A New Method for End-to-End Available Bandwidth Estimation

A New Method for End-to-end Available Bandwidth Estimation Anfu Zhou

Min Liu Yilin Song Zhongcheng Li

Institute of Computing Technology Chinese Academy of Sciences {zhouanfu, liumin, songyilin, zcli}@ict.ac.cn Abstract—Previous Probe Gap Model (PGM) based available bandwidth (AB) estimation methods all request the “busy assumption” that probing packet pairs should be in the same busy period when transmitted on bottleneck link, which is hard to satisfy especially for the low utilization path. In this paper, we first present a new probabilistic methodology to estimate AB under “non busy assumption”. The methodology is quite accurate on the low utilization network path. Secondly, we propose a metric to weigh the busyness of a network path based on the distribution of output probe gap. Using the metric, we combine our new methodology and previous methodology, and present a new AB estimation method called Adaptive Available Bandwidth Estimation (A_ABE) which is fit for both low utilization and high utilization paths. We use NS-2 simulation and reproduce traffic from real Internet links to evaluate A_ABE. Compared with previous methods, A_ABE shows its advantages in terms of accuracy, overhead, and also the robustness when confronted with non-persistent cross traffic in multiple hop situations.

I. INTRODUCTION Available bandwidth (AB) of a network path is an important parameter of many Internet applications such as overlay routing[1], adaptive streaming[2], quality of service control[3], and network diagnosis [4]. Many AB estimation methods and corresponding tools have been developed. Reference [10] categorizes these tools into two classes: Probe Rate Model (PRM) methods, including Topp[6], Pathload[7], Pathchirp[9], and PTR[8], and Probe Gap Model (PGM) methods, including Delphi[5], IGI[8], and Spruce[10]. In PRM methods, the sender iteratively transmits probing streams with different probing rate. PRM methods measure AB by searching the turning point at which the input rate and output rate start matching [10]. The biggest shortcoming of PRM is that it consumes all the AB on the probing path, which is a great waste of network resource, especially when the path has low utilization. PGM assumes single bottleneck of the path, and assumes the bottleneck capacity is known. PGM uses a single probing rate and it infers AB from a direct relation between the input and output probe gap of probing pairs. However, the precondition of the relation is that the probing pairs must be in the same busy period when transmitted on bottleneck link. This precondition is called busy assumption, and AB estimation methodology under this assumption is called busy This work is supported by the National Basic Research Program of China (No. 2007CB310702) and the National Natural Science Foundation of China (No. 0604016 and No. 90604016).

Hui Deng China Mobile [email protected]

Yuanchen Ma Hitachi (China) R&D Corporation [email protected]

estimation (BE). When the network path is not busy, the precondition will not hold, so Delphi is inaccurate on low utilization paths [5]. IGI and Spruce make improvement on PGM and use schemes to keep the bottleneck busy during probing period. IGI use probing rate equals to AB, and Spruce sends back-to-back probing pairs with input rate equal to bottleneck link capacity. However, the improvement has side effect: IGI consumes much bandwidth as PRM methods and Spruce is rather intrusive [14]. There are also works on the theoretic analysis of AB estimation, such as [11, 12, 13]. In this paper, we focus on how to estimate end-to-end AB without busy assumption. We first present a methodology called non busy estimation (NBE) to estimate AB while the probing pairs are not in the same busy period. We show that NBE is quite accurate on non busy (low utilization) network paths. Secondly, we propose a metric called gap symmetry (GS) to weigh the busyness degree of a network path.With GS, we combine NBE and BE, and present a new PGM method called Adaptive Available Bandwidth Estimation (A_ABE) to measure AB of both the busy and non busy network paths. We use NS-2 [15] simulation and reproduce traffic from real Internet links to evaluate A_ABE. Compared with previous methods, A_ABE shows its advantages in terms of accuracy, and overhead. The evaluation also shows that unlike other PGM methods, A_ABE is much more robust when confronted with non-persistent cross traffic in multiple hop situations, and the accuracy is comparable with PRM tools under such scenario. The structure of this work is as follows: Section II we present NBE method. Section III introduces the metric to weigh the busyness of network paths: GS, and also gives the A_ABE method. Section IV presents the evaluation results of A_ABE. Section V concludes the paper. II. AB ESTIMATION UNDER LOW UTILIZATION PATH A. Non Busy Estimation We first define some related terms. Suppose an end-to-end network path that includes w links with capacity C1 , C2 , ….

Cw . We denote available bandwidth on these links with A1 , A2 ,….. Aw . The narrow link is the link with the smallest capacity, the capacity of the narrow link is denoted by C . The tight link is the link with the smallest available bandwidth. The available bandwidth of the path is the smallest one of Al

978-1-4244-2324-8/08/$25.00 © 2008 IEEE. This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.

CT1 arrives between t1 and t2 ; it may not cause increase of probe gap, like CT2 arrives between t3 and t4 in Fig.1. It is up to the CT packet size and

increase of probe gap, like

Fig. 1

AB estimation with NBE

( l from 1 to w), denoted by AB as before. In PGM methods, the narrow link and tight link is assumed to be the same link, and is called bottleneck.

gin , the output probe , and probing packet size by L probe .The

its arrival time. To make an increase of probe gap, the interval between arrive time of the CT packet and arrive time of next probe packet should be less than the transmission time of the CT packet. Taking CT2 for example, Suppose CT2 is of kind j, then the size of

We denote the input probe gap by

g out

gap by

transmission time of probing packet on bottleneck link is

gB =

L probe C

.

Now, we introduce a methodology called NBE to estimate AB on low utilization network path. As other PGM methods, we focus the change of probe gap on bottleneck link. As shown in Fig. 1, we use packet train to probe the path. The input gap gin is fixed, and is set to satisfy (1). (We will explain why set

gin =

L probe C

+

(1)

We use the following assumption called non busy assumption to characterize the low utilization of the bottleneck: z No more than one cross traffic (CT) packet arrive between two consecutive probe gaps, and the arrival time of a cross traffic packet during a probe gap follows the Uniform distribution in the gap. For example, in Fig.1, the assumption requests that no more than one CT packet arrive between t1 and t3 ， and the arrival time of

CT1 is the Uniform distribution between t1

t2 . We will show that the assumption is reasonable for

and

low utilization link since the AB estimation result is accurate under the assumption in simulations later. Suppose there are k kinds of CT packets with different packet size L j (j from 1 to k), and we suppose that the packet size is no more than 1500 Byte. The proportion of j kind of packet in CT is denoted by Pj . We now compute the probability that a probe gap increases. Define： Ppgi

= P {a probe gap increases}

Pctpa

= P {a cross traffic packet arrives during a probe gap}

Ppgi|ctpa

= P {probe gap increases | a cross traffic packet arrives during the gap}

= Ppgi|ctpa × Pctpa

, t4 ], then

C

CT2 will make an increase

only when its arrival time falls in the delay area. Note that the arrival time of CT packet follows the Uniform distribution between 0 and gin under non busy assumption, so the probability that

CT2 makes an increase is

Lj

C

g in

. Multiplying

CT2 is of kind j, we get the

with the probability that

Pj ×

Lj

C

(3)

g in

Sum up all k kinds of CT packets, we get: Ppgi|ctpa

So,

Ppgi

k

Lj

j =1

C × gin

= ∑ Pj ×

P p g i = Pc tp a ×

We

now

(2)

When a CT packet arrives in a probe gap, it may cause

k

∑

Pj ×

j =1

Lj

(5)

C × g in

consider

G = { g | i = 1, 2.....m} +

(4)

is:

the

output

+ i

probe

gaps.

Let (6)

denote the set of output gaps that are bigger than gin , then the frequency that the probe gap increases in a probing is

| G+ | m = n n

(7)

Here n is the number of probe gaps, and n+1 is the number of probing packets. With (5) and (7), we set up the equation between the probability and the frequency that a probe gap increases: k

Lj

j =1

C × gin

Pctpa × ∑ Pj ×

According to Conditional Probability theory, we have: Ppgi

Lj

probability that a probe gap increases because of CT packet of kind j :

gin this way in subsection B)

1500 Byte C

CT2 as [ t4 −

CT2 is L j . Define the “delay area” of

=

m n

(8)

Make a simple transformation, we get k

Pctpa × ∑ Pj × L j j =1

g in

= C×

m n

(9)

978-1-4244-2324-8/08/$25.00 © 2008 IEEE. This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.

Fig. 2

section, we study when NBE is accurate and when NBE loses its accuracy. We use a simple NS-2 simulation to show the accuracy and limitation of NBE. The topology of the simulation is shown in Fig.2. Link capacity between R1 and R2 is set to 10Mb.

Simulation Topology

Capacity of other links is 100Mb. It is a single hop model, where the bottleneck is R1 , and C =10Mb. We use packet train of 1000 packets to probe the path from Ps to Pd. As explained in the last paragraph, we set input gap gin = 1.232 ms , L probe =40bytes . CT is from Cs to Cd . Fig. 3

Evaluation of NBE k

Clearly,

Pctpa × ∑ Pj × L j is the mean of the total CT j =1

traffic that arrives during a probe gap gin , so the left side of (9) is the average rate of CT in gin . The AB of the path can be computed with

m AB = C (1 − ) n

(10)

We call this inference methodology NBE. From the deduction process of NBE, we know that unlike other heuristic methods, NBE has rigid theory background. There is no other additional requests such as the cross traffic should be fluid in a probing gap. B. Input Probe Gap and Packet Size Now we discuss the choice of input probe gap probing packet size

L probe

gin and

L probe . Firstly, gin must satisfy

L . Otherwise, if we suppose C C L L gin = probe + (L0.02, the network path can be considered to be busy, and NBE will not be accurate.

m

A B = C × (1 −

i =1

+ i

− gB ) )

n

∑g

Traffic Type

Ibiblio UNC28 KSCY

Web Server access link University access link Internet2 backbone link

Average Load1 167Mbps 369Mbps 485Mbps

TABLE III. EER OF SPRUCE AND A_ABE (SINGLE HOP)

Trace

B. Adaptive Available Bandwidth Estimation As discussed above, NBE is just fit for the non busy network path, and we propose GS to weigh the busyness degree of network paths. As we all know, under the busy assumption, BE, i.e. (17), holds [8]. Intuitively speaking, when the path becomes busy, it is probable that probing pairs will fall in the same busy period, and we can use BE to estimate the AB.

∑ (g

Trace

EER of Spruce (%) EER of A_ABE (%)

Fig. 4

(17)

Ibibilo 18.4 3.7

UNC28 8.2 6.6

KSCY 7.6 7.1

single hop simulation (CT: Ibiblio)

in

i =1

gi+ is from (6). Although (17) has the same form as that in [8], the probing style is different from that of [8]. We now study how BE behaves with NBE’s lightweight probing style. In the same simulation setting II.D, we use (17) to estimate the CT load, the result is shown in row 3 of Table I. From table I, it is clear that when the network path is not busy, NBE is more accurate; otherwise, BE is more accurate. Combining the above discussion, we get the basic idea of the Adaptive Available Bandwidth Estimation (A_ABE): when the network path is not busy (GS