An Analytical Study of Low Delay Multi-tree-based Overlay Multicast György Dán and Viktória Fodor School of Electrical Engineering KTH, Royal Institute of Technology Stockholm, Sweden Peer-to-Peer Streaming and IP-TV Workshop

Motivation Live peer-to-peer streaming Many proposed systems Push-based vs. Pull-based Tree-based vs. mesh-based vs. unstructured Multi-hop data delivery Failures – node departures, packet losses Delivery time hard to predict Playback delay and playout buffer dimensioning

Does playback delay matter? Designers goal: Control the playback delay (minimize?) Our goal: Identify sources of delay

A packets eye view of the overlay Four components of delay: D d =D p +D tr,o +D pr +D tr,i (a: pkt size, C in : input bandwidth, C out : output bandwidth) R A spanning tree of the overlay traversed by a packet D pr D tr,i =W in +a/C in DpDp D tr,o =W out +a/C out DdDd Tree properties depend on Tree-based: Overlay maintenance Unstructured: Scheduling algorithm

One-hop propagation model Possession-propagation-reception DdDd 1 1 Layer l-1 Layer l h Possession probability h Per-hop delay Reception probability h

One-hop propagation model Possession-propagation-reception DdDd h 1 h 1 Layer l-1 Layer l h Possession probability Per-hop delay Reception probability

Multi-hop propagation model Without FEC Apply the one hop model to every layer Result is the convolution of the per-hop delays R With FEC Apply the one hop model to every layer Calculate the result iteratively

Multi-hop propagation model Probability of reception by time h in layer l for packet j Probability of possession by time h in layer l for packet j Source node – initial condition Numerical solution Converges Scalable A control theoretic interpretation: Dynamical system with Input signal Output signals

Multi-hop propagation model Probability of possession with playback delay b (playout deadline of packet j: h j =b+(j1)a/B) Probability of possession for arbitrary node and packet Inputs of the model Initial condition N l number of nodes in layer l F d (h) node-to-node delay distribution - Source playout strategy - Overlay structure - Scheduling, structure

Application – Multi-tree overlay Source and N nodes Source capacity > m*B t trees, each node forwards in d trees Retransmissions and FEC(n,k) for error control Packets sent at round-robin from the source R R R Tree 2Tree 3Tree 1 P1 P2 P3 h 1 j=1j=2j=3 Initial condition

Overlay structure Number of nodes per layer (N l ) Calculated recursively based on Node output capacity distribution Prioritization scheme Capacity allocation scheme Prioritization schemes Contribution based Contributors prioritized over non-contributors (NP) Priority proportional to potential contribution (P) Capacity allocation schemes In case of excess capacity Proportional contribution (MM) Non-proportional contribution (FU)

Node-to-node Delay Input link D tr,i =W in +a/C in W in waiting time of a packet in a G/D/1 queue Output link D tr,o =W out +uIdat/( r B), whereI [1, r /d] d.r.v W out waiting time as seen by an arriving batch of r /d packets in a GI X /D/1 queue Retransmissions Loss detection, etc Arrival processes What is a realistic model? h

Model validation Discrete event driven simulator Steady state Media server on a 10Mbps-20Mbps link (m=50) Low bitrate media, B=112kbps Nodes buffer 15s worth of packets Input and output capacity constraints Propagation delays Random network topology – GT-ITM Node churn for randomness Results shown for packet losses

Deterministic arrival process Inf.cap. C in = C out = 10 Mbps Inf.incap. C in =10 Mbps C out =128 kbps Fin.cap. C in = C out = 128kbps Number of trees influences the delay – is there an optimal number? D pr plays a minor role – but increasing importance N=10 4,p=0.1

Poisson arrival process Inf.cap. C in =C out =10Mbps Inf.incap. C in =10Mbps C out =128kbps Fin.cap. C in =C out =128kbps Queuing delay significant Decrease utilization N=10 4,p=0.1

Simulation Inf.incap. C in =10 Mbps C out =128 kbps Fin.cap. C in =C out =128 kbps Similar to deterministic arrival process N=10 4,p=0.1

FEC and retransmissions Dynamically adjust playback delay FEC cannot achieve (b)=1 But FEC can help to keep the playback delay low Scalability?

Capacity allocation and prioritization Scen.ShareC out [kbps] CH100%256 CI 65%128 35%512 Prioritization and uneven capacity allocation best: increases the average output capacity of the contributing nodes Inhomogeneous upload capacity can help to achieve better performance Capacity allocation MM: proportional FU: non-proportional Prioritization NP: contributor/non- contributor P: proportional to contribution FU+P MM+P N=10 4

Conclusion Main factors that determine the delay Average upload capacity of contributing nodes Waiting times in queues at the nodes The ways to decrease the end-to-end delay are decreasing the number of layers (by prioritization), FU allocation, and by increasing m as much as possible – no fairness... using an adequate number of trees (though using a few trees only might imperil the stability of the overlay for given n, k, p) dynamically adjusting the FEC redundancy using a bitrate not too close to E[C out ]

Open questions Application to pull-based systems Modeling tree structure and delay distributions Scalability in terms of delay Optimal chunk size and out-degree Easy to control in multi-tree-based overlays (?) How to control in a pull based overlay?

An Analytical Study of Low Delay Multi-tree-based Overlay Multicast György Dán and Viktória Fodor School of Electrical Engineering KTH, Royal Institute of Technology Stockholm, Sweden Peer-to-Peer Streaming and IP-TV Workshop