icy of an algorithm is the procedure to follow at flow
admission, whereas the role of the estimator is to sup-
ply the information required for the admission deci-
sion based on measurements.
2.1 Policy Algorithms
The measured sum algorithm (MS) uses measurement
to estimate the load of existing traffic. Let µ be the
link bandwidth, α the new flow requesting admission,
and r
α
the rate requested by flow α. The new flow is
admitted if the following test succeeds:
ˆ
ν+ r
α
< cµ (1)
where c is a user-defined utilization target and
0 < c < 1. The measured load of existing traffic is
denoted with
ˆ
ν. Upon admission of a new flow, the
load estimate is increased using:
ˆ
ν
′
=
ˆ
ν+ r
α
(2)
A measurement-based approach is doomed to fail
at very high utilization when delay violations become
exceedingly large. It is thus necessary to identify a
utilization target and require that the algorithm strives
to keep link utilization below this level.
The acceptance region algorithms compute an ac-
ceptance region that maximizes the reward of utiliza-
tion against the penalty of packet loss. These algo-
rithms are based on Chernoff bounds. Given link
bandwidth, switch buffer space, a flow’s token bucket
filter parameters, the flow’s burstiness, and desired
probability of actual load exceeding bound, an accep-
tance region can be computed for a specific set of flow
types, beyond which no more flow of those particular
types should be accepted.
Based on different combinations of measured and
declared parameters, four related techniques based
upon Chernoff bounds are presented in (Gibbens and
F.P.Kelly, 1997). The availability and ease of mea-
surement extractions (e.g., per-flow vs. aggregate)
and the need for a priori traffic declarations (e.g., av-
erage rate as well as peak rate) will each affect the
relative practicability of the four approaches, namely:
tangent at peak (ACTP), tangent at arbitrary location,
tangent at slope one, tangent at origin (ACTO). Table
1 illustrates basic features of these four algorithms.
For a better overview let us illustrate the compu-
tation of the effective bandwidth requirement of the
traffic aggregate (all classes added together) for the
tangent at slope one algorithm:
ˆ
ν = X +
C
4
K−1
∑
k=0
p
2
k
n
k
(3)
where,
ˆ
ν is the estimate for traffic load, K is the
number of different flow types, n
k
is the number of
Table 1: Characteristics of acceptance region schemes.
Acceptance region Measurement Per-class
scheme declaration
Tangent at peak Per-class Peak rate
measurements
Number of connections
per class
Tangent at Per-class Peak rate,
arbitrary location measurements
Number of connections Average rate
per class
Tangent at Aggregate (line) Peak rate
slope one measurements
Tangent at origin Aggregate (line) Peak rate
Tangent at origin measurements
individual flows of a particular type, p
k
represents the
peak-rate for a particular flow type, X is the measured
aggregate utilization, andC is a scaling factor. For ad-
mission decision this estimated aggregate load should
be smaller or equal to link capacity µ.
The Hoeffding bounds scheme is in fact the com-
putation base for the equivalent bandwidth algorithm
(Guerin et al., 1991). It sets a probability threshold on
the sum of the source transmission rates.
C(ε) = r
S
+
s
ln(1/ε)
∑
K
k
p
2
k
2
(4)
where, C(ε) represents the equivalent bandwidth,
r
S
is the average aggregate arrival rate, p
k
is the peak
rate, ε is the target loss rate and k is the number of
flows. When a new flow α requests admission, the
admission control check is then based on this crite-
rion:
C(ε) + p
α
≤ µ (5)
2.2 Estimators
In order to be able to maintain a level of service or
guarantee of QoS, the algorithm must have available
an estimate of current resource requirements, typi-
cally bandwidth requirements. Bandwidth estimation
may be based upon predictive traffic models, mea-
surements, or a combination of both. Those based on
measurements are of interest for this study.
As shown in Figure 1 an average load is computed
for every sampling period S with the time window
estimator, where S represents an integer number of
stochastic packet transmission times. At the end of
a measurement window T, which is an integer num-
ber of sampling periods S, the highest average en-
countered within the window is used as the load es-
timate for next window T. Additionally, whenever a
new flow is admitted to the network, the estimate is
increased according to the advertised flow informa-
tion (e.g., peak rate of the requesting flow), and the
window is restarted. The estimate is also increased
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385