Optical Networks: A Practical Perspective - Part 48 pptx

The number of IP router ports required is equal to twice the number of lightpaths that need to be established since each light- path connects a pair of IP router ports.. One reason for t

10 links

l/

(a)

i

(b)

Figure 8.2 (a) The lightpath topology of the three-node network corresponding to Figure 8.1(a) that is seen by the routers Routers A-B and B-C are connected by 10 parallel links (b) The lightpath topology of the three-node network corresponding to Figure 8.1(b) that is seen by the routers All pairs of routers, A-B, B-C, and C-A, are connected by 5 parallel links

In our example the fiber topology is a linear one with three nodes, and the traffic requirement is 50 Gb/s between every pair of these nodes The task is to design

a lightpath topology that interconnects the IP routers and to realize this topology within the optical layer In our example, two lightpath topologies that meet the traffic requirements are shown in Figure 8.2 We call the first problem the lightpath topology design (LTD) problem We call the problem of realizing the lightpath topology within the optical layer the routing and wavelength assignment (RWA) problem, for reasons that will become clear shortly The RWA problem is simple to solve in this example because there is only one route in the fiber topology between every pair of nodes In

a general topology, the RWA problem can be quite difficult The realization of the two lightpath topologies of Figure 8.2 are shown in Figures 8.1(b) and (c)

Another problem we face in the design of wavelength-routing networks is that of grooming the higher-layer traffic The term grooming is commonly used to refer to the packing of low-speed SONET/SDH circuits (for example, STS-1) into higher-speed circuits (for example, STS-48 or STS-192) This is the function provided by digital crossconnects While the term is usually not applied to IP routers, conceptually IP routers can be considered to provide the grooming function at the packet level

In order to reap the benefits of optical passthrough, the higher-layer traffic must be groomed appropriately For example, in Figure 8.1(c), all the traffic destined for node

B must be groomed onto a few wavelengths, so that only these wavelengths need to

be dropped at node B Otherwise, node B will have to drop many wavelengths, and this will increase the network cost

In the rest of this chapter we will discuss several aspects of the design of wavelength-routing networks in some detail In Section 8.1, we will analyze the

cost trade-offs between the higher-layer and optical-layer equipment in a ring net- work We will then discuss the LTD and RWA problems, which we introduced in the discussion of the three-node network above, in Section 8.2 We then discuss the problem of dimensioning the WDM links, that is, determining the number of wavelengths to be provided on each link, in Section 8.3 We discuss statistical di- mensioning methods in Section 8.4 In Section 8.5, we discuss a number of research results that have been obtained regarding the trade-offs between optical crosscon- nects with and without wavelength conversion capability (We will discuss a practical long-haul network design example in Section 13.2.6.)

Example

In this section, we will study the cost trade-offs in designing networks in different ways to meet the same traffic demand by varying the lightpath topology We will consider the trade-offs between the cost of the higher-layer equipment and the optical layer equipment We measure the higher-layer equipment cost by the number of IP router ports (or SONET line terminals) The number of IP router ports required is equal to twice the number of lightpaths that need to be established since each light- path connects a pair of IP router ports An important component of the optical layer cost is the number of transponders required in the OLTs and OADMs Since every lightpath requires a pair of transponders, we club the cost of the transponders with that of the higher-layer equipment This also covers the case where the transponders are present within the higher-layer equipment (see Figure 7.2) We measure the re- mainder of the cost of the optical layer equipment by the number of wavelengths used on a link

Network topologies are usually designed to be 2-connected, that is, to have two node-wise disjoint routes between every pair of nodes in the network While fiber mesh topologies that are arbitrary, but 2-connected, are more cost-efficient for large networks than fiber ring topologies, the latter have been widely deployed and are good for a network that does not have a wide geographic spread For this reason we will consider fiber ring topologies in this section One reason for the wide deployment

of rings is because a ring connecting N nodes has the minimum possible number of links (only N) for a network that is 2-connected, and thus tends to have a low fiber deployment cost

We will consider a traffic matrix where t units of traffic are to be routed from one IP router to all other IP routers in the network We denote the number of nodes

in the network by N and assume the traffic is uniform; that is, t / ( N - 1) units of traffic are to be routed between every pair of IP routers For normalization purposes, the capacity of a wavelength is assumed to be 1 unit As in the three-node linear

A

Hub

\

I

Figure 8.3 Three different lightpath topologies that can be deployed over a fiber ring topology (a) A point-to-point WDM ring where adjacent routers on the ring are con- nected by one or more lightpaths (b) A hub topology where all routers are connected to one central router (hub) by lightpaths (c) A full mesh where each router is connected to every other router by lightpaths

topology above, we divide the network design problem into two: the LTD and RWA problems We will consider three different lightpath topologies, all of which are capable of meeting the traffic requirements The general form of these topologies is shown in Figure 8.3

The first lightpath topology, shown in Figure 8.3(a), is a ring, which we call a

point-to-point WDM (PWDM) ring In this case, the lightpath topology is also a ring, just like the fiber topology, except that we can have multiple lightpaths between adjacent nodes in the ring, in order to provide the required capacity between the IP routers

The second lightpath topology, shown in Figure 8.3(b), is a hub design All routers are connected to a central (hub) router by one or more lightpaths Thus all packets traverse two lightpaths: from the source router to the hub, and from the hub

to the destination router

The third, and final, lightpath topology, shown in Figure 8.3(c), is an all-optical design In this case, we establish direct lightpaths between all pairs of routers Thus, packets traverse only one lightpath to get from the source router to the destination router

We next consider how to realize these lightpath topologies on the fiber network; that is, we solve the RWA problem for these three designs The RWA problem is

to find a route for each lightpath and to assign it a wavelength on every link of

5~ 1

Lightpaths

L2

are shown in the figure for the case t = 3

the route We assume that a lightpath must be assigned the same wavelength on all the links it traverses; that is, the optical layer provides no wavelength conversion capability In addition, no two lightpaths traversing the same link can be assigned the same wavelength

E x a m p l e 8.2 We first consider the P W D M ring The network shown in Fig- ure 8.4 is a PWDM ring At each node, all the wavelengths are received and sent to the IP routers For this network, all lightpaths are "single-hop" lightpaths between adjacent nodes in the ring If W denotes the number of wavelengths on each link, then we can set up W lightpaths between each pair of adjacent nodes The number of IP router ports needed will depend on the algorithm used to route the traffic Suppose we route each traffic stream along the shortest path between its source and destination, and N is the number of nodes in the network Assuming N is even, we can calculate the traffic load (in units of lightpaths) on each link to be

1

N + l q N-1

8

In this case, since all lightpaths are single-hop lightpaths, the number of wave- lengths needed to support this traffic is simply

I N + 1 + N1 ~I t] "

Since all the wavelengths are received and retransmitted at each node, the number

of router ports required per node, Q, is

This example has illustrated the following set of design parameters that need to

be considered in determining the cost of the network:

Router ports Clearly, we would like to use the minimum possible number of IP router ports to support the given traffic Note that since a lightpath is estab- lished between two router ports, minimizing the number of ports is the same as minimizing the number of lightpaths that must be set up to support the traffic Wavelengths At the same time, we would also like to use the minimum possible number of wavelengths since using more wavelengths incurs additional equip- ment cost in the optical layer

Hops This parameter refers to the maximum number of hops taken up by a light- path For the PWDM ring, each lightpath takes up exactly one hop The reason this parameter becomes important is that it becomes more difficult to design the transmission system as the number of hops increases (see Chapter 5), which again increases the cost of optical layer equipment

In general, we will see that there is a trade-off between these different parameters For example, we will see that the PWDM ring uses a large number of router ports, but the smallest possible number of wavelengths In the hub and all-optical design examples that follow we will use fewer router ports at the cost of requiring more wavelengths

E x a m p l e 8.3 Here, we will consider the hubbed network architecture shown

in Figure 8.5 An additional hub router is added to the ring At the hub router, the packets on all the wavelengths are received and routed appropriately This node is identical to a PWDM ring node The other N nodes are simpler nodes that contain just enough router ports to source and sink the traffic at that node (To keep the example simple, we will assume that the hub router itself does not source or sink any traffic This is, of course, not true in practice In fact, the hub node could serve as a gateway node to the rest of the network.) Lightpaths are established between each node and the hub node h Traffic from a nonhub node

i to another nonhub node j is routed on two lightpathsmone from i to h and another from h to j To support this traffic, we will set up [tl lightpaths from

,p4 I

lOAO l I~

L2

Figure 8.5 A hubbed WDM ring architecture The lightpaths and their wavelength assignment are shown in the figure for the case [t] = 1

each node to the hub node Thus the number of router ports needed per node for this configuration is

We assume that the lightpaths are routed and assigned wavelengths as follows: Two adjacent nodes use different paths along the ring and reuse the same set of wavelengths, as shown in Figure 8.5 For this RWA algorithm, the number of wavelengths required can be calculated to be

N

The worst-case hop length is

E x a m p l e 8.4 The final example is the all-optical design shown in Figure 8.6, where data is transmitted on a single lightpath between its source and destination and never sent through an intermediate router enroute In this case, we must set

up [ t / ( N - 1)] lightpaths between each pair of nodes to handle the t / ( N - 1) units of traffic between each node pair The number of router ports per node is therefore

V'l

Q - ( N - 1 ) N - 1 " (8.7)

)~3 x )~2

Figure 8.6 An all-optical four-node network configuration The lightpaths and their wavelength assignment are shown in the figure for the case t = 3

The number of wavelengths will depend on how the lightpaths are routed and assigned wavelengths (see Problem 8.5) It is possible to obtain a suitable routing and wavelength assignment such that (for N even)

it (N2 N)

W - N - 1 8-+-4- " (8.8)

To understand the quality of the designs produced by the three preceding exam- pies, we can compare them to some simple lower bounds on the number of router ports and wavelengths required for any design Clearly, any design requires O > It]

We next derive a lower bound on the number of wavelengths required as follows Let

h ij denote the minimum distance between nodes i and j in the network measured in number of hops Define the minimum average number of hops between nodes as

Hmin -

N ( N - 1) For a ring network, we can derive the following equation on Hmin (N even)"

N + I 1

4 4(N - 1) Note that the maximum traffic load on any link is greater than the average traffic load, which is given by the equation

Hmin x Total traffic Hmin x 1Nt

L > Lavg = Number of links - N

25-

o

= 20

o

~ 15

o

~ 10

o

~ 5

z

i I ' _ _ 1

I I

1 I

i

| J

PWDM I

J I

|

, !

' Single hub

L _ _ _ _ _ _ 1

0

|

1 I ' I

" - L

i, I Lower bound

JI I

, | I i i

Fully optical

I

I

i i i J

8 10 Traffic, t

F i g u r e 8.7 Number of IP router ports required for the different designs of Examples 8.2-8.4, for a ring with N = 8 nodes The lower bound of [t] is also shown

N + I 1 )

= 8 + 8 ( N - 1) t (8.10)

Clearly, we need to have the number of wavelengths W > L

Figure 8.7 plots the number of router ports required for the three different designs, as well as the lower bound, for a network with eight nodes Observe that for small amounts of traffic, the hubbed network requires the smallest number of router ports The PWDM design requires the largest number of router ports This clearly demonstrates the value of routing signals within the optical layer, as opposed

to having just point-to-point W D M links

Unfortunately, the reduction in router ports is achieved at the expense of requiring

a larger number of wavelengths to support the same traffic load Figure 8.8 plots the number of wavelengths required for the three different designs, along with the lower bound derived earlier The PWDM ring uses the smallest number of wavelengths it achieves the lower bound and is the best possible design from this point of view The hubbed architecture uses a relatively large number of wavelengths to support the same traffic load

The all-optical design is a good design provided t is slightly less than or equal

to N - 1 (or some multiple of N - 1) This is because, in these cases, an integral number of lightpaths is needed between each pair of nodes, which is best realized by having dedicated lightpaths between the node pairs without terminating any traffic

40

35

30

tz~o

=

-~ 25

~ 20

O

x~ 15

Z 10

r -*

i , ,

Single hub,

~

: Fully optical

r

PWDM

I

[

Lower bound

r

,

I

I

0 2 4 6 8 10

Traffic, t

Figure 8.8 Number of wavelengths required for the different designs of Examples 8.2-8.4, for a ring with N = 8 nodes The lower bound from (8.10) is also shown

in intermediate nodes This brings out an important point: denote the traffic between

a pair of nodes by m + t t, where m is a nonnegative integer and 0 _< t t < 1 Then the best solution is to set up m lightpaths between that node pair to route m units of traffic, and to handle the residual t' units by some other methods such as the hubbed

or PWDM architectures If t' is close to one unit, then the best solution may be to have another direct lightpath between them

Overall, we have learned that it is possible to save significantly in higher-layer (IP or SONET) equipment costs by providing networking functions (routing and switching of wavelengths) within the optical layer

8.2 LTD and RWA Problems

The general approach of dividing the wavelength-routing network design problem into that of an LTD problem and an RWA problem, which we employed above in the three-node linear network and the ring network, is a good heuristic for practical problems because solving the two problems in a combined fashion is quite hard In both the examples, we considered a few different lightpath topologies and examined the RWA problem for each of them This clarified the cost trade-offs among the different designs In practice, each lightpath topology together with its realization

8.2.1

in the optical layer (the solution of the RWA problem) would result in a net, real (monetary) cost We can then pick the design that results in the lowest cost We will consider one such example in Chapter 13 We will now examine the two component problems, LTD and RWA, in greater detail

Lightpath Topology Design

We now consider a specific, though rather simplified, lightpath topology design problem and examine how it can be solved We will assume that no constraints are imposed by the underlying fiber topology or the optical layer (Examples of such constraints are a limit on the length of a lightpath and a limit on the number of lightpaths traversing a link.)

We assume that all lightpaths are bidirectional (see Section 8.2.2); that is, if we use a lightpath from node i to node j, then we also use a lightpath from node j

to node i This is the case that most frequently occurs in practice since almost all higher-layer protocols, including IP and SONET, assume bidirectional physical layer links

One constraint is that at each node we use an IP router with at most A ports connecting it to other IP routers (In addition, each router would have local interfaces

to Ethernet switches and the like.) This constrains the maximum number of ports per router to A and thus indirectly constrains the cost of the IP routers This also constrains the number of lightpaths in the network to hA, where n is the number

of nodes in the network, since each lightpath starts and ends at an IP router port This constraint is equivalent to a constraint on the lightpath costs if we assume that the tariff for a lightpath is the same regardless of its end points This is an assumption that would clearly not hold in a wide-area environment where we expect longer lightpaths to be more expensive than shorter ones However, it may hold in

a regional network (Many phone companies offer a single rate for all calls made within their region So it is not inconceivable that we could have a single tariff for all lightpaths within a region.) The main reason for the assumption, of course, is that it simplifies the problem

When we design the lightpath topology, we also have to solve the problem of routing packets (or connections) over the lightpath topology This is because whether

or not a given (lightpath) topology supports the traffic requirements depends on both the topology itself and the routing algorithm that is used

To formulate the problem in mathematical terms, we need to introduce a number

of definitions We assume a statistical model for the IP packet traffic: the arrival rate for packets for source-destination (s-d) pair (s, d ) is U d (in packets/second),

s, d - 1 n b i j , i, j - 1 n, i ~ j , are n 2 binary valued (0 or 1) variables, one for each possible lightpath, bij = 1 if the designed lightpath topology has a link from