Side_1_360

increase over the critical limit resulting in a
degradation of the quality. This negative multi-
plexing effect will add on for each router along
the path from the sender to the receiver. How-
ever, for high capacity links this queuing delay
will be more or less negligible, leaving the main
delay contribution to low capacity links in the
access network.

One could hope that deploying the DiffServ
model with traffic classification and PHB prior-
ity scheduling would overcome this problem.
This is however not the case unless there is some
kind of fragmentation of the long IP packets on
lower layers. This means that although most of
the DiffServ implementations (in routers) have
implemented priority among different traffic
classes these priority mechanisms are all non-
preemptive. With this type of priority mecha-
nism a high priority packet cannot interrupt an
ongoing transmission of a packet of lower prior-
ity. This means that the packet length distribution
of the lower priority traffic classes will have an
impact on the delay for the high priority traffic.

The only way to get round the multiplexing
problem for low capacity links is to have some
kind of fragmentation of the long IP packet,
making it possible to interleave small real time
IP packets. By this option the maximum waiting
time due to lower priority traffic will just be the
transmission time for a single fragment. This
fragmentation will be possible if IP is trans-
ported over ATM, and in this case the maximum
disturbance of the high priority traffic due to
lower priority is limited to one ATM cell.

In the following we shall apply two queuing
models to get some quantitative experience with
the problems mentioned above. The first model,
without any kind of fragmentation of the IP
packets, is the classical M/G/1 non-preemptive
priority queuing model. The second queuing
model, which includes the possibility to frag-
ment the long IP packets is a non-preemptive
priority queuing model with batch arrivals. In
this model we segment the long IP packets into
a batch of shorter pieces, i.e. ATM cells. As a
reference model we choose the ordinary M/G/1
model. The derivation of the different perfor-
mance measures such as the waiting time distri-
bution etc. may be found in the literature and we
refer to the book of Takagi [Takagi 1991] for a
thorough treatment of the topic of priority queu-
ing models.

Below we consider a link with output buffer in

an IP network deploying DiffServ where we are

particularly interested in the delay of the EF traf-

fic class (high priority traffic). For simplicity we

consider a model with only two priority classes:

• The EF class which is taken to be the high
  priority traffic;


• All other traffic which we assumed to have
  lower (second) priority.

Further we make the following assumptions:

• Packets arrive according to Poisson processes.


• The link capacity is C(given in bits/sec).


• The packet lengths for the high priority class
  is either constant or exponentially distributed
  with mean PL 1 (given in bits).


• The packet lengths for the low priority class
  are exponentially distributed with mean PL 2
  (given in bits) and the length of a fragment
  is (constant) equal to FRL(given in bits).


• The load from the different traffic classes are
  ρ 1 and ρ 2 (where we assume ρ=ρ 1 + ρ 2 < 1).

With these definitions we get mean service times

for packets and the service time for a fragment

as:

, and

In the case where the high priority traffic is

exponentially distributed the Complementary

Distribution Functions (CDF) of the waiting

time for the highest priority traffic without any

fragmentation and with

fragmentation (of the

lower priority traffic) may be found to be:

W 1 c(t)=

ρ 1

1 −ρ 1

1 −ρ+

ρ 2

1 −μμ^12 ( 1 −ρ 1 )

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

e−μ^1 ()^1 −ρ^1 t

+

ρ 2

1 −ρ 1

1 −

ρ 1

1 −μμ^12 ( 1 −ρ 1 )

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟

e−μ^2 t

Wfc,1(t)=PW( f,1>t)

W 1 c(t)=PW( 1 >t)

bf=FRL

C

b 1 =μ 1 −^1 =PL^1

C

,b 2 =μ 2 −^1 =PL^2

C