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 $w_i = 1/s_i$ and communication delays $z_i = 1/B_i$. The result-size ratio $\beta \in [0,1]$ 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 $i$:

$$T_i = \alpha_i z_i + \alpha_i w_i + \beta \alpha_i z_i = \alpha_i [w_i + (1+\beta)z_i]$$

• For the relay:

$T_0 = (f + \alpha_0) w_0$

The global makespan is $T = \max \{ T_0, T_1, ..., T_N \}$, 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:

$$\begin{align*} \min_{α_0,\ldots,α_N,T} \ & T \ \text{s.t.}\quad & T \ge (f + α_0)\,w_0, \ & T \ge α_i\,\bigl(w_i + (1+\beta)\,z_i\bigr),\ \forall i=1,...,N, \ & \sum_{i=0}^N α_i = γ, \quad α_i \ge 0. \end{align*}$$

Optimality (when all $\alpha_i > 0$) is achieved at equal finish times ($T_0 = T_1 = ... = T_N \equiv T^*$), yielding closed-form expressions for $T^*$ and load shares:

Let $\delta_0 = w_0$ and $\delta_i = w_i + (1+\beta)z_i$ for $i=1...N$, define $S = \sum_{i=0}^N \frac{1}{\delta_i}$.

Two regimes emerge:

Case	Condition	Makespan $T^*$	Load Allocations
1	$$\alpha_0^* \ge 0 \Longleftrightarrow f \le \frac{1}{w_0 S}$$	$T^* = \frac{1}{S}$	$\alpha_i^* = T^* / \delta_i$ $(i=1,...,N)$, $\alpha_0^* = T^*/w_0 - f$
2	$$\alpha_0^* < 0 \Longleftrightarrow f > \frac{1}{w_0 S}$$	$T^* = \max \{ f w_0, \frac{\gamma}{G} \}$, $G = \sum_{i=1}^N 1/\delta_i$	$\alpha_i^* = \gamma \dfrac{1/\delta_i}{G}$, $\alpha_0^* = 0$

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 $T^*$ to a prespecified deadline $D$. The relay-inclusive regime gives the necessary and sufficient condition:

$$\frac{1}{w_0} + \sum_{i=1}^N \frac{1}{w_i + (1+\beta)z_i} \ge \frac{1}{D}$$

Defining each satellite's service contribution $g_i = 1/(w_i + (1+\beta)z_i)$ and relay rate $1/w_0$, let deficit $\Delta = 1/D - 1/w_0$. Then, the minimum number of satellites required to guarantee $T^* \le D$ is

$$N_{\min}(D) = \min \Bigl\{ K : \sum_{i=1}^K g_{(i)} \ge \Delta \Bigr\}$$

with $g_{(1)} \ge g_{(2)} \ge ...$. 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 $\lambda$), each with per-instance $(\gamma_j, \beta_j, f_j,$ and $D_j)$. Upon arrival, the system computes the standalone completion time $T_j^*$ using the closed-form for the current resource configuration.

Admission proceeds by evaluating whether $t_{\text{arr}} + T_j^* \le t_{\text{arr}} + D_j$:

• Admit and reserve constellation for $T_j^*$ units if feasible,
• Block (drop) otherwise.

Blocking probability is analyzed as a function of offered load $a = \lambda \mathbb{E}[T^*]$, 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 $\gamma$, low $\beta$): Parallel execution yields substantial latency reduction; the optimal makespan scales as $T^* \sim 1/\sum_i 1/w_i$. This indicates the benefit of distributing highly divisible, compute-dominated loads.
• Communication-heavy tasks (high $\beta$): Increasing result-size ratio $\beta$ magnifies the impact of ISL limitations, and the term $(1+\beta)z_i$ dominates, curbing the gains from additional satellites with modest bandwidth.
• Satellite heterogeneity: Optimal allocation inherently prioritizes satellites with both high compute rates ($s_i$) and high bandwidth ($B_i$), as $\alpha_i^*$ is inversely proportional to $\delta_i$.
• Operating regimes: "Relay-assist" (Case 1) occurs for small $f$, 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).