Effective bandwidth with link pipelining Pipeline the flight and transmission of packets over the links Overlap the sending overhead with the transport latency and receiving overhead of prior packets Sending overhead Transport latency time overlap Receiving overhead

Injection bandwidth Network injection Reception bandwidth Network reception Aggregate bandwidth Characterizing Performance : Effective Bandwidth Eff. bandwidth = min (BW NetworkInjection, BW NetworkReception ) = min (NxBW LinkInjection, NxBW LinkReception ) = min (2xBW LinkInjection, 2xBW LinkReception )

BW LinkInjection = Packet size max (sending overhead, transmission time) BW LinkReception = Packet size max (receiving overhead, transmission time) Eff. bandwidth = min (NxBW LinkInjection, NxBW LinkReception ) = N x Packet size max (overhead, transmission time) overhead = max (sending overhead, receiving overhead)

Characterizing Performance: Effective Bandwidth A Simple (General) Throughput Performance Model: The network can be considered as a “pipe” of variable width There are three points of interest end-to-end: –Injection into the pipe –Narrowest section within pipe (i.e., minimum network bisection that has traffic crossing it) –Reception from the pipe Injection bandwidth Bisection bandwidth Reception bandwidth

Effective bandwidth = min(BW NetworkInjection, BW Network, σ × BW NetworkReception ) = min(N × BW LinkInjection, BW Network, σ × N × BW LinkReception ) BW Network = ρ × BW Bisection 

BW Network = ρ × BW Bisection × 8/3 Characterizing Performance: Effective Bandwidth Injection bandwidth Network injection Reception bandwidth Network reception Aggregate bandwidth unidirectional ring greedy traffic: node i sends to node i + 3 mod N Bisection Bandwidth   = 3/8

Simple (General) Model Applied to Interconnecting Two Devices: Effective bandwidth = min(2 × BW LinkInjection, BW Network, 1 × (2 × BW LinkReception )) BW Network =  L × 2 × BW Link 1 Dedicated-link network int. network Device A Device B  L = link efficiency resulting from flow control, encoding, packet header and trailer overheads BW Link

2D torus of 16 nodes hypercube of 16 nodes (16 = 2 4, so n = 4) 2D mesh or grid of 16 nodes Network Bisection

An NoC architecture can be uniquely described by the triple Arch(T(R,Ch), P R, Ω(C)), where, 1.The labeled graph T(R,Ch) represents the network topology. The routers and channels in the network are given by the sets R and Ch, respectively 2.{P R (r, i, j)|i, j, r ∈ R} defines the routing policy P R at router r, for any source router i and destination router j, while considering a particular switching technique. 3.Ω : C → R is a function that maps each vertex c i ∈ C in the APCG to a router in R. Network-on-Chip

On-chip-network building block Topology  The on-chip-network topology determines the physical layout and connection between nodes and channel in the network.  Metrics for comparing topology  Degree  Hop Count  Maximum channel node  Path Diversity

Example:

Routing  The routing algorithm is used to decide what path a message will take through the network to reach its destination.  Types of routing algorithm  Deterministic routing algorithm  Oblivious routing algorithm  Adaptive routing algorithm

Deterministic routing algorithm m i = d i − s i mod k Δ i = m i – 0 if m i ≤ k/2 otherwise m i - k This can then be used to compute our preferred directions: D T,i = 0 if |Δ i | = k/2 otherwise sign(Δ i ) Deterministic routing algorithm send every packet from source x to destination y over exactly the same route.

Oblivious routing algorithm Oblivious routing, in which we route packets without regard for the state of the network, is simple to implement and simple to analyze. Intermediate node

Minimal Quadrant Possible routes

Adaptive routing algorithm An adaptive routing algorithm uses information about the network state, typically queue occupancies, to select among alternative paths to deliver a packet. Partial Adaptive routing algorithm

a. Fully Adaptive routing algorithm b. Deadlock condition