Wide-Sense Nonblocking Multicast in WDM Optical Linear Array and

Ring Networks with 3-Length Extension

M. SABRIGIRIRAJ1 K. MANOHARAN2 R. KARTHIK3,

Abstract: - The modern scientific growths in optical networks based on wavelength division multiplexing

networks are extended by directly linking all nodes which are separated by two intermediate nodes with

additional fibers which is referred as linear array and ring network with 3-length extension. The necessary and

sufficient condition on the minimum wavelength number along with wavelength allotment methods are

proposed to realize one-to-many communication over such a WDM optical linear array and ring with 3-length

extension under longest link first routing techniques.

Key-Words: -Wavelength Division Multiplexing (WDM), Multicast, WDM Optical Network, Wavelength

Assignment, Longest Link First Routing

Received: September 15, 2021. Revised: May 12, 2022. Accepted: June 7, 2022. Published: July 5, 2022.

unlimited potential to satisfy the future bandwidth

requirements. WDM optical networks act as the

backbone for telecommunication and high-

performance communication networks. An optical

network is a most commonly and widely employed

communication system that uses light signals to

transmit information between two or more points.

Optical networks are based on optical technologies

and components, and are used to route, groom, and

restore wavelength levels and wavelength-based

type of multicast communication and is used in this

study. Multicast assignment involves establishing

connections between various nodes of a network in

such a way that each destination node should be

connected to only one source node, whereas each

source node may be connected to one or more

destination nodes. All forms of multicast

communication can easily be broken down into

multiple multicast assignments. Due to the absence

of optical buffering at the optical nodes, it is

connections. Such networks are said to be wide-

sense nonblocking [1-6], if the connections are

established by a definite routing algorithm.

studied in electronic switching networks [2] and

network topologies namely linear array, ring, torus,

mesh and hypercube [1].Wide-sense nonblocking

multicast and strict-sense nonblocking multicast is

studied for clos networks [5] and elastic optical

switch [6]. Multicast communication is alsostudied

Linear array [13-17] and ring networks [18-

22] are the basic network topologies suitable for

interconnection networks and for LAN and

WAN.The linear array and ring networks are widely

adopted for LAN, MAN and WAN and also used

ininterconnection networks due to its regularity and

small node degree. The wide-sense nonblocking

multicast communication[23-33] in WDM networks

condition over the minimum wavelength number

needed for the network to be wide sense

nonblocking. Explicit wavelength allotment

techniques are also proposed for each of the network

topologies. The results obtained in this paper can be

applied for practical long-haul networks like mesh

network, since mesh network can be decomposed

into multiple linear array and/or ring networks.

In Section 2, the preliminaries needed to

nonblocking multicast under longest link first

routing is derived and explicit wavelength allotment

techniques are given. Section 4, discusses the result

obtained for the 3-length extension networks.

Finally, section 5, the inference of this paper is

presented highlighting future research direction.

2 Preliminaries

Figure 1 shows a 10-node basic linear array

network. Figure 2 shows 16-node linear array

after 2 nodes away from it. At each node x, data can

vice-versa.

Figure 1. A 10-node basic linear array

Figure 2. A 16-node linear array with 3-length

extension

which is 2 nodes away from it in a basic ring. That

is, each node in the ring is additionally connected to

a node which is placed at the distance of 3 nodes

away from it. At each node, data can directly move

modulo addition of N.

Figure 3. A-12 node basic ring

Figure 4. A-12 node ring with 3-length extension

condition on the minimum wavelength number

required for the network to be wide-sense

nonblocking is derived for linear array,

unidirectional ring and bidirectional ring networks

with 3-length extension under longest link first

routing technique.

Figure 2 shows a 16-node linear array with 3-length

Theorem 1: The sufficient and necessary condition

on the wavelength number for a N node linear array

with 3-length extension to be wide-sense non-

sufficient and necessary condition on the

wavelength number.

Wavelength allotment technique

routing to use minimum number of hops. Theorem

2 is proved based on this assumption.

Theorem 2: The sufficient and necessary condition

on the wavelength number for an N node

unidirectional ring with 3-length extension to be

between various sources and destinations are routed

network, a particular wavelength can be allotted for

multiple lightpaths as long as they do not overlap

with one another. A wavelength released by a

current lightpath during its termination can be again

already existing lightpaths sharing a particular link

in the same direction. To establish the current

connection request, one more lightpath is needed.

connection requests.

multicast assignment can be of the form with 0 as

the source and all other nodes are its destinations

along with another lightpath with 0 as destination

for an arbitrary source. All lightpaths with source

index 0 and destination index greater than 2 use the

longer link joining nodes 0 with 3. The total number

wavelength number.

Wavelength allotment technique

used for managing wavelength allotment to light-

Let x and y be the index of source and destination

node respectively. Then, the wavelength allotment

Tc2.

Tc2.

3.3 Bidirectional ring with 3-length extension

Figure 4 shows a12-node ring with 3-length

hops. Theorem 3 is proved based on this

assumption.

Theorem 3: The sufficient and necessary condition

on the wavelength number for a N node

wide-sense non-blocking is󰇵

Proof:

Sufficiency: All the lightpaths between various

sources and destinations are routed only in the

shortest path direction. If the length of lightpath is

same in both clockwise and anticlockwise direction,

then clockwise direction is always followed. For a

lightwave network, a particular wavelength can be

allotted for multiple lightpaths as long as they do

link in the same direction. To establish the current

connection request, one more lightpath is needed.

So, 󰇵

connection requests.

Necessity:

Case i: N is even: Consider a worst-case multicast

assignment of the form󰇛  󰇜     .

The first group of lightpaths of the form 󰇛   󰇜

namely 󰇛  󰇜 and 󰇛   󰇜 does not share

any link with any of the lightpaths of the previous

group. Therefore, these two lightpaths can be

assigned any two wavelengths from the wavelengths

assigned from the first group.

Hence,

lightpaths of multicast assignment, if N is even.

Case ii: N is odd: Consider a worst-case multicast

This necessitates 

of lightpaths namely 󰇛  󰇜 and 󰇛   󰇜

does not share any link with any of the lightpaths of

the previous group. Therefore, these two lightpaths

can be assigned any two wavelengths from the

wavelengths assigned from the first group.

Hence,

Hence,󰇵

node respectively. Then, the wavelength allotment

procedure for any connection request (x, y) is based

on the index of the destination node which is

mapped to a particular wavelength. The destination

node index to wavelength index mapping is as given

in table 1.

Table 1 The destination node index to wavelength

index mapping.

ring and bi-directional ring with 3-length extensions

when compared with their basic counterpart.

Future work includes extending this study of

wide-sense nonblocking multicast communication

for WDM optical linear array and unidirectional and

bidirectional ring with 4-length and higher length

extensions.

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