Quality of Service Routing for Supporting Multimedia Applications
Zheng Wang and Jon Crowcroft
Department of Computer Science, University College London
Gower Street, London WC1E 6BT, United Kingdom
ABSTRACT
In recent years, several new architectures have been developed for supporting mul-
timedia applications such as digital video and audio. However, quality of service routing
is an important element that is still missing from these architectures. In this paper we
consider a number of issues in QoS routing. We first examine the basic problem of QoS
routing, namely, finding a path that satisfy multiple constraints, and its implications on
routing metric selection, and then present three path computation algorithms for source
routing and for hop-by-hop routing.
1. Introduction
Multimedia applications such as digital video and audio often have stringent quality of service (QoS)
requirements. For a network to deliver performance guarantees it has to make resource reservation and
excise network control. In the past several years, there have been much discussion and research in the area
of resource setup, admission control and packet scheduling, and many new architectures have been pro-
posed [1-3, 5-6, 9-14, 17-19].
One important element that is still missing from these architectures is quality of service (QoS) routing,
namely, routing based on QoS requirements. A typical resource reservation process has two essential steps:
finding resources and making reservations. Resource reservation can only be made when routing has found
paths with sufficient resources to meet user requirements. Therefore, to support resource reservation, rout-
ing has to take into consideration the wide range of QoS requirments.
In traditional data networks, routing is primarily concerned with connectivity. Routing protocols usu-
ally characterize the network with a single metric such as hop-count or delay, and use shortest-path algo-
rithms for path computation. However, in order to support a wide range of QoS requirements, routing pro-
tocols need to have a more complex model where the network is characterized with multiple metrics such
as bandwidth, delay and loss probability. The basic problem of QoS routing is then to find a path that
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satisfies multiple constraints. As current routing protocols are already reaching the limit of feasible com-
plexity, it is important that the complexity introduced by the QoS support should not impair the scalability
of routing protocols.
In this paper, we examine a number of issues in QoS routing in detail. We first look at the complexity
of finding paths subject to multiple constraints, the selection of metrics for QoS routing, and then present
three path computation algorithms both for source routing and hop-by-hop routing.
2. Complexity Analysis and Metric Selection
In this section, we first present some results on the problem of finding a path subject to multiple con-
straints, and then discussion metric selection based on our analysis.
2.1. Selection Criterion
Routing metrics are the representation of a network in routing; as such, they have major implications
not only on the complexity of path computation, but also on the range of QoS requirements that can be sup-
ported. A number of factors have to be taken into consideration here:
1) For any metrics selected, efficient algorithms must exist for path computation, so that the routing proto-
col is able to scale to large networks such as the Internet. The complexity of the algorithms for path
computation should preferably be comparable to that of current routing algorithms. It is also desirable
that any algorithms should be able to work both in a centralized environment and a distributed environ-
ment.
2) The metrics must reflect the basic characteristics of a network. The information they contain should
make it possible to support basic QoS requirements. Note that any QoS requirements have to be
mapped onto the constraints on a path expressed in terms of the metrics, thus the metrics, to some
extend, determine the types of QoS that the network can support. For example, if cost and bandwidth
are the metrics, all QoS requirements have to be mapped onto cost and bandwidth. Some requirements
such as reliability obviously can not be supported by such metrics.
3) Metrics should be orthogonal to each other so that there should no redundant information among the
metrics. Redundant information can introduce inter-dependence among the metrics which makes it
impossible to evaluate each metric independently. Recursive evaluation among metrics can substan-
tially complicate path computation.
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2.2. Single Mixed Metric
Path computation algorithms for a single metric, such as delay and hop-count, are well known and have
been widely used in current networks. Thus, a natural question is whether a single metric can support user
QoS requirements.
One possible approach might be to define a function and generate a single metric from multiple param-
eters. The idea is to mix various pieces of information into a single measure and use it as the basis for rout-
ing decisions. For example, a mixed metric M may be produced with bandwidth B , delay D and loss pro-
bability L with a formula f (p ) =
D (p)×L (p )
B (p )
. A path with a large value is likely to be a better choice in
terms of bandwidth, delay and loss probability.
Single mixed metric, however, can only be used as an indicator at best as it does not contain sufficient
information to assess whether user QoS requirements can be met or not. Another problem has to do with
mixing parameters of different composition rules. For example, suppose that a path has two segments ab
and bc . If metric f (p ) is delay, the composition rule is f (ab +bc ) = f (ab ) + f (bc ). If metric f (p ) is
bandwidth, the rule is f (ab +bc ) = min [f (ab ), f (bc )]. However, if f (p ) =
D (p )×L (p )
B (p )
, neither of the
above are valid. In fact, there may not be a simple composition rule at all.
We believe that the mixed metric approach is a tempting heuristic but it can at best be used as an indi-
cator in path selection.
2.3. Multiple Metrics
Multiple metrics can certainly model a network more accurately. However, the problem is that finding
a path subject to multiple constraints is inherently hard. Polynomial-time algorithms for the problem may
not exist. A simple problem with two constraints called "shortest weight-constrained path" was listed in [8]
as NP-complete but the proof has never been published. Jaffe [11] investigated this particular problem
further and proposed two approximation algorithms that solve the problem in pseudopolynomial-time or
polynomial-time if the lengths and weights have a small range of values. The running time of such NP-
complete problems for real-world network topologies is investigated in [15].
The problem in QoS routing is much more complicated since the resource requirements specified by the
applications are often diverse and application-dependent. The computation complexity is primarily deter-
mined by the composition rules of the metrics. There are three basic composition rules we are most
interested in:
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Definition: Let d(i , j ) be a metric for link (i, j ). For any path p = (i , j, k ,..., l, m ), we say metric d
is additive if
d (p ) = d (i , j ) + d (j , k ) +
. . .
+ d (l , m )
We say metric d is multiplicative if
d (p ) = d (i , j ) × d (j , k ) ×
. . .
× d (l , m )
We say metric d is concave if
d (p ) = min [d (i ,j ), d (j ,k ), ..., d (l,m )]
Let us now look at some parameters that are likely to be considered as routing metrics: delay, delay
jitter, cost, loss probability and bandwidth. It is obvious that delay, delay jitter and cost follow the additive
composition rule, and bandwidth follows the concave composition rule. The composition rule for loss pro-
bability is more complicated.
d (p ) = 1 − ((1−d (i, j )) × (1−d (j , k )) ×
. . .
× (1−d (l , m )))
However, loss probability metric can be easily transformed to an equivalent metric (the probability of suc-
cessful transmission) that follows the multiplicative composition rule.
We now present three general NP-completeness Theorems for additive and multiplicative metrics. They
form the foundation for our metric selection.
Theorem 1: Give a network G = (N , A), n additive metrics d
1
(a ), d
2
(a ), ..., d
n
(a ) for each a ∈A , two
specified nodes i , m , and n positive integers D
1
, D
2
, ..., D
n
, (n ≥ 2, d
i
(a ) ≥ 0, D
i
≥ 0 for i = 1, 2, ..., n ),
the problem of deciding if there is a simple path p = (i , j , k , ..., l , m) which satisfies the following con-
straints d
i
(p ) ≤ D
i
where i = 1, 2, ..., n (the n Additive Metrics Problem) is NP-complete.
lower link
upper link
d
2
= a
i
d
1
= M −a
i
d
2
= 0
d
1
= M
node i +1node i
Figure 1: Assignment to Two Links Between Node i and i +1
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Proof: We proceed by induction. First we show that 2 Additive Metrics Problem is NP-complete. It is
easy to see that 2 Additive Metrics Problem ∈ NP. Since Partition is a well-known NP-complete problem
[8], we show Partition ∝ 2 Additive Metrics Problem to prove its NP-completeness.
Given an instance of Partition, a set of numbers a
1
, a
2,
..., a
n
, construct a network with n +1 nodes and
2n links, two each from node i to i +1, 1 ≤ i ≤ n (see Figure 1). Let S =
i =1
Σ
i =n
a
i
and M =2nS . Let metric
d
1
(i ,i +1) for the two link from node i to node i +1 be M and M −a
i
respectively, and let metric d
2
(i ,i +1)
be 0 and a
i
respectively (0 ≤ a_i ≤ 0).
Consider an instance of 2 Additive Metrics Problem:
d
1
(p ) ≤ nM −S /2 (1)
d
2
(p ) ≤ S /2 (2)
where p is a path between node 1 and node n . Note that for both the upper link and the lower link between
i and i +1, we have
d
1
(i ,i +1) + d
2
(i ,i +1) = M
Therefore, for any possible path p between node 1 and node n ,
d
1
(p )+d
2
(p ) =
i =1
Σ
i =n
(d
1
(i , i +1) + d
2
(i , i +1)) = nM (3)
From (1), we know d
1
(p ) ≤ nM −S /2. Thus,
d
2
(p ) ≥ S /2 (4)
From (2) we also have
d
2
(p ) ≤ S /2
Therefore, we get
d
2
(p ) = S /2
From (3), we also get
d
1
(p ) = S /2
Note that, for the two link from node i to node i +1, d
2
(i ,i +1) be 0 and a
i
. Therefore, there must be a sub-
set of the original numbers with total exactly S /2. This solves the instance of Partition.
Conversely, if there is a subset of the original number set with total exactly S /2. For the two links
between i and i +1, choose the lower link if a
i
is in the subset. Otherwise, choose the upper link. For the
