a Fractal Binomial Noise Driven Poisson Process (FBNDP) in which a sum of M i.i.d. Alternating Fractal Renewal Processes (AFRPs) are added to produce a Fractal Binomial Noise (FBN) process [10]. This FBN process served as the rate function to a Poisson point process. We used M=1 for each source of our simulations. Both ON-OFF periods had identical power-law distribution; probability density function (pdf) for inter arrival times was given by [9]-[10]

γ A −1 e −γ t / A p (t ) =  - γ γ − (γ +1) γ e A t γ

0≤t≤ A t>A

(8)

is a fractal exponent in the range 1 < γ < 2.

5. Simulation Model The variations of delay of self-similar real time traffic against the number of micro flows, Hurst parameter and real time utilisation level were studied. Each micro flow was generated by a self-similar source of ON-OFF type. The ON and OFF periods are drawn from the same distribution, and are independent of each other (i.i.d). As a measure of the proportion of the total aggregated real time traffic we use the term real time fraction (RTF); it is defined as the ratio of the amount of real time traffic serviced to the total

6 00 0

Dp (power-low decay delay component)

delay, even with streams of very high H with an appropriately small utilisation level, which could be predicted to be much higher than the one obtainable in deterministic guarantees approaches suggested in [17]-[18]. Later on we see that this is verified in our simulation results. For aggregated real time traffic serviced in a priority queue scheduler, a lower utilisation threshold can be used at the entrance of the network to overcome effects of self-similarity. As expected, the real time traffic is treated with highest priority and the utilisation of this category is restricted below an appropriate threshold that produces acceptable delays. In this way, the total utilisation level of the whole queue does not get affected as the remaining service capacity can be used to treat lower priority traffic. It provides a solution to the problem of starvation of lower priority traffic for the benefit of the highest priority traffic. Based on the real time utilisation level, statistical guarantees on end-to-end delay can be provided for the users: the lower the real time utilisation level the higher the delay guarantees. As the admission of flows (as opposed to packets) is controlled at the entrance by a real time utilization threshold, the packet loss of the accepted flows is less. This contrasts from a token bucket approach, which police packets, not flows.

5 00 0

4 00 0

3 00 0

2 00 0

100 0

0 200

300

400

500

600

700

800

900

10 00

N (maximum queuesize) Figure 1. Variation Dp with Maximum Queue Size N for an Arbitrarily Small pc Value of 0.01 and M=100

amount of traffic serviced by the queue for a given period of time [20]. The combined designated packet arrival rate of all traffic for all simulations was 1000 packets per second. The service rate was equal to the combined arrival rate of all priority classes; the highest priority or the real time traffic class, for which we obtained all our results, operated at a designated utilisation value of 80% or less throughout. That is, the fraction of non-real time traffic serviced by the queue was (1 - RTF) > 0. The packet size for all traffic was kept constant at 512 bits for all simulations; as a result, all the packets had a constant service time. OPNET Modeler 9.0 was used for the simulation and for simplicity only a single node was considered for measurements. The results were obtained for aggregations of 2, 4, 8 and 12 micro flows, in addition to the single micro flow case. In each of the above cases, two separate self-similar sources of ON-OFF type generated the non real time selfsimilar packets. A Priority queue scheduling scheme was used with 3 priority levels with real time packets being serviced with the highest priority.

6. Results 6.1 Effects of Hurst Parameter on Mean Queue Delay With the increase in Hurst Parameter H the mean queue delay increased considerably, as would be expected (Figure 2) when the only control used at the entrance is a real time traffic threshold. The mean queue delay at the lowest H (0.51 in our simulation) was much higher than in the traditional exponential inter arrival model. For high H and low level of aggregation, the mean queue delay showed relatively high values. As the number of aggregations grew larger, the mean delay showed a general decrease.

In the same way as the mean delay increased with H it also increased with RTF; values for 70% and 80% RTF were very much higher than the value for 60% RTF (Figure 3). A notable observation was that the delay difference between the same two H values decreased significantly as the RTF decreased; the 2 curves for H=0.80 and H=0.82 for 60% RTF almost overlapped. Further, these curves were much closer to the delay region of the exponential inter arrival curve than that of 70% and 80% RTF.

7. Discussion of Results We have observed through simulations that mean queue delay of self-similar models is higher than their traditional Markovian counterparts, when the traffic control used at the entrance to the network is only a real time traffic utilization threshold. The increase in delay is significant under some conditions, as expected, and not so significant in some other cases, for example, when a lower real time traffic threshold is used at the entrance of the network. Mean delay increases with Hurst parameter H and their values at the lowest H (0.51 in our simulations) were higher than traditional short-range-dependent model values, under the above conditions. In the simulation results we observe that instantaneous queue size gets larger as the level of utilisation and H get larger. In fact, it has a dramatic increase beyond a certain H and utilisation level. For example, in Table 1, for the same H value of 0.82, 60% utilisation produces a mean delay of 26ms whereas it was 180ms for 80% utilisation. As the utilisation is decreased the delay decreases towards the lowest values given by traditional exponential inter arrival traffic. That is, when the traffic streams are burstier more packets arrive at the queue in a shorter period of time, thus making the instantaneous arrival rate much greater than the service rate. This causes the instantaneous queue size to rise dramatically. Table 1 shows how the utilisation and H relate to the maximum queue-size and how queue-size in turn affects the maximum mean delay (though different levels of aggregation). Using (1), Figure 4 is obtained for the delay violation probability against the factor d/(sigma/rho) for different levels of real time traffic utilisation threshold levels. When the parameter d/(sigma/rho) is decreased (i.e. when sigma is increased for the same traffic stream to achieve same delay threshold) the amount of traffic policed is reduced. As seen from Figure 4, this reduction is achieved at the expense of delay violation probability. When the utilisation threshold of real time traffic is reduced, the increase in delay violation probability due to decrease in d/(sigma/rho) is reduced considerably. This implies that slight reduction in real time utilisation threshold could reduce the amount of traffic policed considerably while maintaining the same level of delay

violation probability. In essence, it says that same level of delay violation probability can be achieved for much lower packet loss rate when the network operates in at a lower real time utilisation threshold. Though the lower real time traffic utilisation level is not as low as in deterministic guarantees approaches, the overall efficiency of the queue can be increased by supporting different levels of delay tolerable lower priority aggregate traffic. A properly balanced real time traffic utilisation threshold can prevent starvation of lower priority packets, a common problem of these queueing disciplines.

8. Conclusion The level of real time utilisation and the Hurst effects together make a considerable impact on the instantaneous queue size, the effects of which is directly reflected on queue delay, when the only traffic control used at the entrance of the network is a real time utilisation threshold. Unlike the level of real time utilisation, H of a flow allows little control to the network operator. As a result, PQ-LRTU that exploits the ability to reduce delay considerably by controlling the real time utilisation to an appropriately low level is proposed as a candidate scheduling scheme for DiffServ networks. An important positive implication of this approach is that an ideally chosen threshold for real time utilisation possibly avoids starvation of best effort or any other lower priority traffic. Since policing of traffic at the entrance is flow based, unlike in a token bucket approach that uses a packet based approach, the packet loss of an accepted flow is minimized. Further, the end users are provided with statistical delay guarantees by applying minimal control on aggregated traffic, as opposed to the provision of deterministic guarantees using much higher levels of control. Most importantly, the simplicity of PQ-LRTU approach caters a fundamental requirement of the Internet.

200

Mean Queue Delay in milli seconds

6.2 Effects of Real Time Utilisation Level (RTF) on Mean Queue Delay

180 160 140 120 100 80 60 40 20 0 0

2

4

6

8

10

12

14

N u m b e r o f M ic r o F lo w s H = 0 .5 1

H = 0 .6

H = 0 .7

E x p o n e n t ia l

H = 0 .7 5

H = 0 .8 2

H = 0 .8

Figure 2. Variation of Mean Queue delay with Hurst Parameter H and Number of Micro Flows

References

Mean queue delay in ms

200

150

100

50

0 0

2

4

6

8

10

12

14

Number of micro flows H=0.80-RTF 60

H=0.82-RTF 60

H=0.80-RTF 80

H=0.82-RTF 80

Exponential

H=0.82-RTF 70

H=0.80-RTF 70

Figure 3. Variation of Mean Queue Delay with RTF, H and Number of Micro Flows Table I.

Variation of Queue Size and Mean Delay with Different Traffic Conditions Traffic Conditions

Measured Parameter

RTF 80% RTF 80% RTF 60% H = 0.82 H = 0.80 H = 0.82

Exponential

Maximum queue-size

1810

1151

644

15

Maximum mean delay

180

78

26

3.6

0.1

P [delay > d]

0.08 0.06 0.04 0.02 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-0.02

d /(sigma/rho) RT Utilisation = 0.6 RT Utilisation = 0.7 RT Utilisation = 0.8 Figure 4. Variation of Delay Violation Probability with d/(sigma/rho)

The future work will be based on testing PQ-LRTU approach for other QoS parameters such as IPDV. In the longer run, the delay reduction due to multiplexing traffic streams together could be explored; but this could possibly be achieved at the expense of simplicity, as it requires more stringent restrictions on traffic.

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