Computer Networks: Switching and Queuing Ivan Marsic Rutgers University Chapter 4 – Switching and Queuing Delay Models

Switching and Queuing Delay Models Chapter 4

Topic: Packet Switching in Routers  Router Architecture  Forwarding Table Lookup  Switching Fabric Design  How Queuing Happens

Why Routers? (Recall Chapter 1) Avoid needing direct link between all hosts (totally connected graph) Redundancy: If one path fails, find an alternative path

Routing Delays

Router Components

How Router Forwards Packets

Services to Incoming Packets Receiving and storing packets Forwarding decision for packets Moving packets from input to output port Transmission of packets

Distribution of Protocol Layers Note that router has a single (common) Network Layer protocol, but each connection has a dedicate Link Layer protocol

Forwarding Algorithms

Router Architectures First generation routerSecond generation router Third generation router

Switching via Memory / via Bus First generation router Second generation router

Crossbar Switch Fabric Input Output N x N switching elements allows N simultaneous packets switched (in the best case when all packets going to different outputs)

Goal: Reduce # Switching Elements System bus (in 1 st and 2 nd generation arch’s) allows only one packet switched at a time Crossbar allows up to N packets switched at a time Something in the middle? (+cheaper!)

Banyan Switch Fabric (a) (b) (c) 8x8 Banyan has only 12 switching elements (while 8x8 crossbar requires 64) But, much greater likelihood of collisions…

Reducing Collisions (Show slide with a collision example) Collisions can be reduced if packets are ordered on input ports by their output port number The router cannot choose the ordering of arriving packets, but we can insert a sorting hardware between the input network ports and the switching fabric …

Batcher Network (a) (b) (c)

Batcher-Banyan Network

Why Batcher-Banyan Network This figure is meant to illustrate why a concentrator is needed, because otherwise the gap in the input sequence will cause collision in the Banyan, but the example does not work for a 4x4 network -- need an 8x8 network example!!!!

Topic: Router Delays & Queuing Models  Where & Why Queuing Happens  Little’s Law  Queuing Models  M / M / 1, M / M / 1/ m, M / G / 1  Networks of Queues

Delay Components in Forwarding

Road Intersection Analogy Head of Line Blocking

Where & Why Queuing Happens At input ports, Head Of Line queuing At output ports, if output link is “too narrow” (low data rate) for incoming traffic Inside switch fabric, if collision occurred

An Input-queued Switch

General Service Model

Simple Queuing Model

Delay Time

Why Queuing Happens?

Arrival Sequences

Birth and Death Processes

Little’s Law Average number of packets in the system = arrival rate  average time that packet spends in the system N =  T Problem –We would like to know more, such as what are the probabilities of finding different number of customers on arrival, etc.

Intuition for the Balance Principle See: Global Balance Equations

Transition Probability Diagram

M/G/1 Example

Expected Residual Time