Design Insights into Partition Placement and Routing for DNN Inference in Multi-Hop Edge Networks Jinkun Zhang and Poonam Yadav
arXiv:2604.25571v1 [cs.NI] 28 Apr 2026
Department of Computer Science University of York, UK Abstract—Partitioned DNN inference is a promising approach for latency-sensitive intelligent services in edge networks, since it allows different parts of a model to be executed across end devices, edge servers, and the cloud. However, in a multi-hop edge network, partition placement and inference traffic routing are inherently coupled: raw inputs, intermediate features, and final outputs may have very different sizes, while candidate nodes also differ in computation capability. In addition, both communication and computation delays can become congestiondependent under load. In this paper, we study joint partition placement and routing for fixed-partition DNN inference over heterogeneous multi-hop edge networks. We consider a small number of DNN partitions, each placed at exactly one node without replication, and formulate a congestion-aware mixed discrete– continuous optimization problem that captures both routing and execution costs. To solve it, we develop a practical alternating framework that couples partition placement with congestionaware forwarding updates. Through numerical evaluation on hierarchical, regular, synthetic irregular, and real backboneinspired topologies, we show that split flexibility is particularly important in IoT–edge–cloud settings, while congestion-aware refinement becomes increasingly beneficial as the offered load grows. We further illustrate how the preferred operating point depends on the communication–computation tradeoff.
I. I NTRODUCTION Deep neural network (DNN) inference is increasingly becoming a core building block for latency-sensitive intelligent services deployed at the network edge, such as real-time perception and interactive mobile AI applications [1]. However, executing an entire DNN locally is often difficult on resource-constrained end devices, while sending raw inputs to a remote cloud can incur substantial communication latency and bandwidth overhead [2], or raise privacy and security considerations [3]. These limitations have made partitioned or collaborative DNN inference a compelling alternative, in which different portions of a model are executed across end devices, edge servers, and possibly the cloud so as to better exploit distributed computation and communication resources. This paradigm is particularly appealing in collaborative edge environments, where heterogeneous nodes can jointly support DNN inference and model execution naturally interacts with the underlying network. Although partitioned DNN inference has been widely studied, much of the literature still relies on simplified device– edge–cloud pipelines, predetermined collaboration structures, or restrictive communication assumptions [2], [4]. Recent works begin to consider richer distributed settings, including
Inference Request Source
input at � �
raw input
�0
DNN Partition 1
executed at ℎ1 ℎ1
intermediate feature
�1
DNN Partition 2
executed at ℎ2
final output
�2
Result Destination
arrive at �
ℎ2
�
Fig. 1: Inference with DNN partitions in a multi-hop network
heterogeneous edge cooperation, fine-grained partitioning, and network-aware utility optimization [5]–[7]. In multi-hop edge networks, however, inference traffic may traverse multiple intermediate links and nodes, making communication an integral part of execution rather than a single offloading step. This is especially important for partitioned DNN inference, since raw inputs, intermediate activations, and final outputs can differ in size, while candidate nodes may also vary in computation capability [5]. Consequently, partition placement and traffic routing are inherently coupled, yet this coupling is often overlooked through fixed pipelines, fixed paths, or formulations that optimize only part of the end-to-end communication– computation process [4], [8]. These observations motivate us to study congestion-aware partition placement and routing for partitioned DNN inference over multi-hop edge networks. Fig. 1 illustrates the partitioned DNN inference model. The raw input of size L0 originates at source s, the two DNN partitions are executed at nodes h1 and h2 , and the final output of size L2 is delivered to destination d. The intermediate feature of size L1 is transmitted between the two partition locations. Since h1 and h2 may differ and all transmissions may traverse multiple hops, partition placement and routing must be optimized jointly. A recent work studied delay-optimal forwarding and offloading for generic service-chain applications over arbitrary multi-hop networks with congestion-aware communication and computation costs [9]. It closely aligns with our motivation, since partitioned DNN inference can also be viewed as a multi-stage computation service. However, [9] assumes continuous stage-wise forwarding/offloading, allowing each stage flow to be fractionally routed to or processed by an arbitrarily set of nodes. Whereas in practical DNN partitioning, typically only a small number of deployment blocks are involved (in most cases, only 2), since partitioning and
replicating blocks across many nodes can be infeasible due to constraints on communication, memory, power, etc. [10]. Here, we focus on a small number of fixed DNN partitions, each placed at exactly one node without replication, which introduces explicit discrete placement decisions coupled with traffic routing. Our problem is not a direct specialization of the continuous formulation in [9], and our focus shifts from theoretical optimality to application-driven design insights. Our method addresses partitioned DNN inference over a multi-hop edge network with heterogeneous communication and computation resources. We consider a small number of fixed DNN partitions, motivated by the fact that practical deployment typically involves only a few blocks, while finegrained partitioning and replication across many nodes can be prohibitively expensive in communication, memory, and power. Each partition is placed at exactly one node without replication, and the resulting inference traffic is routed through the network from the source to the selected partition locations and finally to the destination. To capture the interaction between networking and computation, we model both transmission and processing costs as congestion-dependent, so that the placement of DNN partitions and the routing of the induced traffic must be determined jointly. This leads to a mixed discrete–continuous optimization problem, in which partition locations are discrete decisions while forwarding is a continuous traffic allocation variable. Rather than pursuing a globally optimal but computationally prohibitive formulation, we develop a practical congestion-aware solution framework that couples partition placement with routing refinement. Using this framework, we further study how the preferred split execution pattern depends on feature-size variation across partitions, heterogeneity in node computation capability, and the level of network congestion. Our contributions are summarized as follows: • We formulate a congestion-aware joint partition placement and routing problem for partitioned DNN inference over heterogeneous multi-hop edge networks, where each fixed DNN partition is placed at exactly one node without replication. • We develop a practical solution framework for the resulting mixed discrete–continuous problem, by coupling discrete partition placement decisions with congestionaware forwarding updates. • Through numerical evaluation, we show how the preferred split execution pattern depends on feature-size variation, resource heterogeneity, and offered load, and we quantify the roles of congestion awareness, alternating refinement, and split flexibility. II. N ETWORK FORMULATION We consider a multi-hop edge network modeled by a directed graph G = (V, E), where V and E denote the sets of nodes and communication links, respectively. A node i ∈ V may represent an end device, an edge server, or the cloud, and both nodes and links are allowed to have heterogeneous computation and transmission capabilities. Let A denote the
set of DNN inference services supported by the network. For presentation simplicity, we assume each a ∈ A uses a DNN with two fixed (vertical) partitions, which are executed sequentially to transform the input data into the final inference result. Each a is associated with a source node sa ∈ V, a destination node da ∈ V, and an exogenous input rate λa (requests/sec)1 . We represent the corresponding inference process by three traffic stages: stage 0 denotes the raw input data, stage 1 denotes the intermediate activation generated after the first partition, and stage 2 denotes the final output generated after the second partition. Let La,k denote the packet size of stage k ∈ {0, 1, 2} for application a. For each application a ∈ A and partition index p ∈ {1, 2}, ∈ {0, 1} for we introduce a binary placement variable xa,p i = 1 indicates that partition p of every node i ∈ V, where xa,p i = 0 otherwise. Since application a is placed at node i, and xa,p i we consider non-replicated partition placement, each partition must be instantiated at exactly one node, i.e.,2 X a,p xi = 1, ∀a ∈ A, p ∈ {1, 2}. (1) i∈V
Under this setting, stage-0 traffic is routed toward the host node of partition 1, where it is processed and converted into stage-1 traffic; similarly, stage-1 traffic is routed toward the host node of partition 2, where it is converted into stage-2 traffic. Therefore, unlike [9], local computation is no longer treated as an independent forwarding option, but dependent on the DNN partition placement scheme. Privacy, security, or hardware constraints can be incorporated via feasible host sets Va,p ⊆ V with xa,p = 0 for i ∈ / Va,p , but are omitted here as i they are not our focus. Inspired by [9], we use a node-based representation to describe traffic forwarding in the network. Let ta,k denote the i traffic rate (requests/sec) of stage k ∈ {0, 1, 2} for application a observed at node i, including both traffic generated locally at i and traffic forwarded from other nodes. For each link (i, j) ∈ E, let ϕa,k ij ∈ [0, 1] denote the fraction of stage-k traffic at node i that is forwarded to node j. Since local computation is fully determined by the placement variables, the forwarding variables satisfy3 X a,0 X a,1 ϕij + xa,1 = 1, ϕij + xa,2 = 1, (2a) i i j∈V
j∈V
for all i ∈ V and a ∈ A. For the final stage, the traffic exits the network once it reaches the ( destination, and hence X a,2 0, i = da , ϕij = (2b) 1, i ̸= da . j∈V Eq. (2a) implies that a DNN partition host node absorbs and processes the incoming flow at corresponding stage, whereas a non-host node simply forwards it onward; (2) guarantees that traffic of each stage is routed and terminated in a manner consistent with the DNN execution process: by being processed 1 s = d corresponds to the common case where inference results are sent a a back to the user generating request. We also allow sa ̸= da . 2 The number “1” in (1) can be changed if allow DNN partition replication. 3 For notational convenience, we let ϕa,k ≡ 0 whenever (i, j) ∈ / E. ij
at the corresponding partition or by exiting the network at the destination. Since each DNN partition execution represents one request, and will generate one next-stage packet, thus4 X a,0 a,0 = tj ϕji + λa 1{i=sa } , ta,0 i j∈V
= ta,1 i
X a,1 a,1 a,0 tj ϕji + xa,1 i ti ,
Note that for networks with 2-hop or longer paths, Dij (Fij ) and Ci (Gi ) are not necessarily convex with respect to (x, ϕ). Problem (7) is a mixed integer non-convex optimization problem, where the binary variables x determine the partition placement and the continuous variables ϕ govern stage-wise traffic forwarding over the network.
(3)
j∈V
ta,2 = i
III. S OLUTION A PPROACH
X a,2 a,2 a,1 tj ϕji + xa,2 i ti . j∈V
We next formulate the communication and computation costs. For each application a ∈ A, stage k ∈ {0, 1, 2}, and link (i, j) ∈ E, let a,k a,k fij = ta,k (4) i ϕij denote the stage-k traffic rate of application a carried on link (i, j). The total traffic load (bit/sec) on (i, j) is then given by 2 XX a,k Fij = La,k fij . (5) a∈A k=0
Let wia,p be the per-request computation workload incurred at node i for processing partition p ∈ {1, 2} of application a. It may be affected by the DNN partition size, the node’s GPU capacity, etc., and can be directly measured from a test run. Since partition execution is fully determined by the placement variables, the total computation load at i is 2 XX a,p−1 Gi = wia,p xa,p . (6) i ti a∈A p=1
We model the nonlinear transmission cost on link (i, j) by Dij (Fij ) and the computation cost at node i by Ci (Gi ), where both Dij (·) and Ci (·) are assumed to be increasing, continuously differentiable, and convex, with Dij (0) = 0 and Ci (0) = 0. Compared to commonly used linear costs, these nonlinear cost functions better capture congestion effects (e.g., queueing) on communication and computation resources. For example, in an M/M/1 queue with service rate µ, F D(F ) = µ−F gives the average number of packets waiting in the queue or being served. Similar convex increasing functions can be used to model congestion at computation nodes hosting DNN partitions. They can also mimic the link/GPU capacity constraints [9]. When both D(·) and C(·) are interpreted as queue lengths, by Little’s law, the aggregate cost is proportional to the expected request end-to-end delay. a,k Let x = [xa,p i ] and ϕ = [ϕij ] denote the global partition placement and forwarding variables. We minimize the aggregate communication and computation cost in the network, cast as the joint partition placement and routing problem: X X min J(x, ϕ) = Dij (Fij ) + Ci (Gi ) x,ϕ
(i,j)∈E
subject to
i∈V
xa,p ∈ {0, 1}, ϕa,k i ij ∈ [0, 1],
(7)
(1)–(6) hold. 4 ta,k can be recursively calculated by (3), where ta,0 = λ at node d . a a i i
Problem (7) is challenging due to the coupling between discrete partition placement and continuous traffic forwarding, together with the nonlinear congestion-dependent communication and computation costs. In particular, binary x and continuous ϕ are tightly coupled, capturing a simple yet fundamental engineering intuition: DNN partitions should be placed at favorable nodes to reduce network cost, but what is favorable itself depends on how stage-wise traffic is routed. To address this difficulty, we adopt a heuristic yet effective alternating optimization framework, which iteratively updates partition placement and traffic forwarding strategies. We alternately update partition placement and traffic forwarding strategies. The key idea is that once one set of variables is fixed, the other becomes significantly easier to optimize. In particular, for a given partition placement, the forwarding step updates the stage-wise traffic routing toward the designated partition hosts. Conversely, for a given forwarding solution, the placement step reselects partition hosts to reduce the anticipated global cost under the current network state. The alternating framework is summarized in Algorithm 1. Algorithm 1: Alternating Optimization (ALT) Start with m = 0, an initial feasible partition placement x0 and forwarding strategy ϕ0 . 2 do 3 Update the forwarding variables under fixed partition placement xm to obtain ϕm+1 . 4 Update the partition placement under the current forwarding state ϕm+1 to obtain xm+1 . 5 Set m ← m + 1. 6 when m < Mmax and algorithm not converged; 1
Specifically, at iteration m, the forwarding subproblem with fixed DNN partition placement xm is given by X min Dij (Fij xm ) ϕ (i,j)∈E (8) a,k subject to (2) (3) hold, ϕij ∈ [0, 1], since when the partition placement is fixed, computation cost Ci are essentially fixed at all nodes i. Then, under current ϕm+1 , the placement subproblem is min J(x, ϕm+1 ) x (9) subject to (1) holds, xa,p ∈ {0, 1}. i The forwarding and placement subproblems are both still nontrivial to solve exactly at every outer iteration. Therefore, we adopt low-complexity inexact updates for both subproblems.
A. Forwarding subproblem. Given a partition placement xm , each application a essentially induces three ordered source–destination pairs: (sa , h1a ), (h1a , h2a ), and (h2a , da ), where h1a and h2a denote the host nodes of partitions 1 and 2 under xm . The forwarding task is therefore to route the three stages of traffic through the multi-hop network in a multi-path manner, so as to reduce the aggregate communication cost. We adopt a node-based inexact update following Gallager’s minimum-delay routing principle [11] and its service-chain extension in [9]. The basic idea is that each node gradually reallocates traffic toward outgoing links with smaller system marginal cost. Here, “marginal cost” represents the marginal increase in the overall system latency, consisting of both the immediate cost incurred on the outgoing link and the downstream cost over the remainder of the route. Specifically, the marginal cost of forwarding stage-(a, k) traffic from i to j can be written as (we omit subscript · xm for simplicity) a,k ′ δij = La,k Dij (Fij ) + qja,k ,
(10)
where qja,k
summarizes the downstream marginal cost-to-go under the current forwarding state, and can be recursively calculated from destination nodes toward upstream [9]. Then, each node performs at most Tϕ local forwarding updates: let a,k a,k δi,min ≜ min δij , j∈V
a,k j ⋆ ∈ arg min δij . j∈V
For each node i, application a, and stage k, we update h i a,k a,k a,k a,k ϕa,k δij − δi,min , j ̸= j ⋆ , (11) ij ← ϕij − αi +
and assign the remaining mass to j ⋆ so that (2) is preserved. We remark that a node-blocking mechanism is used to prevent the formation of routing loops. We omit further implementation details, including the exact blocking and update scheduling rules. Please see [9], [11] for a comprehensive explanation. B. Placement subproblem. Given a forwarding state ϕm+1 , the current traffic rates, link loads, and node computation loads are all determined. The placement task is then to update the partition hosts so as to reduce the anticipated global cost under the current network congestion state. To tackle the NP-hard placement subproblem (9) efficiently, we adopt a marginal-cost-based inexact reassignment rule. The basic idea is to evaluate each candidate host node according to the first-order communication and computation cost it would induce under the current forwarding state. Denote the marginal transmission and computation costs as (we omit subscript · ϕm+1 for simplicity) ′ ℓa,k ij ≜ La,k Dij (Fij ) ,
κa,p ≜ wia,p Ci′ (Gi ) . i
Then, for any two nodes u, v ∈ V, let X Γa,k uv ≜ min P :u⇝v
(i,j)∈P
ℓa,k ij ,
(12) (13)
where P : u ⇝ v denotes a directed path from u to v. Thus, Γa,k uv is the minimum cumulative marginal transmission cost from u to v under the current link marginal weights, and serves
as a first-order surrogate for the communication cost change in the placement update. We then define candidate score for placing partition 1 of application a at node i, a,1 Sa,1 (i) ≜ Γa,0 + Γa,1 sa i + κi ih2 ,
(14)
a
h2a
where is the current host of partition 2. Similarly, the candidate score for placing partition 2 at i is 5 a,2 Sa,2 (i) ≜ Γa,1 + Γa,2 ida , h1 i + κi
(15)
a
where h1a is the new host of partition 1. Each score consists of an upstream communication term, a local computation term, and a downstream communication term. For each a, we sequentially update the placement of partitions 1 and 2 by selecting the minimum-score host: h1a ← arg min Sa,1 (i), i∈V
h2a ← arg min Sa,2 (i). i∈V
(16)
m+1
The corresponding binary placement variables x are then updated accordingly. This yields a low-complexity discrete reassignment step that approximately decreases the placementside objective under the current forwarding state. Discussions. The proposed ALT algorithm is an inexact alternating procedure rather than an exact solver for (7). Its per-outer-iteration complexity consists of a forwarding-update part and a placement-update part. For the forwarding subproblem, since the number of stages is fixed to three, one local forwarding sweep updates all stage-wise variables by computing the current traffic/load state and the corresponding system marginal costs over the network. Assuming the downstream marginal costs qja,k are obtained by one backward recursion as in [9], each such sweep scales linearly with the number of applications and links, i.e., O(|A||E|); hence, performing Tϕ inner forwarding updates incurs complexity O(Tϕ |A||E|). For the placement subproblem, the candidate scores are built from shortest-path distances under the current marginal link weights. Because the stage-dependent edge ′ weight La,k Dij (Fij ) differs across stages only by a positive scalar factor, the shortest-path structure is determined by ′ the base link weight Dij (Fij ). Thus, for each application, it suffices to run at most four single-source shortest-path computations (from sa and h1a on the original graph, and to h2a and da on the reversed graph), followed by an O(|V|) scan over candidate nodes. Using Dijkstra’s algorithm for nonnegative weights, the placement update therefore costs O(|A||E| log |V| + |A||V|) per outer iteration. From an implementation perspective, the forwarding update retains the node-based structure of Gallager-style routing and does not require solving a global optimization problem at each iteration. Therefore, it is naturally amenable to scalable implementation: the update can be carried out in a distributed manner across nodes using marginal-cost message passing, or computed in parallel by a central server with knowledge of the current network state. The placement update is written here in a centralized form for clarity, since it requires comparing 5 We first update partition 1 while fixing the current host of partition 2, and then update partition 2 using the newly selected host of partition 1.
candidate host scores across nodes. Nevertheless, the same logic can also be implemented in a distributed or hierarchical manner through suitable message exchange and coordination protocols; we leave such protocol design to future work. Since both subproblems are solved only approximately, we do not claim convergence to a global optimum. Instead, ALT should be viewed as a practical iterative-improvement algorithm, and we terminate it when the objective value changes by less than a prescribed threshold or when the maximum number of outer iterations is reached. Finally, two limiting cases are worth noting. First, if the communication and computation costs are linear, then the marginal quantities become constant and the method reduces to shortest-path-style routing together with a simple path-plus-processing placement rule. Second, if the two DNN partitions are placed at the same node, the inter-partition communication term vanishes, so the model naturally includes the degenerate case where the entire DNN is effectively executed at a single node. IV. N UMERICAL E VALUATION We evaluate the proposed alternating framework on four representative network scenarios, namely IoT, Mesh, Smallworld, and GEANT. Specifically, IoT captures a hierarchical IoT–edge–cloud system with strongly heterogeneous communication and computation resources. Mesh is a regular 5 × 5 mesh. Small-world is a fixed small-world instance, used to capture irregular shortcut-rich connectivity. GEANT is a real backbone-inspired topology based on GEANT, used to assess the method on a realistic irregular graph. For all scenarios, applications are generated using a fixed random seed, so that the source–destination pairs and arrival rates are reproducible across all algorithms. Unless otherwise specified, the communication stages have sizes (L0 , L1 , L2 ). The first partition is lighter than the second one, reflecting the intended split structure in which the first partition may act as a local compression stage while the second partition performs more computation-intensive inference. We use M/M/1 queuelike costs on both links and computing nodes, with µ and ν denoting link capacity and computing service rates, respectively. We compare the following methods: a. ALT: the proposed alternating congestion-aware placement and forwarding method. Starting from a feasible structured initialization, it repeatedly updates forwarding and partition placement using congestion-aware marginal costs until convergence. This is the full version of our method, combining congestion-aware modeling with iterative alternating refinement. b. OneShot: a single-pass variant of the proposed framework. It uses the same congestion-aware objective and the same structured initialization as ALT, but performs only one round of placement/forwarding update instead of repeated alternation. Comparing ALT with OneShot isolates the benefit of iterative alternating refinement. c. CongUnaware: a congestion-unaware shortest-extendedpath baseline. It constructs the split execution decision by solving a shortest-path problem on an extended graph,
where communication and computation are both modeled as linear costs and no congestion feedback is incorporated. Comparing ALT with CongUnaware isolates the benefit of explicit congestion-aware modeling. d. CoLocated: a baseline that enforces colocated execution of the two partitions. It selects a single common execution node for both partitions and then optimizes forwarding under this restriction. Comparing ALT with CoLocated isolates the benefit of split flexibility, i.e., allowing the two partitions to be placed at different nodes. Table. I summarizes the main experimental settings and the overall comparison, including scenario configurations. Fig. 2 reports the normalized total cost across all four scenarios. The costs are normalized within each scenario by the largest cost among the compared methods, so that the relative gap is emphasized. The results reveal three distinct regimes. Our proposed method ALT achieves the lowest cost in all tested scenarios. We observe that, across all scenarios, CongUnaware performs significantly worse than the other methods, indicating that, in congestion-unaware settings, queue-like costs in highly loaded scenarios can incur large expected delays. In Meanwhile, OneShot is consistently inferior to ALT, since a single placement–forwarding update is generally insufficient to fully capture the mutual dependence between congestion-aware routing and partition placement. Moreover, CoLocated performs poorly because enforcing both partitions to execute at the same node removes the flexibility of split execution, thereby preventing the system from simultaneously exploiting communication-efficient local preprocessing and computationefficient offloading. To provide intuition for the hierarchical setting, Fig. 3 illustrates the IoT topology used in our experiments. The line thickness reflects link bandwidth, the node size reflects computation capability, and the node colors distinguish cloud, edge, and IoT devices. This scenario is intentionally designed to expose the tension between local preprocessing and offloading: IoT devices have weak computation and weak uplinks to edge servers, edge servers are substantially stronger, and the cloud has the highest computation capacity but introduces additional communication cost. This setting explains why split flexibility is particularly valuable in the IoT case. We next study the effect of increasing workload. Fig. 4 plots the objective value against a global input-rate scaling factor. The proposed ALT method consistently attains the lowest objective across the tested load range, while the gap relative to O NE S HOT, C ONG U NAWARE, and C O L OCATED widens as the system becomes more heavily loaded. This behavior is precisely the regime in which congestion modeling matters most: under light load, the queueing costs remain close to their linear region, and all methods behave similarly; under higher load, the nonlinear congestion penalties amplify poor routing or poor placement decisions, thereby making repeated congestion-aware refinement increasingly beneficial. Finally, Fig. 5 illustrates the communication–computation
|V|
|A|
µ̄
ν̄
(L0 , L1 , L2 )
λ̄
IoT Mesh SW GEANT
17 25 30 22
20 30 40 30
8.0 8.0 10.0 10.0
8.0 8.0 10.0 10.0
(2.0, 0.8, 0.3) (2.0, 0.8, 0.3) (2.0, 0.8, 0.3) (2.0, 0.8, 0.3)
3.0 3.0 3.0 3.0
TABLE I: Tested scenarios
Normalized total cost
Name
ALT
1.0 0.8 0.6 0.4 0.2 0.0
OneShot
IoT
CongUnaware
Mesh
CoLocated
Small-world
GEANT
Fig. 2: Normalized objective J in all scenarios Edge
10
IoT
8
Objective
0
1
2
3
3
ALT OneShot CongUnaware CoLocated
weighted computation cost weighted communication cost 2.491
2.5
weighted total cost
Cloud
6
4
4
2.386 2.238
2.202
0.3
0.4
2.260
2.310
2.376
2.438
2.499
2
1.5
1
2 0.5
5
7
8
10
11
13 14
16
0.25 6
9
12
15
Fig. 3: Sample topology (IoT)
0.5
0.75
1
1.25
1.5
Input rate scaling factor
Fig. 4: J versus input-rate scaling factor in IoT.
0 0.1
0.2
0.5
0.6
0.7
0.8
0.9
weight factor
Fig. 5: communication–computation tradeoff in IoT
tradeoff. We solve the problem under a weighted objective
R EFERENCES
Jη = ηJcomm + (1 − η)Jcomp ,
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where η ∈ [0, 1] controls the emphasis on communication cost. The figure reports the weighted total cost together with its communication and computation components. As expected, increasing η shifts the optimized solution toward communication-efficient operation, while decreasing η prioritizes computation efficiency. Interestingly, the total weighted objective exhibits a shallow minimum at an intermediate value of η, indicating that neither extreme communication minimization nor extreme computation minimization is universally optimal in this scenario. This observation confirms that the proposed framework is not merely reducing one cost component at the expense of the other; rather, it meaningfully adapts the split placement and forwarding strategy to the desired operating point. V. C ONCLUSION We studied congestion-aware split execution and forwarding for DNN services in heterogeneous networks with nonlinear communication and computation costs. We proposed ALT, an alternating congestion-aware method that jointly refines placement and forwarding. The numerical experiment results show that split flexibility is especially important in hierarchical IoT–edge–cloud settings, while congestion-aware refinement becomes more beneficial as the offered load increases. They also show that the preferred solution depends on the communication–computation tradeoff, and that the proposed method can adapt to different operating points. ACKNOWLEDGMENT This work is supported, in part, by EPSRC and DSIT under grants: EP/X040518/1, EP/Y037421/1, and EP/Y019229/1.