Virtual Network Function Placement
- Virtual Network Function (VNF) placement is the process of selecting NFV-capable nodes to host VNFs while maintaining the required service order.
- It combines strategies for node selection, VNF allocation, and routing to minimize costs, latency, and resource usage using methods like ILP, MILP, and heuristics.
- Recent advances integrate dynamic, online, and machine-learning driven approaches to adapt placements in diverse environments such as cloud, edge, and satellite networks.
Virtual Network Function (VNF) placement denotes the decision problem of instantiating software-based network functions on substrate nodes and steering traffic through them in the required order. In the literature, that order is expressed as a Service Function Chain (SFC), a VNF-Forwarding Graph (VNF-FG), or a service graph, and the optimization typically combines node selection, VNF allocation, and routing under capacity and QoS constraints. Across the cited work, VNF placement is formulated as MIQCP, ILP, MILP, LP, or integer nonlinear programming, and it is repeatedly characterized as NP-Hard or NP-complete (Mehraghdam et al., 2014, Attaoui et al., 2022, Wang et al., 2022).
1. Conceptual scope and service representations
The canonical setting treats a physical network as a graph and places an ordered sequence of VNFs on NFV-capable nodes while routing traffic between consecutive functions. In “Multiple Service Chain Placement and Routing in a Network-enabled Cloud” (Gupta et al., 2016), a configuration for a chain specifies both the placement of each VNF on NFV nodes and the internal chaining routes between consecutive VNFs. This is representative of a large part of the literature: placement is not only host selection, but also chain realization.
The representation of the requested service varies substantially. “Specifying and Placing Chains of Virtual Network Functions” (Mehraghdam et al., 2014) formalizes chaining requests with a context-free language whose modules include order, optional order, split, and parallel constructs; the request is then expanded into one or more candidate VNF DAGs and mapped to the network. In NFV-based hybrid cloud/fog systems, requests are modeled as a tree whose leaves are VNFs and whose internal nodes are the control sub-structures seq, par, sel, and loop (Mouradian et al., 2019). In CDN value-added services, requests are VNF-FGs with an ordered set of VNF types and one endpoint corresponding to a content server that is unknown prior to placement (Jahromi et al., 2018).
More recent work enlarges the scope further by making the service representation itself a decision variable. “Optimizing Service Function Chain Mapping in Network Function Virtualization through Simultaneous NF Decomposition and VNF Placement” (Asgharian-Sardroud et al., 2024) allows each high-level NF to be decomposed in several ways into primitive NFs, with the decomposition represented as a directed acyclic graph and optimized jointly with host placement. Taken together, these models suggest that VNF placement has evolved from a simple chain-embedding problem into a broader mapping problem over chains, DAGs, trees, and decomposition alternatives.
2. Objective functions and constraint systems
Objective functions differ by deployment context, but they are consistently multi-criteria. One representative multiobjective formulation minimizes total mapping-cost and total communication-latency,
thereby coupling host-resource prices with propagation latency (Asgharian-Sardroud et al., 2024). Other models minimize total bandwidth consumption measured as bandwidthdistance (Gupta et al., 2016), total reconfiguration expense composed of hosting, migration, instantiation, and routing costs (Jahromi et al., 2018), a weighted aggregation of makespan and application execution cost plus deployment cost (Mouradian et al., 2019), the number of active NFV nodes (Savi et al., 2017), or a weighted sum of service delay and resource consumption cost (Wang et al., 2022). In satellite edge computing, the objective may instead maximize a normalized network payoff that incorporates bandwidth, power, and delay costs (Gao et al., 2020).
The constraint structure is correspondingly rich. Typical formulations enforce exact-one placement for each required VNF, server capacity bounds on CPU, memory, and storage, VNF processing-capacity limits, link bandwidth or link-capacity bounds, flow-conservation constraints, preservation of chain order, and end-to-end latency or QoS bounds (Gupta et al., 2016, Jahromi et al., 2018, Asgari et al., 2021). Some settings add admission variables for requests, content-server selection constraints, or coupling constraints between old and new snapshots so that reuse and migration can be modeled explicitly (Jahromi et al., 2018). In multi-domain or path-based formulations, routing variables are further tied to placement variables so that chosen paths are consistent with the locations of consecutive VNFs (Gao et al., 2021).
Several papers refine the resource model beyond raw capacity accounting. “Impact of Processing-Resource Sharing on the Placement of Chained Virtual Network Functions” (Savi et al., 2017) introduces context-switching costs and upscaling costs, so that latency and available CPU depend on how many VNF processes share a node and on how heavily a VNF is spread across cores. “Probabilistic QoS-aware Placement of VNF chains at the Edge” (Forti et al., 2019) treats node capacities and link QoS as probability distributions and evaluates placements by the probability that hardware, IoT, security, bandwidth, and latency constraints hold. “Placement and Allocation of Virtual Network Functions: Multi-dimensional Case” (Sallam et al., 2019) models each flow as consuming multiple resource types through per-resource demands , while “Online Joint Placement and Allocation of Virtual Network Functions with Heterogeneous Servers” (Xu et al., 2020) uses an arbitrary nondecreasing, left-continuous capability cost function to capture heterogeneous server cost-capacity profiles. A plausible implication is that the dominant abstraction is no longer single-resource bin packing, but constrained multi-resource orchestration.
3. Exact formulations, decomposition methods, and approximation frameworks
Exact mathematical programming remains central. The literature includes MIQCP for chain specification and mapping (Mehraghdam et al., 2014), ILP for multiple service chain placement and routing (Gupta et al., 2016), ILP for online CDN reconfiguration (Jahromi et al., 2018), MILP for joint decomposition and mapping (Asgharian-Sardroud et al., 2024), LP for placement with replication (Carpio et al., 2017), and integer nonlinear programming for collaborative satellite edge/cloud placement (Gao et al., 2021). These formulations are valuable as optimization baselines, but the reported runtimes also make their scalability limits explicit. In the chain-specification study, three requests of size six with two optional sub-modules each yielded candidate DAGs; full enumeration took h, while a sorting heuristic returned a solution in min (Mehraghdam et al., 2014). In the hybrid cloud/fog setting, exact ILP became infeasible beyond requests/20 nodes with run-times day (Mouradian et al., 2019). In the replication study, the MIP required s on Nobel-us, 0 min on Janos-us, and timed out or exceeded 1 h on Janos-us-CA and beyond (Carpio et al., 2016).
The main algorithmic families represented in the cited literature are summarized below.
| Method class | Representative techniques | Example papers |
|---|---|---|
| Exact mathematical programming | MIQCP, ILP, MILP, LP, INLP | (Mehraghdam et al., 2014, Gupta et al., 2016, Asgharian-Sardroud et al., 2024, Carpio et al., 2017, Gao et al., 2021) |
| Structured decomposition and relaxations | Column generation; two-level relaxation with sequence submodularity; regularization-based one-shot optimization with dependent rounding | (Gupta et al., 2016, Sallam et al., 2019, Jia et al., 2016) |
| Heuristic and metaheuristic search | GA, RFPA, TSCP, NSGA-II, PSO | (Carpio et al., 2016, Mouradian et al., 2019, Asgharian-Sardroud et al., 2024, Asgari et al., 2021) |
Among decomposition methods, column generation is especially prominent. The network-enabled cloud model starts from a restricted master problem and pricing subproblems per chain, adds negative reduced-cost configurations iteratively, and solves the final master problem as an integer program (Gupta et al., 2016). The multidimensional placement-and-allocation work uses a two-level relaxation, connects the resulting objective to sequence submodularity, and derives approximation algorithms via Sequence-Submodular Greedy plus primal-dual allocation (Sallam et al., 2019). Such formulations are significant because they preserve structural constraints that simple greedy packing would discard, yet avoid the full monolithic search space.
Approximation and search methods are equally important when placement must absorb nonconvex constraints or large deployment scopes. “Replication of Virtual Network Functions: Optimizing Link Utilization and Resource Costs” (Carpio et al., 2017) balances link-utilization cost against the number of used nodes in an LP, while the related comparison of LP, GA, and RFPA provides a heuristic route for larger topologies (Carpio et al., 2016). “Performance-aware placement and chaining scheme for virtualized network functions: a particle swarm optimization approach” (Asgari et al., 2021) solves integrated placement and chaining with PSO and a combined objective over active servers, average propagation delay, and average link utilization. A plausible implication is that VNF placement research is shaped less by a single dominant solver than by recurring attempts to retain enough structure for good solutions while shrinking the search space.
4. Online, adaptive, and data-driven placement
Static planning is only one part of the problem. “Online Scaling of NFV Service Chains across Geo-distributed Datacenters” (Jia et al., 2016) explicitly argues that existing efforts on VNF placement mostly deal with offline or one-time placement and ignore dynamic deployment and scaling under time-varying traffic volumes. Its online algorithm combines a regularization-based approach from online learning literature with an online dependent rounding scheme so that each time slot solves a one-shot regularized problem and feasible integer solutions are maintained across the time horizon. In a different dynamic setting, the CDN reconfiguration model minimizes the differential costs between old and new snapshots and reported total reconfiguration cost \$\times$2550 without reuse in scenario 1; it also observed migration cost $\times$3 in all runs, because the solver preferred fresh instantiation or reuse in place (Jahromi et al., 2018).
Heterogeneity and online arrival further complicate the model. OJPA-HS generalizes classical JPA-VNF by allowing heterogeneous servers and defining cost through a capability function $\times$4; it states that no deterministic online algorithm can achieve a bounded competitive ratio, then gives a stepwise-optimal dynamic program together with Las Vegas and Monte Carlo randomized heuristics (Xu et al., 2020). In the reported experiments on 35 instances with $\times$5 and $\times$6, DP average time was $\times$7 s, LV was $\times$8 s, and LV cost stayed within $\times$9–$\delta_f^r$0 of DP.
Data-driven methods replace explicit combinatorial search by learned decision rules or adaptive policies. “Machine Learning for Performance-Aware Virtual Network Function Placement” (Manias et al., 2020) trains a multi-output CART decision tree on 10 000 placement instances per topology labeled by BACON, reports stable 10-fold cross-validation, and achieves sub-millisecond query time per SFC; on the medium topology it produced a larger fraction of paths under a 2000 ms threshold. “Virtual Network Function Placement in Satellite Edge Computing with a Potential Game Approach” (Gao et al., 2020) formulates placement as an exact potential game and uses PGRA to reach a Nash equilibrium; with $\delta_f^r$1 satellites it admitted $\delta_f^r$2 of users versus $\delta_f^r$3 for Viterbi and $\delta_f^r$4 for Greedy, and typically converged in 10–20 iterations to within $\delta_f^r$5. “Multi-Agent Deep Reinforcement Learning for Cost- and Delay-Sensitive Virtual Network Function Placement and Routing” (Wang et al., 2022) decomposes the joint problem into placement and routing subtasks handled by $\delta_f^r$6 DDPG agents, reports performance within 5–10% of optimal, serves $\delta_f^r$7–30% more total data rate, admits $\delta_f^r$8–25% more requests before resources saturate, and accelerates retraining by $\delta_f^r$9 when adding 5 links. These results do not remove the need for constraint modeling, but they show that adaptive placement has become a distinct line of research rather than a minor extension of offline optimization.
5. Deployment settings and domain-specific formulations
A striking feature of the literature is the diversity of deployment environments. In a network-enabled cloud, multiple service chain placement and routing is treated as a problem of minimizing network resource consumption, and the reported conclusion is that a Network enabled Cloud results in lower network resource consumption than a centralized NFVI while avoiding infeasibility with a distributed NFVI; adding a central DC reduced consumed bandwidth by 10–20% over a pure DC approach (Gupta et al., 2016). Geo-distributed datacenters appear in the online scaling model, where dispersed source and destination pairs and time-varying traffic volumes drive the need for slot-by-slot reoptimization (Jia et al., 2016).
CDN models introduce a distinctive asymmetry: one endpoint may be unknown before placement because the content server is chosen later. “CPVNF: Cost-efficient Proactive VNF Placement and Chaining for Value-Added Services in Content Delivery Networks” (Dieye et al., 2018) therefore places VNFs proactively, minimizing total provider cost while meeting QoS, and its simulations showed that CPVNF uses slightly fewer surrogate servers than ILP but incurs higher communication cost while remaining scalable to larger CDN sizes. The online CDN model extends this by allowing reuse and migration of already-deployed VNFs, with the objective of minimizing reconfiguration cost while satisfying QoS (Jahromi et al., 2018). Together, these works show that content placement and VNF placement are coupled whenever the service ingress is not fixed in advance.
Edge and fog settings emphasize locality, mobility, and uncertainty. In the hybrid cloud/fog model, expected communication latency and transmission cost are computed under the random waypoint mobility model for fog nodes, and the TSCP heuristic achieved a gap from optimal of < 8% on small scale; accounting for fog mobility yielded up to 25% additional gain over models that assume static fog nodes (Mouradian et al., 2019). EdgeUsher approaches the same general problem declaratively: it models dynamic node capacities and link QoS by probability distributions, determines all eligible placements satisfying hardware, IoT, security, bandwidth, and latency requirements, and ranks them by probability of success; on the UC Davis campus Edge testbed it enumerated 4 296 placements in 2 h 48 m without heuristics, but with TH=0.8 it returned 6 placements in 47 s (Forti et al., 2019).
Satellite edge and edge-cloud systems sharpen the resource problem further. “A Distributed Virtual Network Function Placement Approach in Satellite Edge and Cloud Computing” (Gao et al., 2021) combines distributed Viterbi-based edge placement with cloud path selection, treating end-to-end delay as primary and bandwidth usage as secondary; in static experiments it reduced bandwidth by ~21.14 % versus Greedy and ~13.51 % versus Viterbi, while reducing delay by ~4.38 % and ~3.80 %, respectively. This suggests that the environmental context is not incidental: it determines whether the dominant scarcity is compute, bandwidth, latency budget, mobility stability, or reliability under stochastic variation.
6. Trade-offs, misconceptions, and open directions
The core trade-offs of VNF placement recur across otherwise different models. Replication is a clear example. “Replication of Virtual Network Functions: Optimizing Link Utilization and Resource Costs” (Carpio et al., 2017) shows that enabling 1 replica reduced the maximum link utilization by up to ~15–20 % at the cost of using ~2 extra DCs on average, while a second replica yielded only marginal further improvement (<5%); its practical guideline is that a single replica per replicable VNF is often sufficient. The related LP/GA/RFPA comparison reported GA cost at 0 optimal, RFPA cost starting at 1 that of MIP, and a cost reduction of 2 with two replicas in the MIP baseline (Carpio et al., 2016). The controversy is therefore not whether replication helps, but how much replication is operationally justified once server footprint is priced explicitly.
Consolidation creates an equally important counter-pressure. The processing-resource-sharing model identifies two penalties—context-switching costs and upscaling costs—and reports that even small per-process context-switch latencies 3 ms force more distributed placements for latency-tight chains; it also states that a state-of-the-art node-latency model that ignores per-core sharing underestimates both the number of active NFV nodes and the real end-to-end latency (Savi et al., 2017). This directly challenges a common simplification in placement studies: minimizing the number of used nodes does not automatically preserve service latency.
Several misconceptions are addressed explicitly in the cited papers. One is that offline placement is sufficient, whereas dynamic scaling under time-varying traffic is a first-class requirement (Jia et al., 2016). Another is that NF decomposition and VNF placement can be solved independently, even though simultaneous optimization was introduced precisely because previous research had treated them as separate problems (Asgharian-Sardroud et al., 2024). A third is that placement can be studied without chaining, despite the observation that some existing works considered only the placement of VNFs and ignored the chaining part (Asgari et al., 2021). These critiques indicate that the field increasingly views placement as a joint problem over host resources, routing, order, and service semantics.
The survey literature systematizes the open agenda around online and dynamic placement, container-based network functions, edge/fog/IoT scenarios, security and isolation, multi-domain and cross-layer orchestration, learning-driven orchestration, and emerging KPIs such as carbon footprint, real-time QoE metrics, and cost-yield trade-off (Attaoui et al., 2022). A plausible implication is that future VNF placement work will be judged less by whether it can solve a static embedding instance and more by whether it can reconcile scalability, uncertainty, reconfiguration, and heterogeneous execution environments within a single orchestration framework.
