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Latency-Aware Resource Allocation over Heterogeneous Networks: A Lorentz-Invariant Market Mechanism

Saad Alqithami

Abstract

We present a telecom-native auction mechanism for allocating bandwidth and time slots across heterogeneous-delay networks, ranging from low-Earth-orbit (LEO) satellite constellations to delay-tolerant deep-space relays. The Lorentz-Invariant Auction (LIA) treats bids as spacetime events and reweights reported values based on the \emph{horizon slack}, a causal quantity derived from the earliest-arrival times relative to a public clearing horizon. Unlike other delay-equalization rules, LIA combines a causal-ordering formulation, a uniquely exponential slack correction implied by a semigroup-style invariance axiom, and a critical-value implementation that ensures truthful reported values once slacks are fixed by trusted infrastructure. We analyze the incentive result in the exogenous-slack regime and separately examine bounded slack-estimation error and endogenous-delay limitations. Under fixed feasible slacks, LIA is individually rational and achieves welfare at least \(e^{-λΔ}\) relative to the optimal feasible allocation, where \(Δ\) is the slack spread. We evaluate LIA on STARLINK-200, INTERNET-100, and DSN-30 across 52,500 baseline instances with market sizes \(n\in\{10,20,30,40,50\}\) and conduct additional robustness sweeps. On Starlink and Internet, LIA maintains near-efficiency while eliminating measured timing rents. However, on DSN, welfare is lower in thin markets but improves with depth. We also distinguish winner-determination time from the background cost of maintaining slack estimates and study robustness beyond independent and identically distributed (iid) noise through error-spread bounds and structured (distance-biased and subnetwork-correlated) noise models. These results suggest that causal-consistent mechanism design offers a practical non-buffering alternative to synchronized delay equalization in heterogeneous telecom infrastructures.

Latency-Aware Resource Allocation over Heterogeneous Networks: A Lorentz-Invariant Market Mechanism

Abstract

We present a telecom-native auction mechanism for allocating bandwidth and time slots across heterogeneous-delay networks, ranging from low-Earth-orbit (LEO) satellite constellations to delay-tolerant deep-space relays. The Lorentz-Invariant Auction (LIA) treats bids as spacetime events and reweights reported values based on the \emph{horizon slack}, a causal quantity derived from the earliest-arrival times relative to a public clearing horizon. Unlike other delay-equalization rules, LIA combines a causal-ordering formulation, a uniquely exponential slack correction implied by a semigroup-style invariance axiom, and a critical-value implementation that ensures truthful reported values once slacks are fixed by trusted infrastructure. We analyze the incentive result in the exogenous-slack regime and separately examine bounded slack-estimation error and endogenous-delay limitations. Under fixed feasible slacks, LIA is individually rational and achieves welfare at least relative to the optimal feasible allocation, where is the slack spread. We evaluate LIA on STARLINK-200, INTERNET-100, and DSN-30 across 52,500 baseline instances with market sizes and conduct additional robustness sweeps. On Starlink and Internet, LIA maintains near-efficiency while eliminating measured timing rents. However, on DSN, welfare is lower in thin markets but improves with depth. We also distinguish winner-determination time from the background cost of maintaining slack estimates and study robustness beyond independent and identically distributed (iid) noise through error-spread bounds and structured (distance-biased and subnetwork-correlated) noise models. These results suggest that causal-consistent mechanism design offers a practical non-buffering alternative to synchronized delay equalization in heterogeneous telecom infrastructures.

Paper Structure

This paper contains 89 sections, 13 theorems, 30 equations, 3 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation and Context
  3. Challenges in Heterogeneous-Delay Environments
  4. Single-Item Model and Telecom Resources
  5. Our Contributions
  6. Related Work
  7. Auction Theory and Mechanism Design
  8. Latency Arbitrage and Market Microstructure
  9. Distributed Systems and Causal Consistency
  10. Telecommunication Networks and Resource Allocation
  11. Physics-Aware Computing and Relativistic Algorithms
  12. Physics-Aware Perspectives on Computation and Incentives
  13. Synthesis and Distinctions
  14. Mechanism overview.
  15. Paper Organization
  16. ...and 74 more sections

Key Result

Theorem 1

Let $\phi: \mathbb{R}_{\geq 0} \to (0,1]$ be a discount function satisfying: Then $\phi(\delta) = e^{-\lambda \delta}$ for some $\lambda > 0$ (in ms$^{-1}$). $\blacktriangleleft$$\blacktriangleleft$

Figures (3)

  • Figure 1: Spacetime view of two bids. Dashed lines are light-cone boundaries under unit aspect ($c{=}1$). The shaded rectangle marks a causal slab where bids are incomparable; the red line is the frontier where horizon-discounted bids are compared (i.e., where $\theta_1 e^{-\lambda \delta_1}=\theta_2 e^{-\lambda \delta_2}$). Its position depends on the values $(\theta_1,\theta_2)$, the parameter $\lambda$, and how each bid's horizon slack $\delta_i$ changes with emission time. Proper-time lapses $\delta_i$ (horizon slacks) are measured along each worldline from emission to the clearing horizon $H$, with $\delta_i \equiv \Delta\tau_i$.
  • Figure 2: Latency-Arbitrage Index (LAI) curves $g(\Delta)$ for STARLINK-200 and INTERNET-100 at $n=50$ (log scale). For each mechanism, $g(\Delta)$ measures the expected utility gain from reducing a bidder's one-way propagation delay by $\Delta$. Fast-VCG exhibits large timing rents that grow with $\Delta$, frequent batch auctions reduce timing rents only by imposing buffering, and LIA drives the curve to zero (within estimator resolution) while maintaining the horizon-level clearing latency.
  • Figure 3: Empirical evaluation summary. (a,b) Fairness--latency frontier at $n=50$ for Starlink and Internet: timing rent (LAI, $\sup g$) versus mean clearing latency. (c) Winner-determination runtime versus market size (shaded bands show min--max across topologies; $n=1000$ points from Table \ref{['tab:welfare-by-topology']}). (d) Welfare ratio versus market size. (e,f) Robustness of welfare and timing rent under bounded slack-estimation error $\varepsilon$ (iid perturbations, solid; common-mode clock bias, dashed), averaged over Starlink and Internet at $n=50$.

Theorems & Definitions (40)

  • Definition 1: Horizon slack
  • Remark 1: Notation consistency
  • Remark 2: Operational interpretation and non-inertial effects
  • Example 1: Horizon slacks in different network topologies
  • Definition 2: Latency Arbitrage Index
  • Example 2: LAI calculation
  • Theorem 1: Uniqueness of exponential discount
  • proof
  • Corollary 1: Composition property
  • proof
  • ...and 30 more