Delay Optimization in a Simple Offloading System: Extended Version

We consider a computation offloading system where jobs are processed sequentially at a local server followed by a higher-capacity cloud server. The system offers two service modes, differing in how the processing is split between the servers. Our goal is to design an optimal policy for assigning jobs to service modes and partitioning server resources in order to minimize delay. We begin by characterizing the system’s stability region and establishing design principles for service modes that maximize throughput. For any given job assignment strategy, we derive the optimal resource partitioning and present a closed-form expression for the resulting delay. Moreover, we establish that the delay-optimal assignment policy exhibits a distinct breakaway structure: at low system loads, it is optimal to route all jobs through a single service mode, whereas beyond a critical load threshold, jobs must be assigned across both modes. We conclude by validating these theoretical insights through numerical evaluation.

💡 Research Summary

The paper investigates a two‑stage computation offloading system in which jobs first pass through a local server with limited processing capacity and then through a more powerful cloud server. Each incoming job is assigned, with probability p, to service mode 1 (SM1) and with probability 1‑p to service mode 2 (SM2). The two modes differ in how the total workload of a job is split between the local and cloud servers: SM1 is “cloud‑heavy” (a larger fraction of the job is processed in the cloud) while SM2 is “local‑heavy”. For each mode the local and cloud servers reserve fixed fractions of their resources, denoted α and β for SM1 and 1‑α and 1‑β for SM2. The resulting service rates are α μl1, β μc1 for SM1 and (1‑α) μl2, (1‑β) μc2 for SM2, where μl1, μc1, μl2, μc2 are the maximal processing rates of the two servers when dedicated entirely to a single mode.

The authors first introduce a canonical transformation that replaces the four raw service rates with three more interpretable parameters: μ0 (effective local capacity), K > 1 (relative cloud capacity, so the cloud can process K times as many jobs as the local server), and f1, f2 (the fractions of a job’s total workload executed locally under SM1 and SM2, respectively). This representation makes the analysis of stability and delay more transparent.

Stability analysis. By exploiting the Poisson splitting property, the dual‑mode system can be viewed as two independent tandem Jackson networks, one for each mode. The system is stable if and only if the arrival rates into each of the four queues are strictly smaller than the corresponding service rates. This yields a set of linear inequalities (1) involving λ, p, α, and β. Solving these inequalities leads to a closed‑form stability region

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