Multi-Domain Network Dimensioning

A dynamic network domain must be dimensioned for both inter-domain and intra-domain traffic. Inter-domain traffic is routed through its border nodes: the selection of border nodes is thus critical to the performance and fairness for both domains. Such routing introduces additional loads between inter- nal nodes and border nodes in each network domain. This section discusses general multi-domain dimensioning algorithms. For illustration purposes, all discussions are presented for two-domain scenarios, but my results can be readily extended to an arbitrary number of domains using standard informa- tion sharing/hiding techniques, e.g., topology aggregation or virtual topology abstraction.

I assume that every node in each domain can initiate Poisson arrivals to all other nodes in the same domain and to all other nodes in the other domains (equivalent to a full-mesh demand). Domains are joined through their border nodes, on which each border node is connected to a border in the other domain. In most cases, the number of border nodes in both domains is the same. A link connects each pair of border nodes (as shown in Figure 7.1). In practice, it is possible for some border node pairs to be located in the same building/site. In such cases, they may be viewed logically as a single node with finite capacity (equal to the inter-domain link capacity). In fact, the mapping of border nodes between two domains may also not be one-to- one; however, such variations do not affect how dimensioning and routing techniques are designed.

Dimensioning for external traffic for each domain can be treated as dimen- sioning for additional traffic between each pair of internal nodes to border nodes. I separate the capacity of external and internal traffic loads for the purpose of analysis: in practice, the wavelength resources are shared and no distinction in usage is made. I also define the capacity CI

b for the inter-

domain links that connect border node pairs. Each dynamic connection pair (internal or external) has arrival/departure/capacity rates defined.

The intra-domain traffic matrix is defined as it is for a single domain (Chapter 3). Let T ={(λ, µ)}R _{be the traffic matrix, where λ is the arrival}

domain and S be the set of nodes in the other domain. The external traffic matrix is defined by T′ _{={(λ, µ)}}N ×S_{, where the same arrival and departure}

rates, λ and µ, apply for each external request pair. On a given domain, all external traffic comes from its border nodes. Let N′ _{be the set of border}

nodes. The equivalent external traffic on the local network is modeled by a traffic matrix, T′

L, in which the arrival and departure rates between all nodes

n ∈ N and all borders b ∈ N′ _{are defined and the elements are indexed by}

(n, b). The traffic load between any external node s and local node n can come from any one of the borders. Let pn,s,b be the probability that traffic

between n and s comes from border b, such that P_b∈N′pn,s,b = 1. Therefore,

the equivalent external arrival rate for n and b is an aggregated arrival rate of all external nodes, weighted by the probability, pn,s,b. Equation 7.1 presents

the equivalent external traffic matrix on the local network. The entire traffic matrix is then the sum of T and T′

L for the same pair of nodes.

T_L′ =_{(X s∈S λpn,s,b, X s∈S µpn,s,b)}N ×N ′ (7.1)

The projected load of a network is the amount of traffic that the total given network capacity can support without being overloaded. Equation 7.2 defines the projected load for internal traffic. It is the ratio of average traffic load (stochastic arrival/departure rate times the topological shortest path lengths) to the total available network capacity. Topological Shortest Length (TSL) is the minimum number of hops for a connection in an empty network; obviously, available shortest paths selected on residual networks can be longer than their TSL. For external traffic, the average amount of resources used for each connection is the average shortest path lengths to all border nodes. Equation 7.3 defines the external traffic load. All dimensioning techniques use the same load metrics for fair comparison.

proj loadint = λ µ P i∈RT SLi P e∈ECe (7.2)

proj loadext=

|N||S|λ µ P b∈N′ T SL(n,b) |N′_| P e∈ECe′ (7.3) Note that dimensioning a network domain to support traffic to the other domain can be the same as dimensioning a single network with an estimate

of external traffic distribution on borders. I use the basic dimensioning algo- rithm (Algorithm 3.2) to dimension each network separately, using the sum of T and T′

L. The external load (so as to the total capacity) on each domain

network remains the same regardless of dimensioning algorithms. Using a similar dimensioning approach, the capacity of inter-domain links is deter- mined according to Equation 7.4.

C_bI =jλ µ X n∈N X s∈S pn,s,b k (7.4)