Version Age-of-Information (VAoI)

• Version Age-of-Information (VAoI) is a freshness metric that measures the gap in update versions between the source and receiver, capturing semantic staleness.
• It is applied across systems like remote monitoring, energy-harvesting IoT, gossip networks, and federated learning, formalizing freshness as a version-index gap.
• VAoI enables joint optimization of delay, reliability, and semantic accuracy through threshold-based scheduling and MDP control frameworks.

Version Age-of-Information (VAoI) is a version-based freshness metric that quantifies how many source versions the receiver lags behind the source, scheduler, or sensing node, rather than how much time has elapsed since the freshest received update was generated. Across event-triggered remote monitoring, gossip networks, energy-harvesting IoT, federated learning, and multi-user wireless scheduling, VAoI is formalized as a version-index gap—e.g., $V_S(t)-V_R(t)$, $N_s(t)-N_i(t)$, or $G(t,n)-B(t-1,n)$—and is used when semantic staleness is better represented by missed state changes or missed model versions than by elapsed time alone (Khorsandmanesh et al., 24 Jun 2026, Delfani et al., 31 Jul 2025, Pan et al., 26 Jan 2026).

1. Definitions and conceptual scope

In event-triggered remote monitoring, VAoI is defined as

$$\Delta_v(t)=V_{\mathrm{WSN}(t)}-V_{\mathrm{MS}(t)},$$

where $V_{\mathrm{WSN}(t)}$ is the latest source version at the wireless sensor node and $V_{\mathrm{MS}(t)}$ is the latest version available at the monitoring station (Khorsandmanesh et al., 24 Jun 2026). In a discrete-time multi-user status update system, the per-user VAoI is

$\mathcal{D}(t,n)=G(t,n)-B(t-1,n),$

where $G(t,n)$ is the newest packet version at the scheduler and $B(t-1,n)$ is the latest delivered version at the destination (Pan et al., 26 Jan 2026). In gossip networks, the canonical definition is

$\Delta_i(t)=N_s(t)-N_i(t),$

with $N_s(t)-N_i(t)$0 the source version and $N_s(t)-N_i(t)$1 the version known at node $N_s(t)-N_i(t)$2 (Hasan et al., 18 Sep 2025). In single-sensor IoT systems, the same idea appears as

$N_s(t)-N_i(t)$3

or

$N_s(t)-N_i(t)$4

depending on whether the notation emphasizes source and destination versions or source and receiver versions (Delfani et al., 1 Oct 2025, Delfani et al., 2024).

The point of departure from classical AoI is explicit. AoI is typically

$N_s(t)-N_i(t)$5

where $N_s(t)-N_i(t)$6 is the generation time-stamp of the most recently received update. AoI is a temporal metric; VAoI is a version metric. AoI penalizes time since the last update, whereas VAoI penalizes the version gap or the number of missing versions. Several papers state this contrast directly: AoI is appropriate when updates are generated periodically or when freshness is purely temporal, while VAoI is appropriate when updates are event-triggered by state changes, when the monitor cares about version mismatch, and when there is no explicit distortion model or continuous-time source model (Khorsandmanesh et al., 24 Jun 2026, Delfani et al., 2024).

A central structural fact is that VAoI is not merely AoI in different units. VAoI increases only when a new version appears and the receiver does not catch up; it can remain constant between source changes. In the discrete-time Bernoulli version-generation model, if a new version is generated in every slot, $N_s(t)-N_i(t)$7, then VAoI reduces to AoI in the slotted sense; otherwise, it does not (Delfani et al., 31 Jul 2025). This makes VAoI particularly natural for versioned content, latest model dissemination, cached state, firmware, and semantic monitoring, where “how many changes have I missed?” is more meaningful than “how many seconds old is my view?” (Pan et al., 26 Jan 2026, Hasan et al., 18 Sep 2025).

2. Canonical stochastic models and single-link dynamics

A foundational model appears in event-triggered remote monitoring over finite-blocklength wireless links. A wireless sensor node generates updates only when the source state changes, with update arrival probability

$N_s(t)-N_i(t)$8

Each update carries $N_s(t)-N_i(t)$9 information bits, is encoded into a packet of length $G(t,n)-B(t-1,n)$0 channel uses, and is transmitted over a slot of duration

$G(t,n)-B(t-1,n)$1

With transmit power $G(t,n)-B(t-1,n)$2, received SNR $G(t,n)-B(t-1,n)$3, and decoding error probability $G(t,n)-B(t-1,n)$4, the success probability is $G(t,n)-B(t-1,n)$5. Modeling $G(t,n)-B(t-1,n)$6 as a discrete-time Markov chain yields the closed-form average VAoI

$G(t,n)-B(t-1,n)$7

under the stability condition $G(t,n)-B(t-1,n)$8 (Khorsandmanesh et al., 24 Jun 2026).

That same model makes the coupling among freshness, reliability, and latency explicit. The average delay is

$G(t,n)-B(t-1,n)$9

A VAoI constraint $$\Delta_v(t)=V_{\mathrm{WSN}(t)}-V_{\mathrm{MS}(t)},$$0 implies an average-delay bound

$$\Delta_v(t)=V_{\mathrm{WSN}(t)}-V_{\mathrm{MS}(t)},$$1

and a decoding-error bound

$$\Delta_v(t)=V_{\mathrm{WSN}(t)}-V_{\mathrm{MS}(t)},$$2

This shows that, in finite-blocklength event-triggered systems, VAoI jointly constrains delay and decoded packet error probability (Khorsandmanesh et al., 24 Jun 2026).

In energy-harvesting IoT with Bernoulli version generation and unreliable channels, the slot-by-slot VAoI recursion is

$$\Delta_v(t)=V_{\mathrm{WSN}(t)}-V_{\mathrm{MS}(t)},$$3

where $$\Delta_v(t)=V_{\mathrm{WSN}(t)}-V_{\mathrm{MS}(t)},$$4 is the version-generation indicator, $$\Delta_v(t)=V_{\mathrm{WSN}(t)}-V_{\mathrm{MS}(t)},$$5 the transmission action, and $$\Delta_v(t)=V_{\mathrm{WSN}(t)}-V_{\mathrm{MS}(t)},$$6 the channel-success indicator (Delfani et al., 1 Oct 2025). The same paper formulates long-term average VAoI minimization as an infinite-horizon average-cost MDP with state $$\Delta_v(t)=V_{\mathrm{WSN}(t)}-V_{\mathrm{MS}(t)},$$7, where $$\Delta_v(t)=V_{\mathrm{WSN}(t)}-V_{\mathrm{MS}(t)},$$8 is battery state. This representation makes VAoI a controlled stochastic process driven jointly by content evolution, energy availability, and transmission outcomes.

Single-hop and multi-hop slotted networks admit a complementary analytical treatment based on stationary distributions. Under a randomized stationary policy with transmission probability $$\Delta_v(t)=V_{\mathrm{WSN}(t)}-V_{\mathrm{MS}(t)},$$9 and link success probability $V_{\mathrm{WSN}(t)}$0, the average VAoI is

$V_{\mathrm{WSN}(t)}$1

Under threshold scheduling, transmission occurs only when $V_{\mathrm{WSN}(t)}$2, and closed-form stationary distributions and average VAoI expressions are available. In multi-hop networks,

$V_{\mathrm{WSN}(t)}$3

so the destination’s average VAoI equals the single-hop value plus the expected number of versions generated during relaying across the $V_{\mathrm{WSN}(t)}$4 hops (Delfani et al., 31 Jul 2025).

3. Gossip networks, mobility, hierarchy, and reliability-aware dissemination

In gossip networks, VAoI is often analyzed through Stochastic Hybrid Systems (SHS). For a subset $V_{\mathrm{WSN}(t)}$5 of nodes, the steady-state average minimum version age

$V_{\mathrm{WSN}(t)}$6

satisfies a recursion that combines source updates, gossip rates, and, when present, mobility rates. In contact-mobility gossip networks, the mobility terms enter the SHS recursion in exactly the same way as gossip terms, leading to the interpretation that contact mobility can be viewed as additional gossip links (Hasan et al., 18 Sep 2025).

This framework yields explicit scaling laws. In symmetric disconnected and fully connected gossip networks with contact mobility rate $V_{\mathrm{WSN}(t)}$7, the average single-node VAoI scales as

$V_{\mathrm{WSN}(t)}$8

$V_{\mathrm{WSN}(t)}$9

and

$V_{\mathrm{MS}(t)}$0

The same paper shows that contact mobility improves freshness in both disconnected and fully connected gossip networks, and formulates a weighted-sum optimization of version age and mobility cost (Hasan et al., 18 Sep 2025).

Topological effects are equally prominent in static gossip networks. In Erdős–Rényi graphs $V_{\mathrm{MS}(t)}$1, the average version age exhibits a threshold near $V_{\mathrm{MS}(t)}$2: if

$V_{\mathrm{MS}(t)}$3

the average version age of a vertex is $V_{\mathrm{MS}(t)}$4, while if

$V_{\mathrm{MS}(t)}$5

the average version age is $V_{\mathrm{MS}(t)}$6. For random $V_{\mathrm{MS}(t)}$7-regular graphs with fixed $V_{\mathrm{MS}(t)}$8, the worst-case version age is $V_{\mathrm{MS}(t)}$9 asymptotically almost surely. In complete bipartite graphs $\mathcal{D}(t,n)=G(t,n)-B(t-1,n),$0, the scaling moves from $\mathcal{D}(t,n)=G(t,n)-B(t-1,n),$1 when $\mathcal{D}(t,n)=G(t,n)-B(t-1,n),$2 to $\mathcal{D}(t,n)=G(t,n)-B(t-1,n),$3 when $\mathcal{D}(t,n)=G(t,n)-B(t-1,n),$4 (maranzatto, 2024).

Clustered gossip networks introduce another scaling regime. With equal-sized clusters and cluster heads, per-node average version age scalings of $\mathcal{D}(t,n)=G(t,n)-B(t-1,n),$5, $\mathcal{D}(t,n)=G(t,n)-B(t-1,n),$6, and $\mathcal{D}(t,n)=G(t,n)-B(t-1,n),$7 are achievable in disconnected, ring, and fully connected cluster models, respectively. When cluster heads themselves form a ring network, the corresponding scalings become $\mathcal{D}(t,n)=G(t,n)-B(t-1,n),$8, $\mathcal{D}(t,n)=G(t,n)-B(t-1,n),$9, and $G(t,n)$0. For ring networks with $G(t,n)$1 levels of hierarchy, per-user average version age scaling of $G(t,n)$2 is achievable (Buyukates et al., 2021).

VAoI can also be coupled to source reliability. In a two-source gossip network with one reliable and one unreliable source, nodes are willing to sacrifice their version age by up to $G(t,n)$3 versions to switch from an unreliable packet to a reliable packet. The analytical SHS characterization shows that as $G(t,n)$4 increases, fewer nodes have unreliable packet, however, their version age increases as well. This is a direct freshness–reliability trade-off in version space (Kaswan et al., 2023).

4. Optimization, threshold structure, and learning-based control

Many VAoI control problems admit threshold or convex structure. In energy-harvesting IoT with a single sensor and Bernoulli version generation, the infinite-horizon average-cost MDP has a threshold policy in the age dimension: for each battery level $G(t,n)$5, there exists a threshold $G(t,n)$6 or $G(t,n)$7 such that transmitting is optimal above the threshold and idling is optimal below it. The same paper studies fully known, partially known, and unknown models, using Relative Value Iteration Algorithm (RVIA), maximum-likelihood estimation of $G(t,n)$8 and $G(t,n)$9, and average-cost Q-learning, respectively (Delfani et al., 1 Oct 2025).

Query-aware semantics lead to the query-weighted metric

$B(t-1,n)$0

or, in the one-slot-delay formulation,

$B(t-1,n)$1

where $B(t-1,n)$2 is the Bernoulli query process. In the corresponding energy-harvesting MDP, the optimal QVAoI policy is also threshold-based: when a query is present, transmit if the current age metric exceeds a battery-dependent threshold; otherwise idle. The paper reports that, for a target average QVAoI of approximately $B(t-1,n)$3, the QVAoI-optimal policy requires update rate approximately $B(t-1,n)$4, compared with approximately $B(t-1,n)$5 for the QAoI-optimal policy and approximately $B(t-1,n)$6 for the greedy policy (Delfani et al., 2024).

VAoI scheduling in wireless multi-user systems has also been cast as a constrained MDP with long-term transmission cost constraints. In one formulation, the risk-neutral objective minimizes average VAoI, while the risk-sensitive objective minimizes $B(t-1,n)$7 of pooled VAoI samples. The paper introduces D2SAC, a diffusion model-based Soft Actor-Critic algorithm, and RS-D3SAC, a risk-sensitive deep distributional diffusion-based Soft Actor-Critic algorithm. D2SAC targets average VAoI, whereas RS-D3SAC integrates a diffusion-based actor with a quantile-based distributional critic and optimizes CVaR of the return distribution. Simulations show that D2SAC reduces average VAoI, while RS-D3SAC consistently achieves substantial reductions in CVaR without sacrificing mean performance (Pan et al., 26 Jan 2026).

At the physical layer, VAoI optimization under power and general distortion constraints in uplink NOMA leads to a convex formulation under a stationary randomized policy class. The resulting policy is VAoI-agnostic: it jointly optimizes scheduling, bit allocation, and power control without tracking instantaneous VAoI, yet achieves a provable 2-approximation to the globally optimal average VAoI. Lagrangian dual decomposition yields closed-form expressions for scheduling probabilities and power allocations, together with an efficient successive interference cancellation decoding order. Numerical results show that NOMA significantly outperforms TDMA: at high power budgets, NOMA achieves near-zero VAoI, whereas TDMA saturates at a non-zero value (Karevvanavar et al., 30 Mar 2026).

Analytical threshold scheduling also appears in single- and multi-hop networks. For threshold-based scheduling in the single-hop Bernoulli version model, the optimal threshold is

$B(t-1,n)$8

possibly mixed with $B(t-1,n)$9 to meet a transmission-rate constraint exactly. The corresponding average VAoI is available in closed form, and the paper shows that, under tight transmission-rate constraints, threshold scheduling can reduce average VAoI by about 50% compared with randomized stationary scheduling (Delfani et al., 31 Jul 2025).

5. Query-aware, value-aware, and event-aware relatives of VAoI

Several neighboring metrics clarify what VAoI does and does not measure. Query Version AoI (QVAoI) multiplies VAoI by a query indicator, so that semantic lag is penalized only when information is requested. This makes QVAoI both version-aware and query-aware, and it is explicitly contrasted with QAoI, VAoI, and AoI in energy-harvesting IoT (Delfani et al., 2024).

Deviation-of-Information (DoI) provides another version-like perspective. For a counting-process signal $\Delta_i(t)=N_s(t)-N_i(t),$0, DoI is defined as

$\Delta_i(t)=N_s(t)-N_i(t),$1

which counts how many events have occurred since the sample currently held by the monitor. In the deterministic-event case, the paper shows

$\Delta_i(t)=N_s(t)-N_i(t),$2

This does not redefine VAoI, but it demonstrates that event-count freshness and time freshness can coincide under regular event generation and diverge under random event generation. This suggests a close structural relationship between VAoI and signal-aware deviation metrics when versions are themselves generated by counting processes (Noroozi et al., 2022).

Value-aware formulations are also relevant. Multi-class update systems with class-dependent value functions $\Delta_i(t)=N_s(t)-N_i(t),$3 yield threshold policies that minimize a convex combination of AoI and negative VoI, with class-specific minimum inter-update times determined by inversion of

$\Delta_i(t)=N_s(t)-N_i(t),$4

Status-update systems with random initial values and deadlines similarly define VoI as the sum of current values of all packets held by the receiver. These papers do not define VAoI, but they show how age can be coupled to information value, class structure, and deadlines. This suggests that VAoI belongs to a broader family of semantic freshness metrics in which “freshness” is indexed not only by time but also by content, version, or utility (Arafa et al., 2024, Zou et al., 2020, Kosta et al., 2017).

A recurrent misconception is that any semantic freshness metric must collapse to elapsed time once delays are modeled carefully. The literature surveyed here points in the opposite direction: when updates are event-triggered, when versions change sporadically, or when receivers care about the latest semantic state rather than timestamps, version lag, query-weighted version lag, event-count deviation, and value-aware age lead to distinct objective functions and distinct optimal policies (Delfani et al., 2024, Noroozi et al., 2022).

6. Applications, limitations, and research directions

VAoI is already used in event-triggered remote monitoring, industrial automation, IoT status updating, multi-user wireless scheduling, gossip dissemination, contact mobility, federated learning, and versioned state synchronization. In federated learning, a client-specific VAoI process is introduced to capture both timeliness and parameter-version staleness: a client’s version age increments when its local model is sufficiently far from the current global model and resets when the client is selected. The resulting Version Age-based Scheduling policy minimizes a nonlinear function of client VAoIs and empirically reduces average version age relative to random client sampling (Hu et al., 2024). Other papers explicitly name applications such as latest ML model, control policy, cached state, software updates, firmware, blockchain or distributed ledgers, and semantic monitoring (Pan et al., 26 Jan 2026, Hasan et al., 18 Sep 2025).

The same body of work is explicit about its modeling assumptions. Common simplifications include Bernoulli version generation, Bernoulli or Poisson arrivals, i.i.d. fading or channel success processes, single-packet buffers, discrete time slots, and finite state truncation in MDP or CMDP formulations (Delfani et al., 1 Oct 2025, Pan et al., 26 Jan 2026, Delfani et al., 31 Jul 2025). In energy-harvesting models, battery dynamics are often Bernoulli; in gossip models, topologies are frequently symmetric; in reliability-aware gossip, reliability is binary; in NOMA formulations, general distortion is tied to the number of transmitted bits but not to partial buffering across slots (Delfani et al., 2024, Hasan et al., 18 Sep 2025, Kaswan et al., 2023, Karevvanavar et al., 30 Mar 2026).

Research directions stated in the literature include multi-source and multi-device systems, more general query models, non-Bernoulli energy arrivals, Markovian or bursty source dynamics, downlink or general graph topologies, partial observability, POMDP formulations, deeper hierarchy, distributional and risk-sensitive control, and hybrid objectives that combine VAoI with AoI, AoII, distortion, or value-of-information (Delfani et al., 2024, Delfani et al., 1 Oct 2025, Pan et al., 26 Jan 2026, Buyukates et al., 2021). A plausible implication is that VAoI will remain most useful where semantic staleness is dominated by missed discrete changes, while hybrid metrics will be more appropriate when semantic correctness, elapsed time, and information quality must all be controlled simultaneously.