[e2e] Throughput and delay in a theoretical model of network system

Detlef Bosau detlef.bosau at web.de
Wed Feb 25 05:20:45 PST 2009

CaiShun wrote:
> Hello, everyone
> I have a problem on the" throughput and delay " when view ing a
> network in a theoretical way, e.g. multi-commodity flow model, or
> Queueing Network(Stochastic Optimization) .
> Suppose a simple wirless network with 6 nodes. A traffic flow from
> node 1 to node 6, and the rate of each link is shown in the following Fig.

I'm sorry, but I cannot see anything but a checkerboard here...

> Intuitively, the throughput is 6 = 4+2. Although the last hop
> link(4,6) and link(5,6) can not be active simultaneously, the rate of
> the two links is much higher than link24,and link 35.
> But we observe that each node can not receive and transmit simultaneously.

Hm. To be honest, I have a fundamental problem with fluid flow models
and the like. I don't see a convincing way to build an anylitical,
typically _continous_, model for a packet switching network which is
really convincing. Although there is a huge amount of work in this area.

> So it takes 3 slots for a packet to travel from node 1 to node 6.
> Suppose at some slot 6 packets arrives at node 1, then the throughput
> is 6/3 = 2 packets per slot, right?
> I believe there's something wrong to define throughput and delay in
> the way above. But I am really getting confused . why most theoretical
> models concern on the throughput of the system without taking DEDLAY
> into account? Maybe it is about different layers -Network layer and
> MAC layer£¿

The fundamental relationship between delay, throughput and capacity is
given by Little's Law.

In a settled / stable system we have

average number of jobs in a system = average time a job spends in a
system * average birth rate

In computer networks, the birth rate is your throughput, the service
time is your delay and the average number of jobs in a system
- this is the congestion window in TCP ;-)

Detlef Bosau                          Mail:  detlef.bosau at web.de
Galileistrasse 30                     Web:   http://www.detlef-bosau.de
70565 Stuttgart                       Skype: detlef.bosau
Mobile: +49 172 681 9937

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