2011 International Conference on Telecommunication Technology and Applications
Proc .of CSIT vol.5 (2011) © (2011) IACSIT Press, Singapore
Pushout with Differentiated Dropping for High-Speed Networks
Jui-Pin Yang 1 and Yuan-Sun Chu 2
1
Department of Information Technology and Communication, Shih-Chien University
2
Department of Electrical Engineering, National Chung-Cheng University
1
Abstract. Pushout (PO) queue management scheme is capable of fair buffer utilization and good loss
performance, but it is possessed of high implementation complexity and poor protection against short-term
burstiness of lightly loaded flows. To improve above drawbacks, a simple but efficient scheme, pushout with
differentiated dropping (PDD), is proposed in this paper. We design a weight function to estimate the weight
of each active flow according to corresponding traffic intensity, which provides discriminative packet
treatment when the buffer is full. The PDD maintains two records, that is, maximum and sub-maximum
products of queue length and weight value. By comparing both with that of each arrival packet, the PDD can
correctly decide to accept, push out or discard the new arrival. Simulation results show that PDD scheme can
support better fair bandwidth sharing than that of PO.
Keywords: pushout, differentiated dropping, queue management
1. Introduction
When a network router is equipped with an adequate queue management scheme, low packet loss
probability and high throughput are achievable. Furthermore, it is beneficial to enhance fair bandwidth
sharing and make the congestion control mechanisms easier [1-2]. Roughly, we could classify the queue
management schemes into three kinds of categories including static threshold, dynamic thresholds and
pushout. In the static threshold category [3-4], one or more fixed thresholds should be assigned that is used
to limit the growth of queue lengths. In order to adapt to traffic variations, the thresholds should be
dynamically changed that contributes to better performance. Correspondingly, a dynamic thresholds category
is proposed [5-6]. Both threshold-based categories are simple to implement, but they can only perform well
under specific traffic conditions. Consequently, their suitability to be deployed in high-speed networks with
high performance requirement has been questioned.
A well-known pushout (PO) category and several related variants have been proposed [7-8]. The main
idea behind the PO is that the whole of buffer is shared by all queues and then no limit is imposed on the
buffer usage before the buffer is filled up. When an arrival packet encounters a full buffer, one of resided
packets belonging to the longest queue will be pushed out that makes room for the new arrival. The arrival
packet will be discarded directly if it destines to the longest queue. Many previous surveys point out that the
PO is able to support higher throughput and lower loss performance over the threshold-based categories.
In this paper, we principally discuss the performance matrix of fair bandwidth sharing. In the first place,
we estimate the traffic intensity of active flows and then use a weight function to calculate their weight
values. By comparing the product of queue length and weight value of each active flow with two
approximate maximum and sub-maximum products, the arrival packets will be judged as acceptance,
1
Corresponding author. Tel.: + 886-7-6678888 ext. 6404; fax: +886-7-6679999
E-mail address: juipin.yang@msa.hinet.net
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pushout or discard. We named this scheme pushout with differentiated dropping (PDD), because it
differentiates to push out arrival packets according to their products. Various applications require different
quality of services. By marking a parameter in the packet headers of a specific flow, the PDD can support
different degrees of bandwidth sharing. However, the PO is incapable of action.
2. Pushout with Differentiated Dropping Scheme
In the first place, the definition of a flow is a stream of packets which have the same source and
destination IP addresses. We calculate average packet arrival rate for each active flow to represent their
intensity estimation. An active flow with large intensity means that their arrival packets have higher
probability to be discarded. The intensity estimation is an exponential weighted moving average, similar to
random early detection (RED) [9]. Let m j ,k be the amount of arrival packet size belonging to active flow j
during time interval k. The duration of a time interval is of RT and the link capacity is of C . Furthermore,
the W p is a parameter that affects the dependency of estimation on short-term or long-term traffic conditions.
Particularly, we modify the rule that is in charge of the maintenance of each active flow record in the
ActiveList of the DRR. When active flow j has empty queue, we do not remove flow j from the ActiveList
unless m j ,k = 0 . This can reduce the frequency to insert or remove records from the ActiveList. I j ,k denotes
the intensity estimation of active flow j during time interval k, which is computed as:
I j ,k = wp ⋅
m j ,k −1
+ ( 1 − wp ) ⋅ I j ,k −1
C ⋅ RT
(1)
After flow intensity estimation, we would like to design a weight function. The main idea of the PDD is
that those flows with lower flow intensity will be assigned a lower weight value. There are many probable
choices to assign the weight values. The simplest approach is to make the weight value of each flow linearly
increase relative to its flow intensity. However, the may lead to insufficient discrimination. Therefore, a
suitable weight function can greatly upgrade the fairness of bandwidth sharing.
Based on our simulations and analysis, we design a non-linear weight function in which active flows
with lower intensity are given relatively smaller weight values, while active flows with higher intensity are
given relatively larger weight values. We select a particular weight function in equation (2) because it can
differentiate active flows. Here, α is a parameter and WF j , k is the weight value of active flow j during time
interval k.
⎧logα ( 1 + ( α − 1 ) ⋅ I i ,k )
WFi ,k = ⎨
⎩ I i ,k
0 ≤ I i ,k ≤ 1⎫
⎬
I i ,k > 1
⎭
(2)
Next, the PDD maintains two records that have the maximum and sub-maximum products of queue
length and weight value using the max and submax variables. When the full is filled up, the PDD estimates
the product of queue length and weight value of the arrival packet. By comparing its product with that of
flow max and submax, three actions are involved to deal with the arrival including acceptance, pushout or
discard. Equation (3) means that at least h resided packets with product max will be pushed out (from the
head of flow queue max), in order to make sufficient room to accommodate the arrival packet with size L .
Also, the same rule is applied to the product submax.
h
min{ ∑ S max,i } ≥L
(3)
i =1
Where S max,i is the packet size of ith resided packet with product max.
Finally, the complete pseudo codes of the PDD are depicted in Figure 1.
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Fig 1: Pseudo codes of the PDD scheme
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3. Simulation Results
We consider a single congested link between two routers and both have the same configuration which is
composed of PDD (compared PO) queue management and DRR scheduling. All network links have the same
link capacity C = 10 Mbps. The other parameters are set as follows; N = 10 , B = 20 Kbytes, W p = 0.3 ,
RT = 16 ms and α = 10 . Each flow generates packets by a specific ON − OFF traffic model. Furthermore,
each flow has infinite data to transmit. To simplify the computer simulations, we assume that all packets
have the same size of 1 Kbytes. Ultimately, total simulation time is set at 200 seconds and quantum size in
the DRR is set at 1 Kbytes. We compare the performance of fair bandwidth sharing between PDD and PO.
Our previous surveys proved that the PO performs better than threshold-based schemes [6]. Consequently,
only the PO is selected as a comparison with PDD in overall simulations. A pushout operation may involve
one or more resided packets to be pushed out that leads to additional overheads. Therefore, low packet
pushout probability is preferred. Unless otherwise specified, all parameters are applied to our simulations.
In Figure 2, we plot normalized bandwidth ratio for each flow under different buffer sizes. There are 10
flows, indexed from 1 to 10, and flows transmit several times more than max-min fair rate. We describe
average traffic load for each flow as [1 2 3 4 5 6 7 8 9 10 (Mbps)]. The definition of normalized bandwidth
ratio is equivalent to attainable bandwidth rate divided by the max-min fair rate. Under max-min fairness,
each flow should obtain average bandwidth of 1 Mbps. Therefore, the ideal normalized bandwidth ratio for
each flow is equal to 1.0.
Fig. 2: Normalized bandwidth ratio versus per flow under different buffer sizes
and average traffic loads from 1 Mbps to 10 Mbps
When B is set at 10 Kbytes, the fair buffer size for each flow is equal to 1 Kbytes. Undoubtedly, the
buffer is severely insufficient in this case. This causes the most unfair bandwidth sharing either PDD or PO,
respectively. Although DRR is capable of fair bandwidth sharing, but it lacks of resided packets to be
dequeued for some of flows. Consequently, an excellent scheduling algorithm may perform poorly if no
adequate queue management scheme collocates. The PDD supports much better fairness than the PO in this
situation, because PDD allows lightly loaded flows increasing in queue length during short-term traffic
burtiness. Inversely, PDD gives a higher probability to discard arrival packets of heavily loaded flows
because they can rapidly resupply packets to the DRR. When B increases, both PDD and PO achieve better
fairness for the lightly loaded flows (flow 1 or flow 2). From different buffer sizes, the PDD always performs
good fairness over the PO thoroughly.
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The simulation results also show that PO is partial to heavily loaded flows. For example, flow 10
obtains the largest normalized bandwidth ratio near 1.15 when B is set at 10 Kbytes. This may encourage
network users to violate congestion control mechanisms because they are able to occupy more bandwidth.
Therefore, this may greatly aggravate congestion. In the PDD, the flow 8 obtains the largest normalized
bandwidth ratio near 1.08. Higher traffic intensity will result in relatively higher weights, so flow 10 properly
obtains ideal normalized bandwidth ratio near 1.02. When B is set at 60 Kbytes, both schemes equip with
sufficient buffer size that contribute to individual approximately best fairness. From the simulations, the
PDD not only achieves good fairness but also benefits to congestion control mechanisms.
In Figure 3, we discuss the effect of different average traffic loads which consist of [1 1.1 1.2 1.3 1.4
1.5 1.6 1.7 1.8 1.9 (Mbps)]. All flows have close average traffic loads, so their weights are approaching. In
the PO, the flow 10 occupies the largest normalized bandwidth ratio near 1.21 when B is set at 10 Kbytes.
As for the PDD, the flow 10 obtains the largest normalized bandwidth ratio near 1.12 when B is set at 10
Kbytes. Besides, flow 1 obtains better fairness than that of Figure 3 under various buffer sizes. The reason is
that the probability of a full buffer becomes lower, so more arrival packets of flow 1 are admitted to enter the
buffer. From Figure 1 and Figure 2, the PDD always provides better fairness than that of PO under different
traffic conditions.
Fig. 3: Normalized bandwidth ratio versus per flow under different buffer sizes
and average traffic loads from 1 Mbps to 1.9 Mbps
In Figure 4, we change the configuration that consists of different number of flows and average traffic
loads. There are 30 flows, indexed from 1 to 30, and flows transmit several times more than max-min fair
rate. We describe average traffic load for each flow as [0.3333 0.6667 1.0 1.3333 1.6667 2.0 ……. 10
(Mbps)]. According to max-min fairness, each flow should obtain average bandwidth of 0.3333 Mbps. In the
PO, the flow 30 occupies the largest normalized bandwidth ratio near 1.03 when B is set at 30 Kbytes. As
for the PDD, the flow 30 obtains less normalized bandwidth ratio near 0.87 when B is set at 30 Kbytes. The
reason for this phenomenon in the PDD is the same as that of Figure 3. However, the flow 30 performs
worse because more flows have approaching average traffic loads to flow 30. The PDD provides flow 1 with
much better fairness than that of PO when B is set at 30 Kbytes. The PO scheme always allocates more
bandwidth to the heavily loaded flow, but the PDD protects the lightly loaded flows and punishes the heavily
loaded flows by giving less bandwidth. In a word, the PDD has much better performance than that of PO no
matter fairness or congestion control.
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Fig. 4: Normalized bandwidth ratio versus per flow under different buffer sizes
and average traffic loads from 0.3333 Mbps to 10 Mbps
4. Conclusions
In this paper, we proposed the PDD scheme that is not only as simple as the threshold-based schemes,
but performs much better than the PO. From the simulation results, the PDD has better fair bandwidth
sharing, lower implementation complexity and overheads than the PO under a great variety of traffic
conditions. In the future, we would like to extend the PDD to support different packet loss priorities while
keeps the simplicity and efficiency. Finally, we would like to modify current weight function that contributes
to provide more stable and good performance. In a word, the PDD is a simple but effective queue
management scheme suitable for high-speed networks.
5. Acknowledgements
The authors acknowledge support under NSC Grant NSC 99-2221-E-158-003, Taiwan, R.O.C.
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