Routing and Spectrum Assignment (RSA)

RSA in an Elastic Optical Network

A request to establish an optical channel specifies a pair of nodes and a required data rate. For example, an operator may need to create a high-capacity link between a company headquarters and a data center through an existing fiber grid. The algorithm must choose a route in the fiber graph and assign a block of frequency slots whose width follows from the data rate, modulation format, and forward-error-correction overhead. These two decisions form the Routing and Spectrum Assignment (RSA) problem.

RSA is the central optimization challenge in Elastic Optical Networks (EON). A request specifies a source node, a destination node, and a data rate, for example 400 Gbps. A flexible grid can match channel width to the demand instead of reserving one fixed WDM channel for every connection. The algorithm searches for a route and a free block that satisfies contiguity, continuity, and non-overlap requirements. An assignment for one connection changes the spectrum fragmentation seen by later requests, so route and spectrum choices must be considered together. Requests may arrive dynamically, so an assignment must be feasible at decision time rather than after rebuilding the network. The model also checks slot availability on every link and compatibility between the transponder and the selected format. A formally free slot is not sufficient when the transmission budget is exceeded. If no common contiguous block remains on all links, the request is blocked even when the total number of free slots is large.

RSA constraints

An RSA model contains three resource constraints: contiguity within a channel, continuity along its route, and non-overlap with other assignments on the same link.

• 1

  Slot contiguity within a channel

  The slots assigned to one channel must form one unbroken block. If four slots are required, slots 50, 51, 52, and 53 satisfy the condition, while slots 50, 51, 54, and 55 leave a forbidden gap. Optical switching hardware handles continuous spectrum segments, so scattered slots do not form one channel. The block width follows from the requested data rate and the transponder parameters.

• 2

  Slot continuity along the route

  In a transparent channel, the spectrum assignment must remain compatible on every link of the selected route. If a connection between Warsaw and Berlin receives slots 100 through 105 on its first link, the same block must remain available on the following links. The simplest variant keeps the same center frequency and slot width along the path. A network with spectrum conversion can change the slot position between hops while keeping the required width. Without that function, the range cannot move in the middle of the route. The continuity constraint therefore follows from node capabilities as well as from the selected path.

• 3

  Non-overlapping slots

  Two different connections using the same physical fiber link cannot share the same slots. Their blocks must be disjoint to limit interference between signals and prevent overlapping channels. An operator can add a small Guard Band between adjacent connections. In practice, a guard band contains one or more empty slots, and its width depends on the equipment and transmission profile.

Reach and modulation in RSA

Route selection connects spectrum assignment with the transmission budget. A longer route adds attenuation and accumulated noise, so modulation profiles with higher bits per symbol usually have shorter reach. More complex formats are more sensitive to noise. Feasibility also depends on optical signal-to-noise ratio and chromatic-dispersion limits.

In an RSA workflow, the modulation format affects the number of slots required for a given data rate. The route must also satisfy the reach limit associated with that profile.

Example of the dependency for a selected rate-reach table:

The slot count depends on slot width, symbol rate, FEC coding, and transponder parameters. The values below are assumed for this table.

• A request for a 200 Gbps connection arrives.
• The routing algorithm finds two possible paths: a short, direct path of 500 km and a longer backup path of 1500 km. It checks the length and transmission-quality limits of each path, including OSNR and chromatic dispersion.
• In the selected rate-reach table, the short path allows 16-QAM. The 200 Gbps request can then require 4 frequency slots, which must be available across the 500 km path.
• The longer path is beyond the reach of 16-QAM and requires a more tolerant format such as QPSK. The same 200 Gbps rate can then require 8 frequency slots, so the algorithm searches for a wider block on the 1500 km path.

The shortest path does not always minimize occupied spectrum. The result depends on free blocks, transmission quality, and the objective selected by the operator.

Mathematical model of RSA

One way to describe the RSA problem is Integer Linear Programming (ILP). The model contains decision variables, an objective function, and constraints that enforce a valid route and spectrum assignment. All relationships remain linear, while variables describing used links and slot-block boundaries are integer or binary values.

Decision variables

The variables describe the route and the position of the assigned slot block.

• $x_{ij}$: A binary variable. $x_{ij} = 1$ if the path for the connection uses the fiber link from node $i$ to node $j$; otherwise, $x_{ij} = 0$. This variable defines the route.
• $f_a, f_b$: Integer variables that identify the first ($f_a$) and last ($f_b$) slot in the block assigned to the connection. They define the spectrum assignment.
• Additional helper variables like $x'_{ij,l}$ (choosing a specific free block $l$ on link $ij$) and $c^k_{ij}$ (indicating if slot $k$ on link $ij$ is used) are also needed for a complete model.

Objective function

One example minimizes the total length of the selected path:

The sum contains the distances ($d_{ij}$) of links in the network graph ($E$). The variable $x_{ij}$ includes only links belonging to the selected path ($x_{ij}=1$).

Path length is one possible objective. In a congested network, a shorter path can have fewer free blocks, so the objective can also account for occupied spectrum, fragmentation, or blocking probability.

Model constraints

The constraints enforce a valid route and a compatible spectrum assignment.

• Flow conservation: These equations ensure that the chosen links form a path from the source ($s$) to the destination ($d$). At an intermediate node, the number of used incoming links equals the number of used outgoing links.
  $\sum_i x_{ij} - \sum_k x_{jk} = \begin{cases} -1, & \text{if } j=s \\ 1, & \text{if } j=d \\ 0, & \text{otherwise} \end{cases}$
• Slot count: The number of slots follows from the requested capacity $C$ and the capacity of one slot for modulation format $m$.
  $f_b - f_a + 1 = \lceil \frac{C}{C_{slot}(m)} \rceil + G$
  Here, $C_{slot}(m)$ is the capacity of one slot for modulation format $m$, and $G$ is the guard band. A separate non-overlap constraint prevents different connections from using the same slots on one link.
• Continuity and contiguity: These constraints ensure that a compatible block ($f_a, f_b$) is used on the route links ($x_{ij}=1$) and that its slots are adjacent.