Sequential Dispatch Methodology

• Sequential-dispatch methodology is defined as a process where decisions are split into ordered stages with intermediate state updates, ensuring adaptive and efficient resource allocation.
• It is applied across domains—from decentralized token-mediated job assignment and rolling-horizon power dispatch to belief-updating routing and staged benchmarking for GPU runtimes.
• The approach leverages updated information at each stage to improve dispatch efficiency, correct non-sequential failures, and integrate learning-based optimizations.

Searching arXiv for the cited papers and closely related sequential-dispatch work to ground the article. arxiv_search query: "Sequential-Dispatch Methodology" max_results: 10 arxiv_search query: "\"sequential dispatch\" WebGPU LLM inference" max_results: 5 Sequential-dispatch methodology refers to dispatch procedures organized as an ordered sequence of stages rather than as a single simultaneous decision. In the literature surveyed here, the phrase is used in several technically distinct ways: decentralized token-mediated job assignment; multi-stage power-system dispatch with recourse; belief-updating crew or responder routing; patrol-then-dispatch control; amortized dispatch benchmarking for GPU runtimes; and staged optimization pipelines that transform natural-language or coarse design specifications into executable dispatch or synthesis decisions (Boor et al., 2017, Qin et al., 2012, Shuai et al., 2020, Zhao et al., 2023, Maczan, 9 Feb 2026, Yang et al., 25 Jul 2025, Terway et al., 2020). This suggests that the term is best understood as a structural pattern—state evolves between stages, and later decisions are conditioned on earlier allocations, observations, or commitments—rather than as a single canonical algorithm.

1. Scope and principal interpretations

Across domains, sequential dispatch is characterized by temporal ordering, intermediate state updates, and partial commitment. The sequence may be operational, as in real-time market clearing or emergency response; informational, as in token circulation or belief-state updates; or methodological, as in staged benchmarking and automated model construction.

Interpretation	Sequential unit	Representative papers
Token-mediated decentralized dispatch	service completion, token placement, later job assignment	(Boor et al., 2017)
Rolling-horizon or recourse dispatch	current binding decision, later advisory or recourse decisions	(Qin et al., 2012, Zhao et al., 2023, Dvorkin et al., 2018)
Mobile-resource dispatch under evolving information	move, observe, update belief/state, reassign	(Shuai et al., 2020, Repasky et al., 2024, Amani et al., 4 Sep 2025)
Staged measurement or design workflow	repeated dispatches or staged formulation/programming	(Maczan, 9 Feb 2026, Yang et al., 25 Jul 2025, Terway et al., 2020)

The same term therefore spans queueing theory, power systems, reinforcement learning, systems benchmarking, and automated optimization. In some papers the sequential aspect is explicitly the decision process; in others it is the measurement protocol or the architecture of the optimization workflow itself (Maczan, 9 Feb 2026, Yang et al., 25 Jul 2025).

2. Core structural pattern

A common pattern is decomposition into stages with state transfer. In the multi-dispatcher Join-the-Idle-Queue system, the sequence is explicit: a service completion makes a server idle; the server sends a token to a dispatcher; the token is stored locally; a later job arrival uses a local token if present; otherwise the job is blocked or forwarded randomly, depending on the model (Boor et al., 2017). The paper is explicit that this is not a centralized dispatcher-by-dispatcher polling rule; the sequential aspect lies in event ordering and token circulation.

In stochastic risk-limiting dispatch, the sequence is a hierarchy of forward market actions followed by real-time storage operation during delivery. At each market stage, the operator observes an updated information set $Y_r$, chooses an incremental procurement $s_r$, and passes the accumulated schedule $x_{r+1}=x_r+s_r$ to the next stage; after the forward stages close, storage operates over the delivery interval to buffer random deficit fluctuations (Qin et al., 2012). In stochastic look-ahead dispatch for real-time market clearing, the sequential logic is rolling-horizon: the market clears every 5 minutes over a 60-minute look-ahead horizon, but only decisions for the first interval are binding and implemented, while later intervals are advisory and recomputed in the next clearing run (Zhao et al., 2023).

In mobile-response systems, the sequence is observation-driven. In post-storm crew dispatch, the belief state is updated from customer calls and utility-vehicle observations, and routing decisions are revised as information arrives (Shuai et al., 2020). In joint police patrol and dispatch, each iteration first applies patrol moves, then samples new incidents, then solves a dispatch assignment, so that patrol is a positioning decision and dispatch is a service-allocation decision over the updated state (Repasky et al., 2024).

3. Canonical formulations

Several mathematically distinct formulations instantiate the sequential-dispatch pattern. In risk-limiting dispatch with fast-ramping storage, the optimal market action retains a threshold form:

$$s_r^\star(x_r)= \begin{cases} [\psi_r-x_r]_+, & \text{buy stage},\ [\psi_r-x_r]_-, & \text{sell stage}, \end{cases} \qquad c_r+\nabla \hat{J}_{r+1}(\psi_r)=0,$$

so each stage buys or sells only enough to move the accumulated schedule to a stage-dependent target $\psi_r$ (Qin et al., 2012). Here the sequential structure is explicit: forecasts improve across market stages, while the terminal cost-to-go embeds optimal real-time storage recourse.

In multi-dispatcher JIQ, the baseline asymptotic blocking probability in the blocking model satisfies

$$B(R,N,\lambda,\alpha)\to \max\{1-R\alpha_R,\;1-1/\lambda\}\qquad\text{as }N\to\infty,$$

which shows that under dispatcher-load asymmetry the least-loaded dispatcher becomes the bottleneck because tokens accumulate where they cannot be used by more heavily loaded dispatchers (Boor et al., 2017). The same paper gives two corrective sequential mechanisms: non-uniform token allotment with $\beta_r=\alpha_r$, and token exchange at rate $\nu$, with asymptotic optimality restored when

$\nu \ge \frac{\lambda}{1-\lambda}(R\alpha_1-1).$

In fully distributed economic dispatch, the sequential aspect appears as continuous-time local update dynamics rather than staged market clearing. In the constrained case, generator outputs evolve according to

$$\dot P_i = \sum_{j\in N_i} a_{ij}(t)(\tilde w_j-\tilde w_i),\qquad \dot a_{ij}(t)=\beta_{ij}(\tilde w_i-\tilde w_j)^2,$$

where $s_r$0 is the modified incremental cost from a logarithmic-barrier formulation (Pal et al., 14 Mar 2026). The dispatch is therefore reached progressively through local neighbor-to-neighbor exchanges, while total generation continues to match load during the transient.

In power-system market design, the sequential structure may be preserved institutionally even when the operator seeks stochastic efficiency. The reserve-setting methodology for European-style sequential markets uses a stochastic bilevel program: the upper level chooses upward and downward reserve requirements, and the lower level reproduces reserve-capacity clearing followed by day-ahead energy clearing, while expected balancing costs are internalized in the upper objective (Dvorkin et al., 2018). Related work on long-duration energy storage shows that traditional rolling sequential dispatch with 48-hour windows offset 24 hours after the previous problem can become structurally vulnerable to degeneracy in high-VRE systems, while a 192-hour rolling window with 7-day look-ahead reduces, but does not eliminate, those distortions (Thatte et al., 2024).

4. Learning-based sequential dispatch

A large part of the recent literature treats sequential dispatch as a stochastic control problem learned from interaction. In stochastic dynamic power dispatch, the contextual Meta-GRL framework models dispatch as a contextual MDP and conditions the policy on a latent context embedding $s_r$1, so that actions are chosen by $s_r$2 rather than by a context-free state policy (Deng et al., 2024). In the reported 39-bus study, Meta-GRL achieved above $s_r$3 optimality on training-domain scenarios $s_r$4–$s_r$5 and $s_r$6 optimality on unseen scenario $s_r$7, relative to the optimal posterior solution (Deng et al., 2024).

In post-storm restoration, AlphaZero-UVR formulates crew routing as a belief-state sequential stochastic optimization problem. The state combines vehicle location and posterior line-fault probabilities, where the posterior is updated from customer calls and vehicle observations via a Bayesian model (Shuai et al., 2020). The online decision rule is produced by stochastic Monte Carlo tree search guided by a neural policy/value model. On the 8-node test system, the reported average scheduling times were $s_r$8 s for AlphaZero-UVR, $s_r$9 s for traditional MCTS, and $x_{r+1}=x_r+s_r$0 s for OLUCT (Shuai et al., 2020).

Joint police patrol and dispatch uses a heterogeneous multi-agent architecture. Patrol is learned by $x_{r+1}=x_r+s_r$1 independent Q-learners sharing one deep Q-network, while dispatch is solved by a mixed-integer program over assignment variables $x_{r+1}=x_r+s_r$2, informed by learned approximations to the future value of assigning patroller $x_{r+1}=x_r+s_r$3 and incident $x_{r+1}=x_r+s_r$4 (Repasky et al., 2024). The main empirical conclusion is qualitative but consistent across settings: policies jointly optimized for patrol and dispatch outperform policies optimized for patrol alone or dispatch alone (Repasky et al., 2024).

Post-earthquake restoration extends this idea to larger infrastructure systems through a transformer-plus-DRL policy conditioned on a scenario-reduction pipeline and a geospatial impact map (Amani et al., 4 Sep 2025). In the reported 2869-bus case, inference runtimes were about 14–16 s even with 156 to 673 damaged components, and the paper reports up to $x_{r+1}=x_r+s_r$5 runtime reduction relative to mathematical-programming or GA-based baselines (Amani et al., 4 Sep 2025).

5. Sequential dispatch as measurement and workflow design

Not all uses of sequential dispatch are online control policies. In WebGPU benchmarking for batch-1 LLM inference, the central contribution is a sequential-dispatch measurement methodology: issue many dispatches back-to-back, synchronize only once at the end, and amortize the terminal synchronization so that the benchmark isolates steady-state per-dispatch cost (Maczan, 9 Feb 2026). The paper reports that naive single-operation benchmarking overestimates dispatch cost by about $x_{r+1}=x_r+s_r$6, with measured WebGPU API overhead alone of 24–36 $x_{r+1}=x_r+s_r$7 on Vulkan and 32–71 $x_{r+1}=x_r+s_r$8 on Metal, whereas total per-operation overhead in the Python-based stack is about $x_{r+1}=x_r+s_r$9 (Maczan, 9 Feb 2026). In this usage, “sequential dispatch” denotes a dispatch stream used to separate API overhead from forced synchronization artifacts.

In active distribution network automation, sequential dispatch refers to a staged large-language-model pipeline. The architecture contains an Information Extractor, a Problem Formulator, and a Code Programmer; the Problem Formulator itself proceeds through six sequential dialogues: objective function, equipment constraints, power flow and injection equations, additional constraints, complete model organization, and convex relaxation (Yang et al., 25 Jul 2025). For qwen-plus, the reported executability is pass@1 $$s_r^\star(x_r)= \begin{cases} [\psi_r-x_r]_+, & \text{buy stage},\ [\psi_r-x_r]_-, & \text{sell stage}, \end{cases} \qquad c_r+\nabla \hat{J}_{r+1}(\psi_r)=0,$$0 and pass@3 $$s_r^\star(x_r)= \begin{cases} [\psi_r-x_r]_+, & \text{buy stage},\ [\psi_r-x_r]_-, & \text{sell stage}, \end{cases} \qquad c_r+\nabla \hat{J}_{r+1}(\psi_r)=0,$$1 (Yang et al., 25 Jul 2025). The sequentiality here lies in transforming an operator request into a structured optimization workflow.

A related use appears in CPS design-space exploration. DISPATCH for CPS synthesis is a two-step methodology in which a genetic algorithm first searches over discrete architecture or component choices and is terminated before the requirements are fully met, yielding a coarse design; inverse design with a neural-network surrogate and MILP active learning then fine-tunes continuous values (Terway et al., 2020). On the amplifier benchmarks, the paper reports sample-efficiency improvements of $$s_r^\star(x_r)= \begin{cases} [\psi_r-x_r]_+, & \text{buy stage},\ [\psi_r-x_r]_-, & \text{sell stage}, \end{cases} \qquad c_r+\nabla \hat{J}_{r+1}(\psi_r)=0,$$2–$$s_r^\star(x_r)= \begin{cases} [\psi_r-x_r]_+, & \text{buy stage},\ [\psi_r-x_r]_-, & \text{sell stage}, \end{cases} \qquad c_r+\nabla \hat{J}_{r+1}(\psi_r)=0,$$3 over a prior reinforcement-learning synthesis method (Terway et al., 2020). This is sequential dispatch in the sense of coarse-to-fine allocation of computational search effort.

6. Efficiency gains, pathologies, and unresolved issues

Sequential-dispatch methodologies are often introduced to correct specific failure modes of non-sequential or weakly coordinated dispatch. In token-based load balancing, the baseline JIQ mechanism is asymptotically optimal only under equal dispatcher loads; under skewed loads, the least-loaded dispatcher hoards tokens and leaves idle servers stranded, so the sequential staging of availability information becomes the source of inefficiency rather than its remedy (Boor et al., 2017). In rolling power dispatch for storage-rich, renewable-dense systems, short look-ahead horizons create degeneracy and path dependence because end-of-day state-of-charge and commitment states become the initial conditions for the next day; extending the horizon improves realism but materially increases runtime (Thatte et al., 2024).

A second recurrent tension is market compatibility. Full stochastic co-optimization of energy and reserves is more efficient in expected operating cost, but it is incompatible with existing sequential European market designs in which reserves are traded separately from energy (Dvorkin et al., 2018). The reserve-setting bilevel model addresses this by keeping reserve procurement first, day-ahead energy second, and balancing last, while choosing exogenous reserve requirements so that the sequential outcome moves closer to stochastic efficiency (Dvorkin et al., 2018). By contrast, stochastic look-ahead dispatch shows that some forms of stochastic sequential dispatch are already computationally viable in real-time clearing: on an industry-sized transmission system, the reported SLAD instances were solved in under 5 minutes, and yearly average savings were $$s_r^\star(x_r)= \begin{cases} [\psi_r-x_r]_+, & \text{buy stage},\ [\psi_r-x_r]_-, & \text{sell stage}, \end{cases} \qquad c_r+\nabla \hat{J}_{r+1}(\psi_r)=0,$$4 for SLAD versus $$s_r^\star(x_r)= \begin{cases} [\psi_r-x_r]_+, & \text{buy stage},\ [\psi_r-x_r]_-, & \text{sell stage}, \end{cases} \qquad c_r+\nabla \hat{J}_{r+1}(\psi_r)=0,$$5 for SCED+RP, which the paper summarizes as more than $$s_r^\star(x_r)= \begin{cases} [\psi_r-x_r]_+, & \text{buy stage},\ [\psi_r-x_r]_-, & \text{sell stage}, \end{cases} \qquad c_r+\nabla \hat{J}_{r+1}(\psi_r)=0,$$6 additional savings compared to flexiramp products (Zhao et al., 2023). That paper also notes, however, that SLAD-compatible pricing schemes are beyond its scope (Zhao et al., 2023).

A final limitation is terminological. The surveyed papers do not support a single universal definition. This suggests that “sequential-dispatch methodology” should be interpreted by asking three questions in each application: what is dispatched, what stage boundary carries state from one decision to the next, and whether the sequential unit is operational control, information propagation, or workflow decomposition. Under that reading, the concept is unified not by one algorithm, but by the technical principle that dispatch quality depends on preserving and exploiting the state created by earlier actions, observations, or commitments.