## Comparison Between Patermeters in Estimatin Available Bandwidth

```(1) probe stream length: 80/360
(2) valid excursions: 4/8
(3) gap threshold: 1000
(4) smoothing algorithm used after spike to spike averaging: arithmatic or exponential smoothing

```
To remove the impact of algorithms in actual experiments, we run rapid_v0.9.3 version from smithfd-rapid22 to smithfd-rapid21. Each set of experiment was run for five times.

### 1. Experiment 1: No Cross Traffic

#### (1) pstream length= 80

CDF of ABest for each experiment:

CDF of all ABests across the five experiments:

#### (2) pstream length= 360

CDF of all ABests across the five experiments:

### 2. Experiment 2: 500Mbps UDP CBR Cross Traffic

#### (1) pstream length= 80

CDF of ABest for each experiment:

CDF of all ABests across the five experiments:

#### (2) pstream length= 360

CDF of all ABests across the five experiments:

### Change spike to spike smoothing and ABest algorithms:

Spike to spike smoothing: a spike is defined as a burst followed by a series of small values of recvgaps until the next burst occurs. A burst at index i should satisfy: recvgap[i] > recvgap[i-1]+30us && recvgap[i] > recvgap[i+1]+20us. Record the total size of recvgaps and the number of pruned elements in the last spike of a pstream, and use these values to calculate the spike-smoothing recvgaps for the several small values in the beginning of the next pstream.

ABest algorithm: Find excursions the same way as before, but only count the last excursion as a valid excursion in the pstream.

#### (5) Some sample pstreams for probe stream size=80

W/O cross traffic:
```Pstream 3365:
spike averaging only: valid excursion=4 gap threshold= 1us abest= 426 actual ab= 1000
spike averaging only: valid excursion=8 gap threshold= 1us abest= 426 actual ab= 1000
spike+arithmatic averaging only: valid excursion=4 gap threshold= 1us abest= 426 actual ab= 1000
spike+arithmatic averaging only: valid excursion=8 gap threshold= 1us abest= 426 actual ab= 1000
spike+exponential averaging only: valid excursion=4 gap threshold= 1us abest= 426 actual ab= 1000
spike+exponential averaging only: valid excursion=8 gap threshold= 1us abest= 426 actual ab= 1000
```

```Pstream 3420:
spike averaging only: valid excursion=4 gap threshold= 1us abest= 923 actual ab= 1000
spike averaging only: valid excursion=8 gap threshold= 1us abest= 923 actual ab= 1000
spike+arithmatic averaging only: valid excursion=4 gap threshold= 1us abest= 1016 actual ab= 1000
spike+arithmatic averaging only: valid excursion=8 gap threshold= 1us abest= 1277 actual ab= 1000
spike+exponential averaging only: valid excursion=4 gap threshold= 1us abest= 1136 actual ab= 1000
spike+exponential averaging only: valid excursion=8 gap threshold= 1us abest= 1136 actual ab= 1000
```

With 500M CBR cross traffic
```Pstream 4277:
spike averaging only: valid excursion=4 gap threshold= 1us abest= 267 actual ab= around 480
spike averaging only: valid excursion=8 gap threshold= 1us abest= 267 actual ab= around 480
spike+arithmatic averaging only: valid excursion=4 gap threshold= 1us abest= 285 actual ab= around 480
spike+arithmatic averaging only: valid excursion=8 gap threshold= 1us abest= 285 actual ab= around 480
spike+exponential averaging only: valid excursion=4 gap threshold= 1us abest= 288 actual ab= around 480
spike+exponential averaging only: valid excursion=8 gap threshold= 1us abest= 288 actual ab= around 480
```

```Pstream 12777:
spike averaging only: valid excursion=4 gap threshold= 1us abest= 492 actual ab= around 480
spike averaging only: valid excursion=8 gap threshold= 1us abest= 606 actual ab= around 480
spike+arithmatic averaging only: valid excursion=4 gap threshold= 1us abest= 556 actual ab= around 480
spike+arithmatic averaging only: valid excursion=8 gap threshold= 1us abest= 557 actual ab= around 480
spike+exponential averaging only: valid excursion=4 gap threshold= 1us abest= 424 actual ab= around 480
spike+exponential averaging only: valid excursion=8 gap threshold= 1us abest= 484 actual ab= around 480
```

Nov 27: