Download Sparse placement of electronic switching nodes

Sparse placement of electronic switching nodes
for low blocking in translucent optical networks
Gangxiang Shen and Wayne D. Grover
TRLabs, #800 10611–98 Avenue, Edmonton, Alberta T5K 2P7, Canada, and Department of
Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, Canada
[email protected]; [email protected]
Tee Hiang Cheng
NTRC, S2-B3c-23, Nanyang Technological University, Singapore, 639798
[email protected]
Sanjay K. Bose
Department of Electrical Engineering, Indian Institute of Technology, Kanpur 208 016, India
[email protected]
Received 16 July 2002; revised manuscript received 1 November 2002
We evaluate the performance of optical network designs using relatively few
switch nodes at which wavelength conversion and electronic regeneration is
possible. A simple heuristic for placing the fewest such nodes to reach a given
blocking probability is based on the ranked frequency of shortest-path routes
transiting each node. This strategy is found to be efficient in designing a translucent optical network with sparse electronic switch placement that performs very
close in blocking to that of an opaque optical network. In addition, we apply a
new two-dimensional Dijkstra algorithm for routing and wavelength assignment
in the resultant translucent optical network. Simulation results indicate that a
translucent optical network with sparse electronic switch placement based on
the heuristic has much lower blocking than a fully transparent optical network
when the constraint of the maximum transparent distance before regeneration
is also considered. Moreover, when the switches are placed according to the
heuristic, lightpath blocking can approach that of a fully opaque network with
significantly fewer total electronic switches. In our results, lightpath blocking
as low as that with the fully opaque network case was obtained with electronic
switches selectively placed at approximately one node in three on average. The
heuristic also performs well against random searching for an effective subset of
electronic switch nodes and performs better than a prior optimal method that is
based on a combinatorially exhaustive search and that is limited to assuming
fixed shortest-path routing. © 2002 Optical Society of America
OCIS codes: 060.4250, 060.4510.
1.
Introduction
In the current jargon of optical networking, a network is referred to as transparent if all the
nodes on the network are all-optical cross connects (OXCs) without any electronic regeneration function. Each lightpath must be routed from its source to its destination without any
electronic processing at intermediate nodes en route. In practice today this requires a wavelength assignment that must be uniquely reserved for the path on each fiber en route. But in
principle a transparent network will allow a lightpath to occupy different wavelengths on
its links when all-optical wavelength conversion (WC) is available. The opposite of a transparent network is a so-called opaque network in which lightwave channels are detected
at each node, and their payload is then electronically regenerated and switched and can
be reassigned to any new outgoing wavelength.1,2 A transparent optical network possesses
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the advantages of signal transparency, bit-rate transparency, and protocol transparency. Current technological limitations and issues in network control and management, however, still
make these systems difficult to implement.3−5 In addition, payloads may require electronic
regeneration en route to retain required digital signal-to-noise ratios, and a fully transparent network does not provide regeneration en route. On the other hand, an opaque network
would currently require electronic switching nodes6 with a large number of O–E (opticalto-electronic) and E–O transponders at each node. The prohibitive cost involved prevents
this kind of electronic-core optical switch from being widely installed on the network.
A practical approach is therefore to strike a balance between transparency and opaqueness in an optical network in terms of either transparent islands or a translucent optical
network.1 In the former, a large-scale optical network is divided into several domains (i.e.,
islands) of optical transparency. In the same domain, a lightpath can transparently reach any
node without any intermediate signal regeneration. But for communications between different domains, electronic switches (ESs) are used at the domain boundaries. These switches
act as 3R regenerators and wavelength converters while relaying the lightpaths crossing the
domain boundaries.
A translucent optical network is a somewhat more general option with the premise of
having a relatively small number of strategically chosen opaque nodes at which WC and
regeneration is possible, where all other nodes are transparent switch nodes. This is called
sparse placement of the opaque (i.e., electronic) switches in the network. Rather than being
dedicated to routing lightpaths only in and out of transparent islands, these switches are
shared by all paths of the network as a whole. In this paper we focus on such so-called
translucent optical networks, studying the problem of where to put the fewest (i.e., sparsely
placed) ESs and how to route demands once such placements are made so that the overall
blocking of lightpath requests in the network is arbitrarily close to that of a fully opaque
network.
Extensive prior studies have considered the design and performance issues that arise in
optical networks7−12 with a variety of methods. Typical results indicate that a network with
only partial WC capability may still achieve a performance very close to that of a network
with full WC capability, although now one simple principle has emerged for deciding on the
placement of wavelength converter and/or regeneration capabilities. We study the effect of
sparse ES placement on network blocking performance. An important added consideration
in this paper is that we address the need to apply a constraint on the maximum transparent
distance before requiring regeneration while obtaining its route and wavelength assignment(s) on successive hops. This addresses a practical extra aspect of optical networking
in the long-haul context where it would be highly desirable to avoid explicit regeneration
equipment if such a function is inherent in the cross-connect switches that route the lightpaths in any case. We first propose and test a simple strategy of placing a limited number
of ESs at nodes that have the highest frequency of shortest paths transiting their locations.
Next, we propose an efficient algorithm to route and assign wavelengths for the lightpath
requests, taking into account the placement of such nodes and a constraint of the maximum
transparent distance. Performance is then studied through simulations to obtain blocking
probabilities under various arrival distributions and intensities. Simulation is also used to
compare performance of the networks with sparsely placed ESs placed by the heuristic to
results obtained for optimal wavelength converter placement based on the strategy in Ref.
13.
The rest of the paper is organized as follows. In Section 2 we describe the architecture of
a translucent network. In Section 3 we propose a new strategy for selectively placing ESs in
a translucent network. In Section 4 we apply the two-dimensional (2-D) Dijkstra algorithm
to get an integrated lightpath routing and wavelength-assignment (RWA) algorithm for the
translucent network. Simulation studies of this strategy for various kinds of network are
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given in Section 5. Finally, the conclusions are made in Section 6.
2.
Translucent Network
In a translucent optical network the idea is to have a relatively few cross-connect nodes that
are based on a fully digital ES core, henceforth called an ES node, whereas all other nodes
are OXC nodes. The OXC may or may not have WC capabilities. Except where stated otherwise below, we will assume that an OXC does not have WC capability. (Such an OXC is
sometimes also called a purely photonic cross connect, or PXC.) This reflects the reality of
current technology in which WC is based on electronic detection and remodulation onto a
new laser, making an OXC with WC capability essentially the same as an ES for present
purposes. Future technology is expected to lead to the possibility of OXC nodes that can
change wavelengths without entering the electronic domain to do so. In an ES the payload signals on all arriving wavelength channel signals are detected and processed in the
electronic domain. Such a node inherently performs 3R regeneration in the process of accessing the payload for digital electronic switching. An ES node can also apply any change
in wavelength to any signal path, because it applies the switched outgoing signal to a new
laser source. In contrast, the basic OXC node assumed here provides a purely optical (fully
transparent) switching function for optical signals but cannot perform signal regeneration.
The difference between ESs and OXCs is important not just from the standpoint of wavelength blocking, which is the most usually studied factor, but also because in practice there
is a constraint on the maximum transparent distance that a lightpath may be allowed to
traverse without regeneration (i.e., without visiting an ES node). Such limits to the optical
path distance that a payload can travel without regeneration in the electronic domain arise
in practice from the accumulation of losses, noises, and nonlinear distortions in the optical
amplifiers and fibers traversed.
More specifically, in summary, we consider three types of possible node capabilities.
An ES is capable of 3R payload regeneration and WC on any lightpath. An OXC without
WC (OXC-NW) is a node that can cross-connect lightpaths in space, i.e., fiber to fiber,
but cannot change wavelengths (or regenerate the payload). Finally, an OXC with WC
capability (OXC-W) is a node model (assuming future technology for all-optical WC) that
can switch lightpaths in space and change wavelength assignments, but because it stays in
the optical domain it also cannot regenerate the payloads.
3.
Sparse Electronic Switch Placement
It is easy to appreciate the combinatorial complexity of the problem of deciding where
to place a relatively small number of ES nodes in a large network. Given a network with
N nodes in which we consider placing K ES nodes, there are col(N, K) possibilities to
evaluate. Thus, for example, there are over 2 million configurations to test of placing 5 ES
nodes in a 50-node network. But in the complete problem one wants a fast enough solution
to place the K nodes efficiently so that K itself can be varied to find the lowest number and
placement that reduces blocking to adequate levels. That is, we generally want to search
through K itself. Clearly the problem has a prohibitive computational cost when a largescale network is considered. Heuristics are thus well justified. A considerable amount of
prior research has considered the problem of placing wavelength-converting (OXC-W here)
nodes within a lightpath-routed network where regeneration intervals are not considered to
minimize blocking purely from a standpoint of the basic RWA problem. It has been shown
that uniformly arranging the wavelength converters in a regular network provides the best
performance.14 For an arbitrary network, a heuristic algorithm for the placement of limitedrange wavelength converters is proposed.15 An optimal, but somewhat computationally
complex, wavelength-converter placement algorithm has been given for the fixed shortest-
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path routing.13 On the basis of these approaches,13−15 we propose a heuristic algorithm that
will consider not only the need for WC in RWA but will also consider routing constraints
because of the need to regenerate the electrical payload before certain total distance or hop
limits are reached.
Let us now describe the transitional weight (TW) heuristic. We model the network as
an undirected graph G = (V , L) where V represents the set of network nodes and L represents the set of bidirectional optical fiber links in the network. Let the nodes be numbered
0, 1, . . . , N − 1, and let li j represent the bidirectional link between nodes i and j. Let Rsd
be the bidirectional shortest-hop route between nodes s and d and λsd be the forecast or
planned mean value of random traffic load (in Erlangs of lightpath requests) between these
two nodes. We will assume that each node pair has an expected value of random traffic load,
λ sd . (This does not mean that all node pairs have the same mean traffic. Later, confirming
tests are done with numerous different nonuniform patterns of average demand intensity.)
For ES node placement we calculate the routes for lightpaths between each of the node
pairs, using Dijkstra’s shortest-path algorithm based on hop length. The parameter Tksd is
set to one if the route between s and d transits the node k; otherwise, it is zero. Tksd is also
defined to be zero if k = s or d. Using this, we obtain the transitional weight (TW) of each
node k as
Wk = ∑
Tksd λsd ,
k ∈ {0, 1, ..., N − 1}.
∀s,d,s6=d
The idea is simply that TW reflects the total number and traffic loading of shortest
routes that transit the node. The proposed heuristic is to then place ESs in nodes in order of
decreasing TWs. To illustrate, let us first introduce the three test network topologies used
henceforth in the paper. These are labeled NSFNET, ARPA-2, and USANET and are shown
in Figs. 1, 2, and 3, respectively, with the link distances (costs) in arbitrary units marked
on each edge. For the time being we disregard the different shading of some nodes in these
figures. The ranked TWs of nodes for each of these networks are shown in Fig. 4(a), 4(b),
and 4(c), respectively, for the case in which there is an equal unit average load on each node
pair and the shortest paths between node pairs for TW counting is based on the hop-lengths
of paths. In the proposed method these TW charts are used directly to identify at which
nodes to place the ES capability, depending on the number being considered.
Fig. 1. Fourteen-node NSFNET backbone network.
Of course, the TW values could also be computed from an initial distance-based shortestpath routing of demands, not hop-based shortest paths. But the significance of using hop
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Fig. 2. Twenty-one–node ARPA-2 network.
Fig. 3. USA carrier’s 24-node IP backbone network, USANET.
count as the measure of shortest routes is that with respect to blocking related to lightwave
channel allocation conflicts, it is the hop count of a path that matters most, not its distance.
More hops means more chances for the lightpath request to be blocked, because no single
wavelength is free on all hops. On the other hand, it is absolute distance that is relevant
to blocking arising from an inability to route a lightpath within the regeneration limit distances. In practice, however, regeneration distance limits with current technology are high
and increasing, and it is deemed more important to overall blocking reduction to address
primarily wavelength blocking. For this reason hop count, not distance, is used in the initial
shortest-path routing. It should be noted, however, that in the later blocking performance
evaluation the shortest physical length is used as the criterion in the 2-D Dijkstra algorithm
that routes actual paths once the ES nodes are placed.
The basic idea is that the TW is a reflection of how “central” or important each node is
to the characteristic routings of demand flows within the given network. When ES nodes
are placed at only a few locations, placing them at the nodes of highest TWs makes it
more likely that regeneration and/or WC can be applied as needed to a given lightpath
without having to perturb the route of the lightpath from its shortest (i.e., least-cost) route.
By placing available ES resources at highest TWs, we get a good payback of capability for
investment made in that the greatest number of shortest-path routes contain at least one ES
node as soon as the first placement is made. Subsequent ranked placements increase the
number of routes having at least one ES node en route and shorten the distance between the
remainder now with at least two ES en route, and so on. In other words, nodes with high
TWs are in a sense the “natural hub nodes” of the given network.
TW ranking is thus a simple criterion that seems intuitively to be truly relevant to the
issue of ES placement. Because the criterion can be so easily computed for even very large
networks, it should be practical for us to consider a wide variety of different forecast de-
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(a)
(b)
(c)
Fig. 4. Ranked TW distributions of the three networks: (a) NSFNET network, (b) ARPA-2
network, and (c) USA carrier’s IP backbone network, USANET.
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mand patterns, looking for those key nodes that show high TWs under almost all plausible
future demand pattern. Such nodes would be, in a very strong sense, the most important
natural wavelength switching hubs of the particular network and represent good candidate
locations for ES placement under almost any plausible demand pattern. Thus, if the basic
idea can be made to perform well, it suggests a simple means of also future proofing an
optical network architecture in the sense of ES placement against a range of uncertain future demand patterns. The corresponding methods for building in such future proofing in
optimal node placement models are very likely to be intractable on networks of practical
sizes.
4.
Routing and Wavelength Assignment in Translucent Optical Networks
RWA of lightpaths in optical networks is usually done in two steps.7−9 The first step tries
to find a route between the node pair, and the second assigns wavelengths for links on
the route. Both steps must succeed for a lightpath to be established. Typically, the regeneration distance constraint is ignored in such RWA algorithms. However, in real systems,
nonlinearities and additive noises from optical amplifiers limit the maximum distance that
a lightpath may transit without its payload undergoing electronic signal regeneration. In a
translucent optical network, especially a long-haul network, this constraint should be taken
into account when lightpaths are being established. ESs, even if they are sparsely distributed, can provide both the regeneration function and the WC function to support practically
feasible lightpath routing. In this section we propose a new approach to RWA for translucent optical networks, which directly takes into account the regeneration limit and the need
to use the sparsely placed ESs for both WC and regeneration requirements in the routing
solutions.
As in the Refs. 15–17, a wavelength graph (WG) may be used to handle the lightpath
RWA both for networks with full or limited conversion and/or with sparse converter placement. We use this approach as well with an additional constraint applied on the maximum
distance that a lightpath can travel without signal regeneration (at an ES).
If there are N physical nodes in the network, then we label each of them with a vector,
(hn, 0i, hn, 1i, . . . , hn,W − 1i), where n is the physical node index ∈ {0, 1, 2, . . . , N − 1}, and
W is the maximum number of wavelengths on each link. Each unit in the vector corresponds
to a virtual node in the WG. We use Chn,ii∼hm, ji to denote the cost of the edge between
the nodes hn, ii and hm, ji. Note that here the cost can be any format as desired, such as
number of hops, physical distance, and so on. A limited cost exists only when (i) (m =
n) ∩ (i 6= j) or (ii) (m 6= n) ∩ (i = j); for the other cases, the costs are set to be infinite.
Case (i) corresponds to WC in the physical node, i.e., the conversion from wavelength i
to wavelength j at the node m(n). The cost of this edge is the WC cost. Note that this can
happen only at an ES or at an optical switch node with WC capability. Case (ii) corresponds
to the wavelength edge cost between two neighboring nodes, m and n. The two virtual nodes
are on the same ith ( jth) wavelength plane. We use tmn to denote the span distance between
two neighboring nodes m and n. Also, we use uhn,ii to represent the total cost of a shortest
path from the source node to the current virtual node hn, ii, and rhn,ii to represent the total
traversed physical distance since the last OEO regeneration. We use sets S and V to record
the virtual nodes that are on the shortest path from the source node and the virtual nodes that
have been visited but still not on the shortest path, respectively. The algorithm searching
for the shortest path between the source node s and the destination node d in the WG is
given below.
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4.A.
Two-Dimensional Dijkstra Algorithm for Translucent Optical Networks
A. 2-D Dijkstra’s algorithm for translucent optical networks
Step 1 (Initialization)
1) S: =Φ; V: =Φ;
2) For i=0 to W-1
{u<s,i>=0; r<s,i>=0; V:=V∪ {<s,i>};}
Step 2: (Find the next node on the shortest path route)
1) If V=Φ, then stop for failure;
Else, find the virtual node <n, k> from V, which has the minimum cost u<n,k>;
2) If n=d, then stop for the success in finding the shortest path between the nodes s and d;
3) V: =V- {<n, k>}; S: =S∪ {<n, k>}
Step 3: (Update costs for those nodes in V and add those unvisited nodes into V)
1) From the first neighboring node <b0, k> to the last neighboring node<bm-1, k> of the current node <n, k>
in the wavelength plane k, do
// Assume there are m neighboring nodes of node n
If <bi, k>∉S, then
(i=0,…,m-1)
If ( r< n , k > + tnbi ≤ maximum transparency distance)
//Lightpath does not break the constraint of maximum transparent distance if it goes via node<bi, k>
{
If <bi, k>∈V, then
 r<bi , k > u<bi , k > ≤ u< n , k > + C< n , k > ~ <bi , k >
;
r< n , k > + tnbi u<bi , k > > u< n , k > + C< n ,k > ~ <bi , k >
{ r<bi , k > = 
u<bi , k > = min{u<bi , k > , u< n , k > + C< n , k > ~ <bi , k > } ;
}
Else,
{ V: =V∪ <bi, K>;
r<bi , k > = r< n ,k > + tnbi
u<bi , k > = u< n , k > + C< n , k > ~ <bi , k > ;
}
}
2) If node n is an optical node with full wavelength conversion capability, then
For i=0 to W-1
{
If <n, i>∉S, then
If <n, i>∈V, then
 r< n ,i > u< n ,i > ≤ u< n ,k > + C< n ,k > ~ < n ,i >
;
r< n ,k > u< n ,i > > u< n ,k > + C< n ,k > ~ < n ,i >
{ r< n ,i > = 
//Here we ignore the signal degradation due to all optical wavelength conversion
u<n,i>=min{u<n,i>, u<n,k>+C<n,k>~<n,i>};
}
Else,
{ V: =V∪ <n, i>;
r< n ,i > = r< n ,k > ;
}
u<n,i>= u<n,k>+C<n,k>~<n,i>.
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}
3) If node n is an electronic switch, then
For i=0 to W-1
{
r< n ,i > = 0; //ES regeneration
If <n, i>∉S, then
If <n, i>∈V, then
u<n,i>=min{u<n,i>, u<n,k>+C<n,k>~<n,i>};
Else,
{ V: =V∪ <n, i>;
u<n,i>= u<n,k>+C<n,k>~<n,i>.
}
}
4) Go to Step 2.
The result of the algorithm is an implicit specification of the route on the physical
graph and the wavelength assignment on each span of the route so that regeneration limits
are satisfied and any needed WCs occur at an ES node en route. If no combination of
wavelength assignments and route are feasible under the regeneration limit, the algorithm
returns with a null set V indicating that the requested lightpath is blocked under the current
network state.
4.B.
Computational Complexity of the Algorithm
The computational complexity of the 2-D Dijkstra algorithm is O[(N + W )NW ] if all the
nodes in the network are ESs or optical nodes with full WC capability. This complexity is
O[N 2W ] if all the nodes in the network are optical nodes without any WC capability. For
the intermediate case, if there are only M ESs or optical nodes with full WC capability in
the network (M < N), then the complexity is O[MW 2 + N 2W ].
5.
Numerical Results
In this section we describe a series of test-case results involving the TW heuristic for sparse
ES placement and application of the 2-D Dijkstra algorithm for RWA to demands such that
they both obey the lightpath transparent distance limits and make wavelength changes only
at ES locations. The point of view in assessing performance is to compare the blocking
probability in situations of dynamic lightpath arrival and departure network by use of simulations. In this regard the blocking probability of the case for full electronic switching in
every node (FES) serves as the theoretical best performance that could be achieved (because under FES, any blocking at all is purely due to capacity saturation, not wavelengthmatching or regeneration limits). The main interest in the results is in how rapidly sparse
ES placement by the TW criterion approaches the limiting case of FES. For the TW heuristic for ES placement to prove its worth, it should be able to approximate the FES blocking
levels with fewer ES nodes than random ES node placement would require and/or produce lower blocking with its choice of ES nodes than prior ES node solutions using other
published methods.
The results include curves for five cases:
(i) FES. Here all nodes are ESs (denoted FES for full ESs). FES is equivalent to an
opaque network. In this network, blocking can occur only as a result of sheer capacity
limitations on the network spans, because every node is capable of regeneration and
WC as needed.
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(ii) FOC. Here all nodes are OXC-W optical switches with full WC capability but no
regeneration capability, and the lightpath transparency constraint length (md) is taken
into account in the blocking. (FOC stands for full optical conversion, but without
regeneration). The FOC case models a fully transparent optical network without a
wavelength continuity constraint, because all-optical WC is assumed. Blocking can
occur in FOC either from pure capacity limitations or (more commonly) because no
route is feasible, with a currently free (but not the same) wavelength on all required
spans, which does not exceed the regeneration limit.
(iii) SES, SOC (md = infi). Next are cases in which sparsely placed nodes may be either
of an OXC-W or an ES nature (not mixed, however), but there is no limit on the
regeneration distances. These are denoted SOC (or SES) cases with (md = infi). SOC
is also a fully transparent network based on sparse OXC-W node placements, and
SES is the regular case of sparsely placed ES nodes, but in cases with no regeneration
distance limit, it can be appreciated that SOC and SES are equivalent blocking-wise,
so they are grouped together in results. Nodes that are not OXC-W (in SOC) or ES
(in SES) are by default OXC-NW nodes. Blocking can occur in these networks from
capacity limitations or wavelength-assignment infeasibilities only, since there is no
regeneration path length limit. These cases are used to let us separately diagnose the
contribution to blocking from RWA limitations as opposed to regeneration limitations
in the final two types of network.
(iv) SOC (md = fini). This is the case of a transparent optical network with sparse wavelength converter placement (i.e., OXC-W nodes) and in which the lightpath regeneration constraint length is finite. There are no ES nodes in these test cases. Blocking
can arise from capacity, regeneration, or simple RWA limitations given the limited
locations for WC and the absence of any regeneration nodes for routing that would
otherwise be over finite transparent distance.
(v) SES (md = fini). In this test case, ES nodes are sparsely placed and all other nodes
are OXC-NW nodes (i.e., without WC capability), and routing feasibility depends
on using the limited number of ES nodes to satisfy requirements for either WC or
regeneration. Results for this case correspond to the real types of translucent optical
network that we wish to support with this research. All prior cases are for comparative and diagnostic understanding of which factors contribute most to the blocking
and to provide a framework for assessing performance of SES md = fini networks
with sparse ES node placement derived from the TW heuristic.
For application of the 2-D Dijkstra algorithm we set the WC cost to be zero, and the
wavelength edge cost to be the physical distance of each span. Span distances are as marked
in Figs. 1–3. Under these conditions the cost of a lightpath in the 2-D Dijkstra algorithm
is its physical distance. In the simulations each node pair will generate lightpath requests
following a Poisson process with rate λi /s, with i indexing N(N − 1)/2 lightpath request
generators for an N-node network. λi is chosen as a random value uniformly distributed
within range [0, 2λave ] with mean λave . Note that this creates a nonuniform allocation of
average traffic intensities on each node pair for each test case, although for determination of
the ES node set only the average traffic intensity λave is used for all node pairs in computing
TW. This duly reflects performance of the system in general circumstances where the ES
placement heuristic selects ES nodes based on an expected average traffic weight on each
node pair, but is then tested under random variation of the actual demand intensity on
each pair. Once established, a lightpath is held for a negative-exponentially distributed
time with unit mean (so that the lightpath traffic for node pair i is λi Erlangs). Each link
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is bidirectional with W wavelengths per fiber in each direction. Our experiments all use
W = 8 wavelength channels per fiber. In all results, blocking probabilities are estimated
on a minimum of 10,000 lightpath requests on the network as a whole for each trial. In
general, blocking levels below 10−3 were estimated with 50,000 arrivals.
The first main results to examine are the curves for network average blocking over all
node pairs versus the average offered load λave in Erlangs of lightpath demand on each node
pair. These are shown in Figs. 5, 6, and 7, respectively, for the three test networks. In each of
these plots, the (SOC, md = fini) curve serves as an upper bound on blocking. It represents
the blocking of a network where only a limited number of nodes are OXC-W nodes and
the rest are pure OXC-NW nodes. At the other extreme each family of curves includes an
FES case that represents the lowest blocking architecture as every node is an ES capable
of regeneration and WC. The various SES curves are the cases of most initial interest here.
These show the blocking versus load curves for various numbers and locations of ES as
determined by the TW heuristic. Following each SES symbol in the legend of these figures
is the list of actual ES nodes in round brackets and/or other notes as to the criterion and
number of ES nodes tested. One of the main points of interest in Figs. 5–7 is to observe the
fewest number of ES nodes at which the SES blocking effectively merges with that of FES.
This is the smallest number of ES nodes (chosen by TW) that can effectively eliminate
blocking that is due to both regeneration limits and wavelength-matching conflicts. This
happens with 5 (out of 14) ES nodes for NSFNET, 7 ES nodes (out of 21) ARPA-2, and
7 (out of 24) in USNET. These particular sets of ES nodes are the ones that are shaded in
Figs. 1–3. Obviously this represents a major cost savings over the FES solution in which all
nodes are ES. Over the three networks, only one out of three nodes on average needs to be
an ES node; the rest can be simpler OXC-NW nodes, while achieving essentially the same
blocking as the FES case. (The remaining blocking differences are ∼10−4 or smaller.)
Fig. 5. NSFNET backbone network with eight wavelengths on each fiber and the maximum transparent distance, md = 474. FES, full ESs; FOC, full optical conversions; SOC,
sparsely placed optical conversion nodes; SES, sparse ES nodes.
The few cases in which SES blocking is strictly somewhat below FES is an artifact of
traffic theory where we are measuring arrivals blocking, not time congestion per se. The
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Fig. 6. ARPA-2 network with eight wavelengths on each fiber and the maximum transparent
distance, md = 300.
point is that the performance of an incomplete set of ES-switched (K < N) can be slightly
better than FES now and then because of detailed differences in the lightpaths that are
actually carried, inadvertently given a random but beneficial call-admission-like effect in
some cases. This phenomenon is related to issues that are like those behind determining
a policy for call admission control. What happens here is that, given a certain maximum
distance for a lightpath without regeneration, a network with more ES nodes has a greater
chance of establishing longer lightpaths both in hop length and in physical length than a
network with a smaller number of ES nodes. However, a longer lightpath always consumes
more wavelength resources than a shorter one. Thus if there are more long lightpaths on
a network, it is more likely to block later lightpath requests, owing to insufficient wavelength resources. But with a small number of ES nodes, a network has fewer chances to
establish a long lightpath, because a longer lightpath more severely incurs the constraint
on wavelength continuity as well as on transparent distance limitation. On the other hand,
a smaller number of ES nodes can experience more lightpath-blocking events because of
the constraint of limited transparent distance and less WC capability around the network.
The overall blocking performance is the net interaction of the above factors. In summary,
network conditions that pick up more useful carried load can inherently look somewhat
worse from an arrivals ratio estimate of the blocking. This can permit some test cases that
do not have the full number of ES nodes, and are not carrying the same actual load as the
FES case, to perform slightly better on the simple count of blocked-to-offered lightpath
requests.
The particular solutions shown are for a regeneration distance limit of 474, 300, and 400
distance units, respectively, on the graphs shown in Figs. 1–3. Let us discuss the NSFNET
case results of Fig. 5 as a specific example, general to all for the other curves present. The
transparent distance (md) limit of a lightpath is set to be 474, which is the length of the
longest shortest-path in the graph. It has been found experimentally that this is the minimum md value at which it is possible for SES with five ES nodes to converge with the FES
blocking curve. At the other extreme, Fig. 5 shows an optical network with full WC capabil-
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Fig. 7. USANET network with eight wavelengths on each fiber and the maximum transparent distance, md = 400.
ity but also with the lightpath constraint length i.e., the case (FOC, md = 474) in which the
lightpath regeneration constraint has a severe negative effect on the network’s performance.
On the other hand, without the limit on the lightpath regeneration length, the transparent
optical network with sparse wavelength converter placement (SOC, K = 5, md =infi) and
the translucent optical network with sparse ES placement (SES, K = 5, md =infi) perform
similarly, and much better than (FOC, md =474). This can be explained by realization that
if enough nodes are capable of WC, then the regeneration function of an ES is not really
of any additional advantage because a basic RWA solution will almost always be possible
if the constraint of lightpath regeneration length is not taken into account. This would not
be the case if the network diameter were significantly greater than the regeneration limit,
however.
We also see in the results that the (SOC/SES, K = 5, md =infi) case performance is
close to that of the FES (opaque) network, as is the sparse (SES, K = 5) case at md = 474.
For the (SOC, K = 5, md =infi) case this is in line with the reported results that a network
with partial WC capability shows a performance that is close to that of a network with full
WC capability (if there is no regeneration limit).11,15 If, however, because of the lightpath
transparent distance limitation in real communication systems, we also add the lightpath
regeneration constraint length, we obtain the corresponding (SOC, K = 5, md = 474) and
(SES, K = 5, md = 474) cases. In the former, with sparsely placed OXC-W nodes, we
find that performance degrades severely, indicating a major importance of the regeneration
limit. In contrast, however, this performance degradation is almost totally avoided in the
(SES, K = 5, md = 474) case, which performs almost as well as the corresponding FES
(opaque) network. This can be ascribed to the function of 3R regeneration in ESs, which
helps the network to be immune to the impact of the lightpath constraint length.
For further examining the effectiveness of the TW approach, some other testing strategies were employed. One of the simplest was just to compare blocking results with the node
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selections for one of the same test networks (NSFNET) produced by an optimized placement strategy reported for the fixed shortest path13 . Figure 8 contains this data. The TWs of
all the nodes were computed, and the ES nodes were selected on the basis of ranked TW,
whose locations are recorded in Table 1 together with those reported in Ref 13. In comparing the overall blocked traffic loads of various combinations with the same number of ES
nodes chosen by TW or from Ref. 13 in Table 1, we find that the TW nodes (with RWA
by means of 2-D Dijkstra) always yield a lower overall blocking. It is important, given
that the TW-based SES designs outperform those from Ref. 13 in Fig. 8, to note the sense
in which optimality pertains to Ref. 13. Results in Ref. 13 are optimal (by combinatorial
search) specifically for the case in which the subsequent routing of lightpaths through the
SES network is based on fixed shortest-path routing and identical uniform traffic load on
each node pair. Here we test under nonuniform load patterns, and we use the 2-D Dijkstra
algorithm for RWA, which does not require that each lightpath follow a fixed shortest route
for each node pair. In other words, the set of ES nodes decided upon by the TW heuristic
is more suitable to the 2-D Dijkstra algorithm.
Table 1. Node Locations of the ES Nodes in the NSFNET Networka
K
1
2
3
4
5
6
Strategy in Ref. 13 3 3,5 3,5,7 3,5,7,8 3,4,5,7,8 3,4,5,7,8,10
TW
5 5,8 5,8,3 5,8,3,7 5,8,3,7,4
5,8,3,7,4,1
a The node indices as published in Ref. 13 have been converted on the basis of topological
equivalence to the node numbering used here.
Fig. 8. Performance comparison between the TW strategy and the strategy in Ref. 13.
NSFNET backbone network with eight wavelengths on each fiber and the maximum lightpath transparent distance, md = 474. Electronic switches are sparsely placed at the nodes.
As a further way of challenging or testing the TW heuristic design method, we also
compared the results of several random selections of the same number of ESs as used in
the heuristic designs, again with NSFNET. The logic was that if the random ES node sets
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also produced blocking levels similar to the FES lower bound, then one could conclude that
it is not the exact set of node that matters as much as their number, and there would be no
particular merit to the TW strategy. The results, shown in Fig. 9 and Table 2 are, however,
quite to the contrary, and thus the TW-based selection approximates FES, whereas the
random selections are all far higher in blocking. Results of the random selection strategy
(Ran.) were obtained by simulation to obtain the blocking probabilities for 10 five-node
random placement cases. We first randomly selected a group of nodes, which are placed
with ES; then we ran simulations for the network to find the blocking probability. Following
this, we randomly selected another group again and carried out the same processes. In
Fig. 9 the averaged blocking results of these ten groups are plotted to represent a random
placement strategy. (In Table 2 the individual random trial results are detailed.) From Fig. 9
we can see that the TW strategy shows a much better performance than that of the random
placement strategy. For instance, we observe that curve SES (5, 8, 3) (K = 3, [TW]) is
in fact under curve SES (K = 5, Ran.), even though the network of the latter has almost
double the number of ES nodes as that of the network of the former. This result convinces
us again that the TW heuristic is an efficient solution to the problem of sparse ES/OXC-W
node placement.
Fig. 9. Performance comparison between the TW strategy and the random selection strategy. NSFNET backbone network with eight wavelengths on each fiber and the maximum
lightpath transparent distance, md = 474. Electronic switches are sparsely placed at the
nodes. Ran., random selection strategy.
In the penultimate and in the final results to be presented we try to isolate the effect of
blocking due to regeneration distance limits from that due to wavelength matching. They
are not strictly separable effects per se: A route that respects the regeneration limits may
be directly infeasible for some node pair under a given set of ES nodes, leading to a direct kind of md-related blocking. But even if the route is feasible, it may often have to
exceed the shortest route to respect the regeneration limit. But the longer route itself makes
wavelength blocking more likely and consumes more network capacity as well. Figure 10,
however, allows certain insights about these conceptually separate causal factors in block-
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Table 2. Lightpath Blocking Performance for the Three Placement Strategies when Five ES
Nodes Are Placed in the NSFNET Networka
ES Positions\Erlang
0.20E
0.25E
0.30E
0.35E
0.40E
0.45E
0.50E
R(0,2,4,8,9)
0.0013 0.0082 0.0221 0.0534 0.0942 0.1347 0.1831
R(0,2,4,5,11)
0.0010 0.0055 0.0117 0.0423 0.0696 0.1311 0.1701
R(0,2,5,10,13)
0.0012 0.0047 0.0165 0.0488 0.0698 0.1148 0.1734
R(1,3,6,8,12)
0.0041 0.0081 0.0175 0.0501 0.0924 0.1347 0.1625
R(1,4,6,7,10)
0.0014 0.0064 0.0177 0.0527 0.0912 0.1283 0.1814
R(2,6,9,11,12)
0.0032 0.0099 0.0203 0.0542 0.0922 0.1369 0.1721
R(2,4,8,10,12)
0.0011 0.0044 0.0167 0.0382 0.0772 0.1194 0.1590
R(3,4,8,10,13)
0.0013 0.0058 0.0153 0.0418 0.0706 0.1085 0.1447
R(3,6,9,11,13)
0.0024 0.0075 0.0195 0.0457 0.0860 0.1060 0.1158
R(4,6,8,12,13)
0.0022 0.0091 0.0251 0.0501 0.0920 0.1245 0.1644
Average of rand.
0.0019 0.0070 0.0182 0.0477 0.0835 0.1239 0.1627
Positions of TW& Ref. 13 0.0009 0.0038 0.0142 0.0365 0.0753 0.1048 0.1625
a The
first ten rows are the results of the random strategy; the eleventh row is the average result of the above
ten random strategy results; the twelfth row is the result of both the TW strategy and the strategy in Ref. 13 with
ES node positions (3, 4, 5, 7, 8).
ing. Figure 10, which is for NSFNET, has essentially the same characteristics in this regard
as the results for the other two networks, so we show only it. It plots the same blocking
probability measure as in tests above, but for the specific case of 0.30 Erlangs per node
pair, using the five ES nodes placed at the locations selected by TW, as the maximum distance (md) for regeneration is increased. The result of an opaque network (FES) is again
the lower bound on the other results. It is flat because the regeneration distance is never
a significant consideration when every node has ES. For the SES case, blocking drops
steeply and essentially vanishes (relative to the pure capacity blocking limits of FES) as
md approaches the network diameter (the length of the longest shortest-path between node
pairs). The difference between the SES and SOC curves shows the added value of regeneration in the ES relative to WC only to combat blocking with the same sparse placement of
OXC-W nodes if the transparent distance is less than the network diameter. Below md ∼
network diameter (i.e., 474 for NSFNET), the lightpath transparency limitation has the predominating effect. For results on the right of this threshold, the predominating effect is that
of the WC capability (as evidenced by the SOC curve). Still further out, all blocking is due
only to finite capacity saturation effects. The curves indicate that in general the transparent
distance has to be much higher to approach FES blocking with a sparse set of OXC-W
nodes rather than ES nodes. Alternately these results suggest that even if an all-optical WC
technology is developed, it will not significantly address the network blocking compared
to the same number of ES nodes, unless md is very high, as much as double the network
diameter.
6.
Concluding Discussion
We have approached the problem of sparse ES node placement so as to minimize lightpath
blocking in a translucent optical network through a simple but effective strategy for ES
node selection and subsequent RWA ES nodes are placed on the basis of their TWs, and
RWA is performed by the 2-D Dijkstra algorithm. The novelty lies in how simple, and yet
how well, the proposed approach works in an area where prior research has mostly considered only combinatorial optimization approaches and rarely involved consideration of
the regeneration limit and flexible routing behavior at the same time. The overall strategy
of ranked-TW node placement and 2-D Dijkstra routing is found essentially to eliminate
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blocking that results from either regeneration limits on routing and wavelength-matching
conflicts, with ∼1/3 of the ES nodes required by a fully opaque network solution—one
with the full ES capability in every node. Results also indicate that a translucent optical
network with even a few ES nodes placed by the TW criterion will show a much better
blocking performance than a fully transparent optical network, especially when the constraint of the maximum lightpath transparent distance is considered.
In conducting this research, we tested several variations on the basic ranking of nodes by
a one-time evaluation of TW. One notion was that, especially when regeneration distance
limits are considered as a factor that aggravates the blocking, one could improve the ES
node choice by iteratively updating the TW counts after each node is chosen. The idea
would be to use a distance-weighted TW measure and that after the highest TW node
is identified, paths through it would be “chopped” at the node, leaving only shorter path
segments behind to be considered in another round of distance-weighted TW evaluation.
The notion was that if, say, only two ES nodes were to exist, they should probably not be
Fig. 10. Effect of the maximum transparent distance on the network performances.
NSFNET backbone network with eight wavelengths on each fiber and mean traffic load
per node pair, λave = 0.30 Erlang. Electronic switches are sparsely placed at the nodes
(5, 8, 3, 7, 4).
immediate neighbors, as they often are under the current TW method (for example nodes
7 and 8, which commonly appear together in TW sets at K > 2 in NSFNET). It was hoped
that the iterative updating of the TW evaluation to choose one node per iteration would tend
to place ES nodes farther apart on the network. The benefit would be if FES-like blocking
was reached with fewer ES nodes than with a basic one-time TW analysis and ranking, or
if lower blocking occurred at the same number of ES nodes. The interesting outcome is
that the iterative distance-weighted reevaluation of TW after each ES node choice did not
outperform the basic TW approach in any of our tests. For this reason, and for space, we
do not document the latter trials in detail, but we mention it as a possible line of further
investigation to be pursued based on the general idea we have introduced of TW-based ES
node selection for efficient translucent networks.
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Acknowledgment
The authors thank Teck Yoong Chai for his valuable input.
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