Brief description
Given a network topology, the capacities in the links and the offered traffic, this algorithm obtains the traffic routing that minimizes the average number of hops using a flow-path formulation. For each demand, the set of admissible paths is composed of the ranking of (at most) k-shortest paths in km, between the demand end nodes. k is a user-defined parameter. Paths for which its propagation time sums more than maxPropDelayMs, a user-defined parameter, are considered not admissible. The routing may be constrained to be non-bifurcated setting the user-defined parameter nonBifurcated to true
Algorithm description table
| Algorithm inputs | Requires a topology (nodes and links) and a demand set within the netPlan object. Algorithm parameters:
|
|---|---|
| Algorithm outputs | Routes are added to netPlan object. No protection segments are defined. Any previous routes are removed. |
| Required libraries | JOM library for solving the optimization problem |
| Keywords | Flow assignment (FA), JOM, LP formulation, MILP formulation |
| Authors | Pablo Pavón Mariño, José Luis Izquierdo Zaragoza |
| Date | May 2013 |
| Code | FA_minAvNumHops_xp.java |
Detailed description
The algorithm solves the following formulation:
Given:
- \( D \): The set of demands comprising the offered traffic. For each demand \( d \in D \), \( h_d \) is the demand volume, and \( a(d) \) and \( b(d) \) denote the input and output node of the demand.
- \( G(N,E) \): The network topology, where \( N \) is the set of nodes, and \( E \) the set of unidirectional network links. For each link \( e \in E \), \( a(e) \) and \( b(e) \) denote its input and output nodes, \( u_e \) the link capacity (in the same units as the offered traffic). For each node \( n \in N \), \( \delta^+(n) \) and \( \delta^-(n) \) denote the set of links outgoing and incoming node \( n \), respectively.
- \( P \): A list of candidate paths for each demand
Find:
- \( x_{p} , p \in P \): Fraction \( \in [ 0 , 1 ] \) of the traffic of demand \( d \) that traverses path \( p \). If the routing is non-bifurcated, this variable is constrained to get integer numbers: \( x_{p} \in \lbrace 0 , 1 \rbrace \).
- \( y_{e}, e \in E \): Amount of carried traffic (in Erlangs) for link \( e \).
\(
\text{minimize } \left( \frac{\sum_{e \in E}y_e}{\sum_{d \in D} h_d} \right) \text{ subject to: } \\
\sum_{p \in P_{d}} x_{p} = 1 \quad \forall d \in D \\
\sum_{d\in D}h_{d} \sum_{p \in P_{e}\cap P_{d}} x_{p} = y_{e} \quad \forall e \in E \\
y_{e} \leq u_{e} \quad \forall e \in E \\
0 \leq x_{p} \leq 1 \quad \forall p \in P \\
x_{p} \in \lbrace 0 , 1 \rbrace \quad \forall p \in P \text{ (if routing is non-bifurcated) }
\)
