Flow Networking in Grid Simulations - Grid Computing: Infrastructure, Service, and Applications - page 381

More generally, a l ow f with a source u and destination v that is not
directly connected has an expected duration of

f

SIZE

Â

T = LAT +

(15.2)

f u v ,

f

min BW

(, uv ¢¢ ) Œ f

where min BW f is the smallest bandwidth available on any edge on the path
f between u and v (i.e., the bottleneck link), and latency LAT f =  ( u',v' )Œ f LAT u,v
is the sum of the latency of all edges ( u ¢, v ¢) that connec t the source u to the
destination v .
We note that the above equations and discussions are only valid for a
single active l ow at a time, as it does not account for any bandwidth shar-
ing between multiple l ows on common (overlapping) links. Where mul-
tiple l ows are active over links, then min BW f is the smallest bandwidth
allocated by edge (based on some bandwidth sharing model) on the
path f between u and v. The implications of this will be discussed in the
following section.

15.5 Bandwidth Sharing Models
Earlier, we examined a simple theoretical model to compute the duration
of each l ow i n a system based on t he bot t lenec k ba ndw idt h. T h i s approac h
signii cantly improves the speed of grid simulations by avoiding the need
to packetize large network transfers, instead of taking a macro or l uid
view of network trafi c in a given topology.
In order for this approach to be effective we need to calculate the appro-
priate bandwidth given to l ows on each segment of their respective route.
More importantly, we must model how the bandwidth is shared when
many l ows are active over one or many links. As a proof of concept for the
GridSim l ow networking implementation, we have implemented simple
MIN-MAX bandwidth fair sharing, where each l ow that shares a link is
allocated an equal portion of the bandwidth. That is, an edge ( u , v ) with
available bandwidth BW u , v that has n active l ows will allocate each l ow
( BW u,v / n ) bandwidth. While it has been found that other bandwidth shar-
ing models are closer to actual TCP/IP behavior [10], MIN-MAX band-
width sharing is a useful candidate model with minimal state to track in
the implementation.
We intend to include other bandwidth sharing models that more
closely approximate TCP/IP in the near future, such as proportional
bandwidth sharing that considers latency, round-trip times, and class-
based priorities [11,12].