Performance Analysis of Non-stationary Peer-assisted VoD Systems - - PowerPoint PPT Presentation

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Performance Analysis of Non-stationary Peer-assisted VoD Systems - - PowerPoint PPT Presentation

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Performance Analysis of Non-stationary Peer-assisted VoD Systems Delia Ciullo 1 , Valentina Martina 1 , Michele Garetto 2 , Emilio Leonardi 1 , Gianluca Torrisi 3 1 Politecnico di Torino 2 Universit` a di Torino 3 CNR - Instituto per le

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Performance Analysis of Non-stationary Peer-assisted VoD Systems

Delia Ciullo1, Valentina Martina1, Michele Garetto2, Emilio Leonardi1, Gianluca Torrisi3

1Politecnico di Torino 2Universit`

a di Torino

3CNR - Instituto per le Applicazioni di Calcolo

March 26-th, 2012

  • E. Leonardi

Performance of P2P-VOD systems

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Introduction

In peer-assisted Video-on-Demand (VoD) systems:

  • E. Leonardi

Performance of P2P-VOD systems

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Introduction

In peer-assisted Video-on-Demand (VoD) systems: users browse a catalog of available videos and asynchronously issue requests to watch a given content;

  • E. Leonardi

Performance of P2P-VOD systems

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Introduction

In peer-assisted Video-on-Demand (VoD) systems: users browse a catalog of available videos and asynchronously issue requests to watch a given content; content is divided into chunks that can be retrieved either from

  • E. Leonardi

Performance of P2P-VOD systems

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SLIDE 5

Introduction

In peer-assisted Video-on-Demand (VoD) systems: users browse a catalog of available videos and asynchronously issue requests to watch a given content; content is divided into chunks that can be retrieved either from

the servers

  • E. Leonardi

Performance of P2P-VOD systems

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SLIDE 6

Introduction

In peer-assisted Video-on-Demand (VoD) systems: users browse a catalog of available videos and asynchronously issue requests to watch a given content; content is divided into chunks that can be retrieved either from

the servers

  • ther peers currently retrieving the same video (leechers)
  • E. Leonardi

Performance of P2P-VOD systems

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SLIDE 7

Introduction

In peer-assisted Video-on-Demand (VoD) systems: users browse a catalog of available videos and asynchronously issue requests to watch a given content; content is divided into chunks that can be retrieved either from

the servers

  • ther peers currently retrieving the same video (leechers)

peers storing the whole video (seeds);

  • E. Leonardi

Performance of P2P-VOD systems

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SLIDE 8

Introduction

In peer-assisted Video-on-Demand (VoD) systems: users browse a catalog of available videos and asynchronously issue requests to watch a given content; content is divided into chunks that can be retrieved either from

the servers

  • ther peers currently retrieving the same video (leechers)

peers storing the whole video (seeds);

chunks must be retrieved by peers almost in sequence to guarantee small play-out delays;

  • E. Leonardi

Performance of P2P-VOD systems

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Introduction

In peer-assisted Video-on-Demand (VoD) systems: users browse a catalog of available videos and asynchronously issue requests to watch a given content; content is divided into chunks that can be retrieved either from

the servers

  • ther peers currently retrieving the same video (leechers)

peers storing the whole video (seeds);

chunks must be retrieved by peers almost in sequence to guarantee small play-out delays; a minimum average download rate equal to the video playback rate must be sustained to guarantee service continuity; the system (exploiting servers bandwidth when needed) is able to steadily meet this constraint.

  • E. Leonardi

Performance of P2P-VOD systems

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Assumptions

  • E. Leonardi

Performance of P2P-VOD systems

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Assumptions

Video is downloaded by each user at constant rate d, greater or equal to the playback rate dv;

  • E. Leonardi

Performance of P2P-VOD systems

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Assumptions

Video is downloaded by each user at constant rate d, greater or equal to the playback rate dv; upload available bandwidth Ui of peer i is a random variable with a assigned distribution (Ui are i.i.d.);

  • E. Leonardi

Performance of P2P-VOD systems

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Assumptions

Video is downloaded by each user at constant rate d, greater or equal to the playback rate dv; upload available bandwidth Ui of peer i is a random variable with a assigned distribution (Ui are i.i.d.); users contribute their upload bandwidth to the video distribution as long as they are in the system;

  • E. Leonardi

Performance of P2P-VOD systems

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Assumptions

Video is downloaded by each user at constant rate d, greater or equal to the playback rate dv; upload available bandwidth Ui of peer i is a random variable with a assigned distribution (Ui are i.i.d.); users contribute their upload bandwidth to the video distribution as long as they are in the system; the arrival process of requests (and users) for a video is a (possibly non-homogeneous) Poisson process with intensity λ(t);

  • E. Leonardi

Performance of P2P-VOD systems

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Assumptions

Video is downloaded by each user at constant rate d, greater or equal to the playback rate dv; upload available bandwidth Ui of peer i is a random variable with a assigned distribution (Ui are i.i.d.); users contribute their upload bandwidth to the video distribution as long as they are in the system; the arrival process of requests (and users) for a video is a (possibly non-homogeneous) Poisson process with intensity λ(t); user’s sojourn time is described by an arbitrary random variable T with finite mean T and complementary cumulative distribution function GT(x).

  • E. Leonardi

Performance of P2P-VOD systems

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Preliminary Observations

The number of active users N(t) follows a Poisson distribution with mean N(t) = ∞ λ(t − x)GT(x) dx;

  • E. Leonardi

Performance of P2P-VOD systems

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Preliminary Observations

The number of active users N(t) follows a Poisson distribution with mean N(t) = ∞ λ(t − x)GT(x) dx; τd = L/d is the time needed to download the whole video, and T d = τd

0 GT(x)dx is the average time spent by peers downloading

the video, taking into account premature abandonments;

  • E. Leonardi

Performance of P2P-VOD systems

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Preliminary Observations

The number of active users N(t) follows a Poisson distribution with mean N(t) = ∞ λ(t − x)GT(x) dx; τd = L/d is the time needed to download the whole video, and T d = τd

0 GT(x)dx is the average time spent by peers downloading

the video, taking into account premature abandonments; Nd(t) is the number of downloading users with mean Nd(t) = τd

0 λ(t − x)GT(x) dx, and Nseed(t) the number of seeds

with mean Nseed(t) = N(t) − Nd(t);

  • E. Leonardi

Performance of P2P-VOD systems

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Preliminary Observations

The number of active users N(t) follows a Poisson distribution with mean N(t) = ∞ λ(t − x)GT(x) dx; τd = L/d is the time needed to download the whole video, and T d = τd

0 GT(x)dx is the average time spent by peers downloading

the video, taking into account premature abandonments; Nd(t) is the number of downloading users with mean Nd(t) = τd

0 λ(t − x)GT(x) dx, and Nseed(t) the number of seeds

with mean Nseed(t) = N(t) − Nd(t); we define the average system load as: γ = dT d U T .

  • E. Leonardi

Performance of P2P-VOD systems

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Goal

Our goal is:

[1] D.Ciullo, V.Martina, M.Garetto, E.Leonardi, G.L.Torrisi, “Stochastic Analysis of Self-Sustainability in Peer-Assisted VoD Systems”, Session TS05, Thursday, h. 8.30-10.00

  • E. Leonardi

Performance of P2P-VOD systems

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Goal

Our goal is: to characterize the bandwidth requested from the servers S (and its average S);

[1] D.Ciullo, V.Martina, M.Garetto, E.Leonardi, G.L.Torrisi, “Stochastic Analysis of Self-Sustainability in Peer-Assisted VoD Systems”, Session TS05, Thursday, h. 8.30-10.00

  • E. Leonardi

Performance of P2P-VOD systems

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Goal

Our goal is: to characterize the bandwidth requested from the servers S (and its average S);

we develop an approximate efficient and accurate fluid model to compute S;

[1] D.Ciullo, V.Martina, M.Garetto, E.Leonardi, G.L.Torrisi, “Stochastic Analysis of Self-Sustainability in Peer-Assisted VoD Systems”, Session TS05, Thursday, h. 8.30-10.00

  • E. Leonardi

Performance of P2P-VOD systems

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Goal

Our goal is: to characterize the bandwidth requested from the servers S (and its average S);

we develop an approximate efficient and accurate fluid model to compute S;

  • ur approach is able to capture several stochastic effects related to

peer churn, upload bandwidth heterogeneity, non-stationary traffic conditions;

[1] D.Ciullo, V.Martina, M.Garetto, E.Leonardi, G.L.Torrisi, “Stochastic Analysis of Self-Sustainability in Peer-Assisted VoD Systems”, Session TS05, Thursday, h. 8.30-10.00

  • E. Leonardi

Performance of P2P-VOD systems

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SLIDE 24

Goal

Our goal is: to characterize the bandwidth requested from the servers S (and its average S);

we develop an approximate efficient and accurate fluid model to compute S;

  • ur approach is able to capture several stochastic effects related to

peer churn, upload bandwidth heterogeneity, non-stationary traffic conditions;

  • ur methodology can be exploited to design efficient peer-assisted VoD

systems and optimal resource allocation strategies.

[1] D.Ciullo, V.Martina, M.Garetto, E.Leonardi, G.L.Torrisi, “Stochastic Analysis of Self-Sustainability in Peer-Assisted VoD Systems”, Session TS05, Thursday, h. 8.30-10.00

  • E. Leonardi

Performance of P2P-VOD systems

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Goal

Our goal is: to characterize the bandwidth requested from the servers S (and its average S);

we develop an approximate efficient and accurate fluid model to compute S;

  • ur approach is able to capture several stochastic effects related to

peer churn, upload bandwidth heterogeneity, non-stationary traffic conditions;

  • ur methodology can be exploited to design efficient peer-assisted VoD

systems and optimal resource allocation strategies.

In [1] we obtain rigorous bounds for the sequential delivery scheme and asymptotic results as the number of users increases.

[1] D.Ciullo, V.Martina, M.Garetto, E.Leonardi, G.L.Torrisi, “Stochastic Analysis of Self-Sustainability in Peer-Assisted VoD Systems”, Session TS05, Thursday, h. 8.30-10.00

  • E. Leonardi

Performance of P2P-VOD systems

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A simple Lower Bound

A simple universal lower bound to S(t) for any chunk distribution scheme is S(t) ≤ max{0, dNd(t) − U N(t)}. Intuition: The additional server bandwidth is given by users requested bandwidth minus their total upload bandwidth.

Note that this trivial lower bound was already shown in: C. Huang, J. Li, and K. W. Ross, Can Internet Video-on-Demand Be Profitable? in ACM SIGCOMM, 2007.

  • E. Leonardi

Performance of P2P-VOD systems

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Analysis

  • E. Leonardi

Performance of P2P-VOD systems

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Analysis

Let Sd be the aggregate bandwidth requested by the downloading users. The aggregate upload bandwidth offered by the seeds is Sseed =

Nseed

  • i=1

Ui.

  • E. Leonardi

Performance of P2P-VOD systems

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Analysis

Let Sd be the aggregate bandwidth requested by the downloading users. The aggregate upload bandwidth offered by the seeds is Sseed =

Nseed

  • i=1

Ui. The bandwidth requested from the servers is: S max{0, Sd − Sseed} where Sd is the bandwidth demanded by downloading peers.

  • E. Leonardi

Performance of P2P-VOD systems

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Analysis(2)

We define Sd(k) (Sd(t) | Nd(t) = k)

  • E. Leonardi

Performance of P2P-VOD systems

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Analysis(2)

We define Sd(k) (Sd(t) | Nd(t) = k) Theorem Sd(k) satisfies the following recursive equation: Sd(k) = d k = 1 d + max{0, Sd(k − 1) − Uk} k > 1

  • E. Leonardi

Performance of P2P-VOD systems

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Analysis(3)

  • E. Leonardi

Performance of P2P-VOD systems

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Analysis(3)

We characterize the distribution of the server bandwidth using a second-order approximation;

  • E. Leonardi

Performance of P2P-VOD systems

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Analysis(3)

We characterize the distribution of the server bandwidth using a second-order approximation; we approximate the distribution of the quantity Sd(k − 1) − Uk (for each k ≥ 2) with a normal distribution matching the first two moments of this quantity;

  • E. Leonardi

Performance of P2P-VOD systems

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Analysis(3)

We characterize the distribution of the server bandwidth using a second-order approximation; we approximate the distribution of the quantity Sd(k − 1) − Uk (for each k ≥ 2) with a normal distribution matching the first two moments of this quantity; we apply standard formulas of the truncated normal distribution to derive the first two moments of Sd(k) as a function of the first two moments of Sd(k − 1);

  • E. Leonardi

Performance of P2P-VOD systems

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Analysis(3)

We characterize the distribution of the server bandwidth using a second-order approximation; we approximate the distribution of the quantity Sd(k − 1) − Uk (for each k ≥ 2) with a normal distribution matching the first two moments of this quantity; we apply standard formulas of the truncated normal distribution to derive the first two moments of Sd(k) as a function of the first two moments of Sd(k − 1); a similar approximation is subsequently applied to take into account the effect of the seeds.

  • E. Leonardi

Performance of P2P-VOD systems

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Swarm size effect

d = dv = 1, T = T d = τd

0.1 1 10 100 1 10 100 1000 Average server bandwidth Average number of users approx - U = 0.9 sim - U = 0.9 sim lower bound - U = 0.9

  • E. Leonardi

Performance of P2P-VOD systems

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Swarm size effect

d = dv = 1, T = T d = τd

0.1 1 10 100 1 10 100 1000 Average server bandwidth Average number of users approx - U = 1.2 sim - U = 1.2 sim lower bound - U = 1.2

  • E. Leonardi

Performance of P2P-VOD systems

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Download rate impact

U = 1.2, dv = 1, T = T d = τd

0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 1 1.2 1.4 1.6 1.8 2 2.2 download rate, d sim approx sim lower bound

  • E. Leonardi

Performance of P2P-VOD systems

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Extension to non sequential download

  • E. Leonardi

Performance of P2P-VOD systems

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Extension to non sequential download

A common approach in P2P-VoD is to allow users to receive also

  • ut-of-sequence chunks of the video within a limited sliding window
  • f data starting from the point currently played;
  • E. Leonardi

Performance of P2P-VOD systems

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Extension to non sequential download

A common approach in P2P-VoD is to allow users to receive also

  • ut-of-sequence chunks of the video within a limited sliding window
  • f data starting from the point currently played;

for simplicity, instead of considering an actual sliding window, we divide the video into a fixed number W of non-overlapping segments

  • f size LW = L/W ;
  • E. Leonardi

Performance of P2P-VOD systems

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Extension to non sequential download

A common approach in P2P-VoD is to allow users to receive also

  • ut-of-sequence chunks of the video within a limited sliding window
  • f data starting from the point currently played;

for simplicity, instead of considering an actual sliding window, we divide the video into a fixed number W of non-overlapping segments

  • f size LW = L/W ;

we assume that, within a segment, chunk based out-of-sequence distribution can be exploited, and we extend our approximate model to deal with partially non-sequential chunk delivery.

  • E. Leonardi

Performance of P2P-VOD systems

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Impact of non-sequential delivery

1 2 3 4 5 6 0 10 20 30 40 50 60 70 80 90 100 Average server bandwidth Average number of users sim - sequential sim - W = 32 sim - W = 16 sim - W = 8 sim - W = 4 sim - W = 2 sim - lower bound 1 2 3 4 5 6 10 20 30 40 50 60 70 80 90 100 Average number of users approx - sequential approx - W = 32 approx - W = 16 approx - W = 8 approx - W = 4 approx - W = 2 approx - W = 1

  • E. Leonardi

Performance of P2P-VOD systems

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Impact of non stationarity

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 12 18 24 6 12 18 24 6 200 400 600 800 1000 1200 video request rate, λ(t) number of downloaders / seeds λ downloaders seeds

10 20 30 40 50 60 70 12 18 24 6 12 18 24 6 average server bandwidth time of day (hours) sim - trace approx approx - λ = 1

  • E. Leonardi

Performance of P2P-VOD systems

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Conclusions

We have proposed a computationally-efficient methodology to estimate the server bandwidth requested in non-stationary P2P-VoD systems;

  • E. Leonardi

Performance of P2P-VOD systems

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Conclusions

We have proposed a computationally-efficient methodology to estimate the server bandwidth requested in non-stationary P2P-VoD systems; we have discovered several interesting properties:

the server bandwidth can be minimized by a proper selection of the download rate;

  • E. Leonardi

Performance of P2P-VOD systems

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SLIDE 48

Conclusions

We have proposed a computationally-efficient methodology to estimate the server bandwidth requested in non-stationary P2P-VoD systems; we have discovered several interesting properties:

the server bandwidth can be minimized by a proper selection of the download rate; the server bandwidth increases with the variation coefficient of the peer upload bandwidth;

  • E. Leonardi

Performance of P2P-VOD systems

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Conclusions

We have proposed a computationally-efficient methodology to estimate the server bandwidth requested in non-stationary P2P-VoD systems; we have discovered several interesting properties:

the server bandwidth can be minimized by a proper selection of the download rate; the server bandwidth increases with the variation coefficient of the peer upload bandwidth; the gain achievable by non-sequential schemes over the simple sequential scheme depends critically on the size of the sliding window and the number of downloading users;

  • E. Leonardi

Performance of P2P-VOD systems

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Conclusions

We have proposed a computationally-efficient methodology to estimate the server bandwidth requested in non-stationary P2P-VoD systems; we have discovered several interesting properties:

the server bandwidth can be minimized by a proper selection of the download rate; the server bandwidth increases with the variation coefficient of the peer upload bandwidth; the gain achievable by non-sequential schemes over the simple sequential scheme depends critically on the size of the sliding window and the number of downloading users; non-stationary systems are affected by a misalignment problem between downloaders and seeds.

  • E. Leonardi

Performance of P2P-VOD systems

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Thank you!

  • E. Leonardi

Performance of P2P-VOD systems