<s>
In	O
telecommunication	O
and	O
computer	O
engineering	O
,	O
the	O
queuing	B-Protocol
delay	I-Protocol
or	O
queueing	B-Protocol
delay	I-Protocol
is	O
the	O
time	O
a	O
job	O
waits	O
in	O
a	O
queue	B-Application
until	O
it	O
can	O
be	O
executed	O
.	O
</s>
<s>
It	O
is	O
a	O
key	O
component	O
of	O
network	B-Protocol
delay	I-Protocol
.	O
</s>
<s>
In	O
a	O
switched	O
network	O
,	O
queuing	B-Protocol
delay	I-Protocol
is	O
the	O
time	O
between	O
the	O
completion	O
of	O
signaling	O
by	O
the	O
call	O
originator	O
and	O
the	O
arrival	O
of	O
a	O
ringing	O
signal	O
at	O
the	O
call	O
receiver	O
.	O
</s>
<s>
Queuing	B-Protocol
delay	I-Protocol
may	O
be	O
caused	O
by	O
delays	O
at	O
the	O
originating	O
switch	O
,	O
intermediate	O
switches	O
,	O
or	O
the	O
call	O
receiver	O
servicing	O
switch	O
.	O
</s>
<s>
In	O
a	O
data	O
network	O
,	O
queuing	B-Protocol
delay	I-Protocol
is	O
the	O
sum	O
of	O
the	O
delays	O
between	O
the	O
request	O
for	O
service	O
and	O
the	O
establishment	O
of	O
a	O
circuit	O
to	O
the	O
called	O
data	O
terminal	O
equipment	O
(	O
DTE	O
)	O
.	O
</s>
<s>
In	O
a	O
packet-switched	O
network	O
,	O
queuing	B-Protocol
delay	I-Protocol
is	O
the	O
sum	O
of	O
the	O
delays	O
encountered	O
by	O
a	O
packet	B-Protocol
between	O
the	O
time	O
of	O
insertion	O
into	O
the	O
network	O
and	O
the	O
time	O
of	O
delivery	O
to	O
the	O
address	O
.	O
</s>
<s>
This	O
term	O
is	O
most	O
often	O
used	O
in	O
reference	O
to	O
routers	B-Protocol
.	O
</s>
<s>
When	O
packets	B-Protocol
arrive	O
at	O
a	O
router	B-Protocol
,	O
they	O
have	O
to	O
be	O
processed	O
and	O
transmitted	O
.	O
</s>
<s>
A	O
router	B-Protocol
can	O
only	O
process	O
one	O
packet	B-Protocol
at	O
a	O
time	O
.	O
</s>
<s>
If	O
packets	B-Protocol
arrive	O
faster	O
than	O
the	O
router	B-Protocol
can	O
process	O
them	O
(	O
such	O
as	O
in	O
a	O
burst	O
transmission	O
)	O
the	O
router	B-Protocol
puts	O
them	O
into	O
the	O
queue	B-Application
(	O
also	O
called	O
the	O
buffer	B-General_Concept
)	O
until	O
it	O
can	O
get	O
around	O
to	O
transmitting	O
them	O
.	O
</s>
<s>
Delay	O
can	O
also	O
vary	O
from	O
packet	B-Protocol
to	O
packet	B-Protocol
so	O
averages	O
and	O
statistics	O
are	O
usually	O
generated	O
when	O
measuring	O
and	O
evaluating	O
queuing	B-Protocol
delay	I-Protocol
.	O
</s>
<s>
As	O
a	O
queue	B-Application
begins	O
to	O
fill	O
up	O
due	O
to	O
traffic	O
arriving	O
faster	O
than	O
it	O
can	O
be	O
processed	O
,	O
the	O
amount	O
of	O
delay	O
a	O
packet	B-Protocol
experiences	O
going	O
through	O
the	O
queue	B-Application
increases	O
.	O
</s>
<s>
The	O
speed	O
at	O
which	O
the	O
contents	O
of	O
a	O
queue	B-Application
can	O
be	O
processed	O
is	O
a	O
function	O
of	O
the	O
transmission	O
rate	O
of	O
the	O
facility	O
.	O
</s>
<s>
The	O
average	O
delay	O
any	O
given	O
packet	B-Protocol
is	O
likely	O
to	O
experience	O
is	O
given	O
by	O
the	O
formula	O
1/	O
(μ-	O
λ	O
)	O
where	O
μ	O
is	O
the	O
number	O
of	O
packets	B-Protocol
per	O
second	O
the	O
facility	O
can	O
sustain	O
and	O
λ	O
is	O
the	O
average	O
rate	O
at	O
which	O
packets	B-Protocol
are	O
arriving	O
to	O
be	O
serviced	O
.	O
</s>
<s>
This	O
formula	O
can	O
be	O
used	O
when	O
no	O
packets	B-Protocol
are	O
dropped	O
from	O
the	O
queue	B-Application
.	O
</s>
<s>
The	O
maximum	O
queuing	B-Protocol
delay	I-Protocol
is	O
proportional	O
to	O
buffer	B-General_Concept
size	O
.	O
</s>
<s>
The	O
longer	O
the	O
line	O
of	O
packets	B-Protocol
waiting	O
to	O
be	O
transmitted	O
,	O
the	O
longer	O
the	O
average	O
waiting	O
time	O
is	O
.	O
</s>
<s>
The	O
router	B-Protocol
queue	B-Application
of	O
packets	B-Protocol
waiting	O
to	O
be	O
sent	O
also	O
introduces	O
a	O
potential	O
cause	O
of	O
packet	B-Protocol
loss	I-Protocol
.	O
</s>
<s>
Since	O
the	O
router	B-Protocol
has	O
a	O
finite	O
amount	O
of	O
buffer	B-General_Concept
memory	O
to	O
hold	O
the	O
queue	B-Application
,	O
a	O
router	B-Protocol
which	O
receives	O
packets	B-Protocol
at	O
too	O
high	O
a	O
rate	O
may	O
experience	O
a	O
full	O
queue	B-Application
.	O
</s>
<s>
In	O
this	O
case	O
,	O
the	O
router	B-Protocol
has	O
no	O
other	O
option	O
than	O
to	O
simply	O
discard	O
excess	O
packets	B-Protocol
.	O
</s>
<s>
When	O
the	O
transmission	O
protocol	O
uses	O
the	O
dropped-packets	O
symptom	O
of	O
filled	O
buffers	B-General_Concept
to	O
regulate	O
its	O
transmit	O
rate	O
,	O
as	O
the	O
Internet	O
's	O
TCP	O
does	O
,	O
bandwidth	O
is	O
fairly	O
shared	O
at	O
near	O
theoretical	O
capacity	O
with	O
minimal	O
network	B-Protocol
congestion	I-Protocol
delays	O
.	O
</s>
<s>
Absent	O
this	O
feedback	O
mechanism	O
the	O
delays	O
become	O
both	O
unpredictable	O
and	O
rise	O
sharply	O
,	O
a	O
symptom	O
also	O
seen	O
as	O
freeways	O
approach	O
capacity	O
;	O
metered	O
onramps	O
are	O
the	O
most	O
effective	O
solution	O
there	O
,	O
just	O
as	O
TCP	O
's	O
self-regulation	O
is	O
the	O
most	O
effective	O
solution	O
when	O
the	O
traffic	O
is	O
packets	B-Protocol
instead	O
of	O
cars	O
)	O
.	O
</s>
<s>
Failing	O
to	O
drop	O
packets	B-Protocol
,	O
choosing	O
instead	O
to	O
buffer	B-General_Concept
an	O
ever-increasing	O
number	O
of	O
them	O
,	O
produces	O
bufferbloat	O
.	O
</s>
<s>
In	O
Kendall	O
's	O
notation	O
,	O
the	O
M/M/1/K	O
queuing	O
model	O
,	O
where	O
K	O
is	O
the	O
size	O
of	O
the	O
buffer	B-General_Concept
,	O
may	O
be	O
used	O
to	O
analyze	O
the	O
queuing	B-Protocol
delay	I-Protocol
in	O
a	O
specific	O
system	O
.	O
</s>
<s>
Kendall	O
's	O
notation	O
should	O
be	O
used	O
to	O
calculate	O
the	O
queuing	B-Protocol
delay	I-Protocol
when	O
packets	B-Protocol
are	O
dropped	O
from	O
the	O
queue	B-Application
.	O
</s>
