618 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 8, NO. 5, OCTOBER 2000
Cost-Effective Traffic Grooming in WDM Rings
Ornan Gerstel, Member, IEEE, Rajiv Ramaswami, Fellow, IEEE, and Galen H. Sasaki, Member, IEEE
Abstract—We provide network designs for optical add–drop
wavelength-division-multiplexed (OADM) rings that minimize
overall network cost, rather than just the number of wavelengths
needed. The network cost includes the cost of the transceivers
required at the nodes as well as the number of wavelengths. The
transceiver cost includes the cost of terminating equipment as
well as higher-layer electronic processing equipment, which in
practice can dominate over the cost of the number of wavelengths
in the network. The networks support dynamic (i.e., time-varying)
traffic streams that are at lower rates (e.g., OC-3, 155 Mb/s) than
the lightpath capacities (e.g., OC-48, 2.5 Gb/s). A simple OADM
ring is the point-to-point ring, where traffic is transported on
WDM links optically, but switched through nodes electronically.
Although the network is efficient in using link bandwidth, it has
high electronic and opto-electronic processing costs. Two OADM
ring networks are given that have similar performance but are
less expensive. Two other OADM ring networks are considered
that are nonblocking, where one has a wide-sense nonblocking
property and the other has a rearrangeably nonblocking property.
All the networks are compared using the cost criteria of number
of wavelengths and number of transceivers.
Index Terms—Electronic traffic grooming, nonblocking net-
works, optical networks, wavelength division multiplexing.
I. INTRODUCTION
A
N OPTICAL add–drop wavelength-division-multiplexed
(WDM) ring network (OADM ring), shown in Fig. 1, con-
sists of
nodes labeled in the clockwise di-
rection, interconnected by fiberlinks.Eachlink carries high-rate
traffic on optical signals at many wavelengths. The network has
a fixed set of wavelengths for all links which we denote by
, where denotes the number of wave-
lengths. OADM ring networks are being developed as part of
test-beds and commercial products, and are expectedto be an in-
tegral part of telecommunication backbone networks. Although
mesh topology WDM networks will be of greater importance in
the future, at least in the near term, ring topologies are viable be-
cause SONET/SDH self-healing architectures are ring oriented.
OADM rings support lightpaths, which are all-optical com-
municationconnectionsthatspanoneormorelinks.Wewillcon-
sidernetworkswhereeachlightpath isfull duplex,and its signals
intheforwardandreversedirection use thesame wavelengthand
route.Sinceeachlightpathisfullduplex,it is terminated by apair
Manuscript received May 15, 1998; revised August 16, 1999; approved by
IEEE/ACM T
RANSACTIONS ON NETWORKING Editor B. Mukherjee. This work
wassupported in part by the Defense Advanced Research Projects Agency under
Grant MDA-972-95-C-0001, and in part by the Defense Advanced Research
Projects Agency and Rome Laboratory, Air Force Materiel Command, USAF,
under Grant F30602-97-1-0342.
O.GerstelandR.RamaswamiwerewithTellabs,Hawthorne,NY10532USA.
Theyare nowwith Xros, Sunnyvale,CA 94086 USA (e-mail: ori@ieee.org).
G. H. Sasaki is with the Department of Electrical Engineering, University of
Hawaii, Honolulu, HI 96822 USA.
Publisher Item Identifier S 1063-6692(00)09123-8.
Fig. 1. Optical WDM ring.
Fig. 2. Optical node.
of transceivers. Here, a transceiver is generic for such systems
as line terminating equipment (LTE) and add/drop multiplexers
(ADM) (or more accurately, half an ADM). All lightpaths have
thesame transmissioncapacity, e.g., OC-48 (2.5 Gb/s) rates.
A node in a OADM ring is shown in Fig. 2. Note that some
of the lightpaths pass through the node in optical form. They
carry traffic not intended for the node. The remaining lighpaths
are terminated at the node by transceivers, and their traffic is
converted to electronic form, and processed electronically. The
electronic processing (and switching) includes systems such as
SONET/SDH ADMs, IP routers, and digital crossconnect sys-
tems (DCSs) that crossconnect traffic streams. To simplify the
presentation, we shall assume DCS systems in the sequel, but
the very same discussion holds for the other type of electrical
nodes. In Fig. 2, the DCS is shown representing all the elec-
tronic processing, and the transceivers are located at the inter-
face of the DCS and lightpaths. Now some of the received traffic
may be intended for the node, in which case it is switched to a
local entity through local access ports. The rest of the traffic is
forwarded on other lightpaths via the transceivers. In our model,
the cost of transceivers is a dominant cost.
A special case of an OADM ring network is the point-to-
point WDM ring network (PPWDM ring) shown in Fig. 3. Here,
each link in the network has one-hop lightpaths on each of its
wavelengths.The network is called a point-to-point ring because
each lightpath implements a point-to-point connection between
neighboring nodes. For the network, each node has a single DCS
1063–6692/00$10.00 © 2000 IEEE
GERSTEL et al.: COST-EFFECTIVE TRAFFIC GROOMING IN WDM RINGS 619
Fig. 3. Point-to-point OADM ring with three wavelengths.
that cross connects traffic from all the lightpaths. The DCS is
wide-sense nonblocking, which means that a traffic stream may
be routed through it without disturbing existing traffic streams.
Note that this network does not have a true optical node because
lightpaths do not pass through nodes, i.e., traffic at each node is
processed electronically.
The PPWDM ring has the advantage of being able to effi-
ciently use the link bandwidth for time-varying traffic. The net-
work can route a traffic stream through it without disturbing
other traffic streams as long as there is enough spare capacity
along each link of the route. Hence, due to its capability to
switch traffic streams between spare capacity on different wave-
lengths, it will be wavelength efficient. Its disadvantage is that
its nodes do not have optical pass-through, resulting in max-
imum transceiver cost. For instance, in a typical carrier net-
work, each link may have 16 wavelengths, each carrying OC-48
data. Suppose an OADM ring node needs to terminate only one
lightpath worth of traffic. In this case, the node would ideally
pass through the remaining 15 lightpaths in optical form without
“processing” them. On the other hand, a PPWDM ring would re-
quire the traffic from all 16 wavelengths to be received, possibly
switched through an electronic DCS, and retransmitted.
In practice, however, the situation is somewhat more com-
plicated. Each lightpath typically carries many multiplexed
lower-speed traffic streams (e.g., OC-3 streams, which are at
155 Mb/s). An OADM ring node cannot extract an individual
lower-speed stream from a wavelength without first receiving
the entire wavelength. Thus, in the example above, if we had
to extract an individual OC-3 stream from each of the 16
wavelengths at a node, and all the remaining traffic were not
intended for that node, all 16 wavelengths must be received.
Note that the problem of designing networks that efficiently
grooms traffic (i.e., multiplex/demultiplex lower-speed traffic
streams onto and off of higher capacity lighpaths) is nontrivial,
and its solution can have a great impact on network cost.
A. Design Assumptions and Approach
In this paper, we will address the problem of designing
OADM rings for cost-effective traffic grooming. Our approach
will be to propose and analyze a collection of OADM ring
networks under the following assumptions and criteria:
1) Network costs will be dealt with explicitly. The costs of
interest are as follows:
a) Number of Wavelengths
.
b) Transceiver Cost
: The cost is defined to be the
average number of transceivers per node in the net-
work. As it turns out, transceiver cost may reflect
actual costs better than the number of wavelengths.
Note that
is equal to twice the average number
of lightpaths per node since two transceivers termi-
nate each lightpath.
c) Maximum Number of Hops
: The cost is de-
fined to be the maximum number of hops of a light-
path. It is desirable to minimize
since it leads to
simpler physical layer designs.
While most of the previous work on WDM networks
dealt with minimizing the number of wavelengths, our
work, which first appeared in [11], is the first to consider
transceiver costs. In addition, our cost analyses give for-
mulas that quantitatively relate network resources with
traffic parameters.
2) Lightpaths are fixed, although their placement may
be optimized at start up. This is a reasonable assump-
tion for practical WDM networks at least in the near term
because: a) the traffic in a lightpath is an aggregation of
many traffic streams, making it less likely to fluctuate sig-
nificantly; b) automatic network switching for lightpaths
is not yet cost effective; and c) rerouting lightpaths may
cause disruption of service.
3) The networks are circuit-switched and support lower-
speed full-duplex end-to-end connections, all at the
same rate. For example, the lightpaths may be at the
OC-48 rate and support only OC-3 circuit-switched con-
nections. We will refer to these connections as traffic
streams. We will let
denote the number of traffic streams
that can be supported in a lightpath, i.e.,
traffic streams
lightpath. For example, for OC-48 lighpaths and
OC-3 traffic streams,
.
4) Each node has a wide-sense nonblocking DCS that is
large enough to crossconnect all traffic between its
transceivers and local ports. This assumption is real-
istic for many practical situations, and will simplify our
subsequent discussion. Notice that the cost of the DCS is
not considered in this paper. This is reasonable assuming
that the interface-ports rather than switch-fabric dominate
DCS costs because then total DCS cost is proportional
with total transceiver cost.
The overallnetwork design problem comprises of twophases:
first the lower-speed traffic must be aggregated on to lightpaths,
so as to minimize transceiver costs as well as wavelength costs.
This is the focus of our paper. The second phase may incor-
porate constraints in organizing the lightpaths. For instance, an
OADM network may be called upon to realize multiple SONET
rings. This phase of network design is treated in a follow-up
paper that also includes transceiver (ADM) costs [9]. Here, an
OADM network must realize multiple SONET rings (one ring
per wavelength). However, the lightpaths are already assumed
to be given and the focus is on arranging them in rings. Besides
[9], the only other studies that consider transceiver costs are
[14], [19], which focus on ring networks without DCSs and for
specific static (i.e., fixed over time) traffic, e.g., uniform static
traffic. Typically, researchers have concentrated on numbers of
wavelengths, congestion, delay, or probability of blocking. We
should mention that there is previous work on WDM network
620 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 8, NO. 5, OCTOBER 2000
design for lower-speed traffic streams [2], [4], [8], [17], [18], as-
suming static traffic.There are also a number of papers on WDM
networks with dynamic (i.e., time-varying) traffic (e.g., [3], [1],
[10], [13], [16]), but where lightpaths are switched and lower
speed traffic streams are not considered. The study of (nonstatis-
tical) dynamic traffic and fixed lightpaths for OADM networks
seems to be unique to this paper.
B. Traffic Models
When considering a network architecture, the traffic time de-
pendent behavior, distribution, and routing are of paramount im-
portance. We consider three traffic types insofaras their time de-
pendency is concerned: static, dynamic, and incremental. Static
traffic means that lower-speed traffic streams are set up all at
once, at some initial time, and fixed thereafter. Dynamic traffic
means that traffic streams are set up and terminated at arbi-
trary times. Incremental traffic is dynamic traffic, but the traffic
streams never terminate. This models the situation when traffic
streams are expected to have a long holding times, as is usually
the case with provisioning of high-speed connections today.
The traffic distribution will be represented by a traffic matrix
, where equals the number of traffic
streams between nodes
and . Thus, is the number of
“lighpaths of traffic” between nodes
and . Note that
can be fractional. For example, if 24 OC-3 connections (1
OC-48
16 OC-3s) are to be supported between and , then
. If the traffic is static, then is fixed for all time,
while if the traffic is dynamic then
is time-varying. Note that
placement of transceivers is dependent on the traffic pattern.
For example, for each node
, is a lower bound
on the number of transceivers it requires.
The routing of traffic affects the traffic loads on links, which
in turn affect bandwidth requirements. We consider traffic that
either requires routing or are pre-routed, i.e., they come with
their own pre-computed routes. In addition, pre-routed traffic
are assumed to have simple routes, which means that they visit a
node at most once. In this sense, they are routed efficiently in the
network. Note that the pre-routed traffic model holds for many
practical scenarios, such as when traffic is routed according to
shortest paths or traffic loads. It allows us to define a maximum
“traffic load” over links, which is a lower bound on the number
of wavelengths to accommodate the traffic.
We consider three different traffic assumptions (i.e., sce-
narios), given below. The first assumes dynamic traffic that
only has restrictions on the amount of traffic that terminates
at the nodes. The next assumption has pre-routed traffic and a
maximum traffic load parameter. The parameter is a measure of
the required bandwidth (wavelengths) on the links. This model
may be more appropriate when wavelengths are limited because
then the load parameter value can be chosen appropriately. The
final assumption is a uniform traffic assumption used in the
literature as a benchmark to compare different architectures.
Traffic Assumption A: Traffic is dynamic, i.e.,
is time-
varying. The traffic has integer parameters
. At any time, each node can terminate at most
traffic streams. Thus, at any time, for each node ,
and .
Traffic Assumption B: The traffic is dynamic, with traffic
streams being pre-routed and having simple routes. The traffic
has integer parameters
and .
At any time, the number of traffic streams over any link is
at most
, assuming no blocking. In addition, each node
may terminate at most traffic streams from the clock-
wise or counter-clockwise direction along the ring. Thus, node
can terminate up to traffic streams, but then half
must come from the clockwise direction and the other half must
come from the counter-clockwise direction. [Note that
is
a lower bound on the number of transceivers at node
to insure
no blocking.]
Traffic Assumption C: This is the static uniform traffic.It
has an integer parameter
, and has exactly traffic streams be-
tween every pair of nodes. Thus,
if , and
if . This traffic is commonly used to compare
networks in the theoretical literature because it requires good
network connectivity since all nodes are connected to one an-
other, and its uniformity simplifies analysis.
C. Proposed Network Architectures
In this paper, we will consider six OADM ring networks. To
define these networks we need to specify the placement of light-
paths (and the corresponding transceivers) and a routing algo-
rithm for the traffic streams onto lightpaths. Note that the place-
ment of a lightpath requires finding a route and wavelength for
it.
The six networks assume different constraints on the traffic.
The following are brief descriptions of each OADM ring and
theircorresponding traffic constraints. In Section II, we will pro-
vide a more detailed description of the networks and their costs.
The following network assumes static traffic.
Fully Optical Ring: For this network, between each pair
of nodes
and there are lightpaths between them.
Traffic streams between the nodes are carried directly by these
connecting lightpaths. We consider this network because it
has no electronic traffic grooming (which is why it is called
“fully optical”). It is therefore the opposite of the PPWDM
ring which has maximal traffic grooming capability. Note that
it becomes bandwidth efficient if the traffic is high enough to
fill the lightpaths.
The next two networks are for Traffic Assumption A. Under
the assumption, they are nonblocking, which means that they
will not block any arriving traffic stream. Note that
is a
lower bound on the number of transceivers at node
to insure
no blocking.
Single-Hub: This network has a unique node designated as
a hub, which has lightpaths directly connecting it to all other
nodes. It is wide-sense nonblocking, i.e., traffic streams may be
added without disturbing existing ones.
Double-Hub: This network has two hubs, which have light-
paths connecting them to all other nodes. This network is rear-
rangeably nonblocking, which means that it may have to rear-
range existing traffic streams to make way for new ones. Note
that rearranging existing traffic streams is undesirable in prac-
tical networks. However, the double-hub network is reasonably
efficient in
and , so it could be used for static traffic.
GERSTEL et al.: COST-EFFECTIVE TRAFFIC GROOMING IN WDM RINGS 621
Fig. 4. Setting up a lightpath between the first two nodes.
The single-hub and double-hub networks are nonblocking for
dynamic traffic, with the only constraint that each node
can
terminate at most
traffic streams. They result in large
to accommodate worst-case traffic distributions that lead to
high traffic loads on links. The next three ring networks are for
Traffic Assumption B. They require
to insure no traffic
blocking. Notice that the requirement is necessary for any net-
work to be nonblocking. However, the inequality by itself is in-
sufficient because trafficcannot use spare bandwidth at different
wavelengths if they cannot be switched at intermediate nodes.
PPWDM Ring: This is the PPWDM ring network described
earlier. For Traffic Assumption B and
, it is wide-sense
nonblocking.
Hierarchical Ring: This is a simple network composed of
two PPWDM subrings, and is wide-sense nonblocking for
Traffic Assumption B. The network uses more wavelengths
than a PPWDM ring, but it often uses less transceivers.
Incremental Ring: This a ring network that is organized
(recursively) from sections of the ring. For Traffic Assump-
tion B, the network is wide-sense nonblocking for incremental
traffic. It requires the same
wavelengths as the PPWDM ring,
but a smaller number of transceivers. Since it is wide-sense
nonblocking for incremental traffic, it is rearrangeable non-
blocking when the traffic is fully dynamic and satisfies Traffic
Assumption B. Here, rearrangeably nonblocking means that
traffic streams may change wavelengths, but not their routes, to
make way for a new traffic stream.
These six OADM rings are for different traffic models, but
they can all support static traffic. Hence, in Section III, we com-
pare their costs
, , and under Traffic Assumption C. Our
conclusions are given in Section IV.
II. O
PTICAL WDM RING ARCHITECTURES
A. Fully Optical Ring
Consider a network where traffic must be routed on a single
lightpath from its source to its destination. This will require set-
ting up lightpaths between each source and destination node
between which there is any traffic. We will compute the costs
for the ring assuming the static uniform traffic with parameter
. Then we need to set up one lightpath between each pair
of nodes. This type of a network has been considered in [7].
Next, the lightpath set-up will be described using a recursive
definition, that appeared in [11] and was also independently dis-
covered in [6]. Other definitions of fully optical rings can be
found in [21].
We first consider the case when
is even.
1) Start with two nodes on the ring (see Fig. 4). The sole
lightpath that needs be set up will require one wavelength.
Fig. 5. Setting up the lightpaths for two new nodes.
2) (Recursive step) Let denote the number of nodes cur-
rently in the ring. While
, add two more nodes
tothering such that theyarediametricallyopposite to each
other, i.e., separated by the maximum possible number of
hops(seeFig.5).Thetwonewnodesdividetheringinhalf,
where each half has
old nodes. In one half, each old
node sets up a lightpath to each new node. This requires
one wavelength per old node since each old node can fit
its two lightpaths in a wavelength(since the lightpaths use
disjoint routes). Thus, a total of
new wavelengths are
required. The old nodes in the other half of the ring can do
the same thing and use the same
wavelengths.Finally,
the two new nodes require an additional wavelength to set
up a lightpath between them. Thus, we need to add a total
of
newwavelengths.
So the number of wavelengths needed to do the assignment is
For arbitrary the wavelength assignment can be done with
wavelengths, where is even.
When
is odd, we start the procedure abovewith three nodes
and add two nodes each time. The number of wavelengths in this
case can be calculated to be
Clearly, the number of transceivers required per node is given
by
The maximum hop length is
(1)
B. Single-Hub Ring
The single-hub ring network is for Traffic Assumption A.
It has a node designated as the hub, which will be referred to
as node
. An example of a single-hub network is shown in
Fig. 6. The hub node is chosen such that it achieves the max-
imum
. As we shall see, this choice for the hub
622 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 8, NO. 5, OCTOBER 2000
Fig. 6. Single-hub network for the case when
t
(
i
)=1
for all nodes
i
.
minimizes the required number of wavelengths. For simplicity,
we will denote
by .
Each node
is directly connected to the hub by light-
paths.Thus,thelogicaltopologyofthenetworkisastartopology.
Traffic streams are routed between nodes by going through the
hub. The networkis wide-sense nonblocking because the DCS at
the hub is wide-sense nonblocking, and for each node
there are
enough lightpaths provisioned to the hub to accommodate all of
its traffic. Thus, we havethe following theorem.
Theorem 1: For Traffic Assumption A, the single-hub ring is
wide-sense nonblocking.
The number of wavelengths required is
because there are lightpaths, and we can fit two
lightpath connections into a wavelength (the lightpaths on the
same wavelength use disjoint routes along on the ring).
We have the following properties of the single hub ring:
•
.
•
since there are
lightpaths.
•
since lightpath routes may be forced to cir-
cumvent the ring to minimize wavelengths.
Now, note that since the single-hub ring is wide-sense non-
blocking, it is also rearrangeably nonblocking. The following
theorem gives a simple lower bound on the number of wave-
lengths required for such a OADM ring, and we give its proof
for completeness. Notice that the number of wavelengths for
the single-hub ring is about twice as much as the lower bound.
However, in the next subsection, a rearrangeably nonblocking
OADM ring is given that almost meets the lower bound.
Theorem 2: Consider a rearrangeably nonblocking OADM
ring network under Traffic Assumption A. Suppose
is even,
and for each node
, , where
is some integer. Then the number of wavelengths is at least
.
Proof: Consider the case where for
, there is traffic streams between the pair of
nodes
and . Since each traffic stream must traverse
links, there are pairs of nodes, and there are links,
the average number of traffic streams going through a link must
be at least
(2)
which is equal to
. The theorem is implied.
Fig. 7. Double-hub network when
t
(
i
)=2
for all nodes
i
.
C. Double-Hub Ring
The double-hub ring network is for Traffic Assumption A. It
has two nodes that are hubs. An example of a double-hub ring
is shown in Fig. 7. Without loss of generality, assume one of
the hubs is node 0, and denote the other hub by
. Each node
has communication connections to each hub, and the aggregate
capacity to each hub is equivalent to
lightpaths. This
allows node
to send (and sink) up to traffic streams
to (and from) each hub.
We will now describe how the communication connec-
tions are realized by lightpaths. We will use the following
terminology and definitions. The nodes
will be referred to as side 1 of the ring. The rest of the nodes
will be referred to as side 2 of the ring. We
will also use the notation
to denote the fractional
part of
. Note that is zero if is even
and
if is odd. We will refer to nodes that have odd
as odd traffic nodes.
Wewill nowdescribe how nodes in side 1 connect to the hubs.
(Note that the nodes in side 2 are connected to the hubs in a sim-
ilar way.) Each node
in side 1 uses wavelengths
to carry
lightpaths directly to each hub. The light-
paths are routed only using links on side 1 of the ring. Note that
it is possible to use only
wavelengths because light-
paths going to the two hubs have disjoint routes.
Note that if
is odd then node must have an additional
( ) worth of lightpath connection to each hub.
These “half-a-lightpath” connections are realized by having two
odd-traffic nodes share a wavelength. For example, if
and
are odd-traffic nodes sharing a wavelength and then there
would be lightpaths between the pairs
, , and .
Thus, if
then there would be three lightpaths, and if
then there would be two lightpaths. Now nodes and can use
half the bandwidth of a lightpath to carry
traffic streams to
and from each hub.
It is straightforward to check that number of wavelengths
required for side 1 of the ring is
. Note that
nodes 0 and
each have transceivers to
terminate lightpaths on side 1. Each node
have transceivers to terminate lightpaths with a
“full lightpath worth” of connection, and has
transceivers to terminate lightpaths with “half a lightpath
worth” of connection. Thus, each node