MPCC-DLT: Multi-Port Load & Comm Theory

• MPCC-DLT is a framework that extends divisible load theory to optimize simultaneous data exchanges and processing in satellite constellations.
• It formulates optimal load allocation and makespan minimization as a convex program, ensuring equal finish times across heterogeneous nodes.
• The framework integrates deadline feasibility and admission control, enabling efficient resource provisioning and low blocking probabilities under stochastic task arrivals.

Multi-Port Concurrent Communication Divisible Load Theory (MPCC-DLT) extends classical divisible load theory to account for simultaneous multiport data exchanges and on-board processing heterogeneity in relay-centric distributed satellite system (DSS) constellations. The framework rigorously models and optimally exploits concurrent (multi-port) communication links and nonuniform computation/communication rates for low-latency, deadline-driven task execution under practical system constraints, such as mandatory relay-local processing and variable workload structure.

1. System Model and Parameterization

MPCC-DLT targets relay-centric, single-level "star" topologies prevalent in next-generation DSS architectures. The constellation comprises a central relay node (indexed 0) interfaced with $N$ neighboring satellites (indexed $1$ to $N$) via dedicated inter-satellite links (ISLs). The pivotal multi-port concurrent communication (MPCC) assumption posits that the relay can simultaneously distribute arbitrary-size load partitions to its neighbors and, in parallel, receive returned computational results on all links.

The task model features a normalized input load $L=1$, partitioned into a mandatory local fraction $f \in [0,1]$ at the relay (accounting for security or hardware-imposed constraints) and a distributable fraction $\gamma = 1-f$ allocable between relay and satellite nodes. Explicit task allocation variables $\alpha_0, ..., \alpha_N$, summing to $\gamma$, specify each node's share. Onboard compute speeds $s_i$ and ISL bandwidths $B_i$ are respectively abstracted via per-unit computation delays $1$0 and communication delays $1$1. The result-size ratio $1$2 prescribes the fraction of the input that must be sent back after processing.

Completion times per node integrate load transfer, local processing, and result return:

• For satellite $1$3:

$1$4

• For the relay:

$1$5

The global makespan is $1$6, capturing concurrency and potential heterogeneity-induced bottlenecks (Veeravalli, 3 Jan 2026).

2. Optimal Load Allocation and Makespan Analysis

The MPCC-DLT framework formalizes the load allocation and makespan minimization problem as a convex program:

$1$7

Optimality (when all $1$8) is achieved at equal finish times ($1$9), yielding closed-form expressions for $N$0 and load shares:

Let $N$1 and $N$2 for $N$3, define $N$4.

Two regimes emerge:

Case	Condition	Makespan $N$5	Load Allocations
1	$N$6	$N$7	$N$8 $N$9, $L=1$0
2	$L=1$1	$L=1$2, $L=1$3	$L=1$4, $L=1$5

In Case 1, the relay participates in distributed computing; in Case 2, it becomes exclusively responsible for the non-offloadable fraction, and all distributable load is partitioned among neighbors.

3. Deadline Feasibility and Sizing Cooperative Clusters

For time-critical tasks, feasibility is addressed by comparing $L=1$6 to a prespecified deadline $L=1$7. The relay-inclusive regime gives the necessary and sufficient condition:

$L=1$8

Defining each satellite's service contribution $L=1$9 and relay rate $f \in [0,1]$0, let deficit $f \in [0,1]$1. Then, the minimum number of satellites required to guarantee $f \in [0,1]$2 is

$f \in [0,1]$3

with $f \in [0,1]$4. This explicit sizing criterion enables construction of cooperative clusters tailored to deadline requirements and resource profiles.

4. Real-Time Admission Control Under Stochastic Task Arrivals

Practical network operation must account for random task arrivals and stringent latency or deadline constraints. In MPCC-DLT, task arrivals are modeled as a Poisson process (rate $f \in [0,1]$5), each with per-instance $f \in [0,1]$6 and $f \in [0,1]$7. Upon arrival, the system computes the standalone completion time $f \in [0,1]$8 using the closed-form for the current resource configuration.

Admission proceeds by evaluating whether $f \in [0,1]$9:

• Admit and reserve constellation for $\gamma = 1-f$0 units if feasible,
• Block (drop) otherwise.

Blocking probability is analyzed as a function of offered load $\gamma = 1-f$1, elucidating the interplay between system utilization, task structure, and deadline satisfaction (Veeravalli, 3 Jan 2026).

5. Insights: Latency Regimes and Resource Heterogeneity

MPCC-DLT reveals distinct scaling behaviors and trade-offs depending on task and network parameters:

• Compute-intensive tasks (high $\gamma = 1-f$2, low $\gamma = 1-f$3): Parallel execution yields substantial latency reduction; the optimal makespan scales as $\gamma = 1-f$4. This indicates the benefit of distributing highly divisible, compute-dominated loads.
• Communication-heavy tasks (high $\gamma = 1-f$5): Increasing result-size ratio $\gamma = 1-f$6 magnifies the impact of ISL limitations, and the term $\gamma = 1-f$7 dominates, curbing the gains from additional satellites with modest bandwidth.
• Satellite heterogeneity: Optimal allocation inherently prioritizes satellites with both high compute rates ($\gamma = 1-f$8) and high bandwidth ($\gamma = 1-f$9), as $\alpha_0, ..., \alpha_N$0 is inversely proportional to $\alpha_0, ..., \alpha_N$1.
• Operating regimes: "Relay-assist" (Case 1) occurs for small $\alpha_0, ..., \alpha_N$2, while "neighbor-only" offload (Case 2) is triggered by high mandatory relay fractions.

Admission control exhibits lower blocking probabilities for tasks with high distributability and low result overhead, suggesting a pathway for priority-based scheduling and differentiated service in multi-tenant deployments.

6. Significance and Applications in Satellite System Design

MPCC-DLT constitutes the first analytically tractable, closed-form model for load-balancing, scheduling, and admission control in DSSs harnessing MPCC primitives under practical constraints. The framework provides actionable guidance for:

• Deciding optimal load allocation across heterogeneous satellites,
• Explicitly sizing clusters to meet application-dependent deadlines,
• Managing admission control for stochastic arrivals and deadline-constrained operation,
• Quantifying the impact of result size, bandwidth variations, and required local computation.

A plausible implication is that the adoption of MPCC-DLT could enable systematic, application-aware scheduling and cost-effective resource provisioning in future satellite constellations, particularly in time-sensitive, computationally intensive mission profiles (Veeravalli, 3 Jan 2026).