Metrics

To quantitatively assess the performance of Network Function Virtualization Resource Allocation (NFV-RA) algorithms, Virne employs a suite of critical and commonly used performance metrics. These metrics provide insights into the effectiveness, efficiency, and economic viability of different allocation strategies. The definitions for these metrics are detailed in Appendix C.4 of our research paper.

Core Performance Metrics

Request Acceptance Rate (RAC)

The Request Acceptance Rate (RAC) measures the proportion of Virtual Network (VN) requests that the system successfully accepts and embeds over a total operational period. A higher RAC indicates better resource utilization and service provisioning capability.

Formally, it is given by:

\[RAC = \frac{\sum_{t=0}^{\mathcal{T}}|\tilde{\mathcal{I}}(t)|}{\sum_{t=0}^{\mathcal{T}}|\mathcal{I}(t)|} \times 100\%\]

where:

  • \(\mathcal{T}\) is the total operational time of the network system.

  • \(\mathcal{I}(t)\) is the set of all VN requests arriving at time slot \(t\).

  • \(\tilde{\mathcal{I}}(t)\) is the subset of VN requests arriving at time slot \(t\) that are successfully accepted.

  • \(|\cdot|\) denotes the cardinality of a set.

Long-term Revenue-to-Cost Ratio (LRC)

The Long-term Revenue-to-Cost Ratio (LRC) evaluates the economic efficiency of the NFV-RA strategy by comparing the cumulative revenue generated from accepted VNs to the cumulative cost of the resources consumed for their embedding over a period. A higher LRC signifies greater profitability and resource efficiency.

It is formulated as:

\[LRC = \frac{\sum_{t=0}^{\mathcal{T}}\sum_{I \in \tilde{\mathcal{I}}(t)} REV(S) \times \varpi}{\sum_{t=0}^{\mathcal{T}}\sum_{I \in \tilde{\mathcal{I}}(t)} COST(S) \times \varpi}\]

where:

  • \(S = f_{\mathcal{G}}(I)\) is the embedding solution for an instance \(I\).

  • \(REV(S)\) is the revenue generated by embedding VN \(\mathcal{G}_v\) (typically the sum of its requested resources).

  • \(COST(S)\) is the resource consumption in the PN due to embedding \(\mathcal{G}_v\) (typically the sum of its node resources and bandwidth resources scaled by path length).

  • \(\varpi\) is the lifetime of the corresponding VN.

Long-term Average Revenue (LAR)

The Long-term Average Revenue (LAR) quantifies the average revenue generated by the system per unit of time over a period, reflecting the economic benefits of processing VN requests.

It is defined as:

\[LAR = \frac{1}{\mathcal{T}}\sum_{t=0}^{\mathcal{T}}\sum_{I \in \tilde{\mathcal{I}}(t)} REV(S) \times \varpi\]

where symbols are as defined previously.

Average Solving Time (AST)

The Average Solving Time (AST) measures the average computational time (typically in seconds) an NFV-RA algorithm takes to find a solution for a single VN request or simulation run. This metric is crucial for assessing the algorithm’s efficiency and its suitability for online, real-time decision-making environments. Lower AST values are generally preferred, especially for dynamic scenarios.

Metric Categories

Performance Dimensions

These metrics collectively cover three essential performance dimensions:

Economic Efficiency

  • LRC and LAR provide insights into the financial viability and profitability of embedding strategies.

Service Quality

  • RAC reflects the system’s ability to satisfy incoming service demands and maintain high service availability.

Computational Efficiency

  • AST evaluates the practical feasibility of algorithms for real-time deployment scenarios.

Note

When analyzed together, these metrics provide a comprehensive understanding of an algorithm’s performance characteristics within the Virne benchmark, enabling fair comparison across different NFV-RA approaches.