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arxiv: 1906.10549 · v1 · pith:OUACI4OPnew · submitted 2019-06-24 · 💻 cs.NI

An End-to-End Performance Analysis for Service Chaining in a Virtualized Network

Emmanouil Fountoulakis , Qi Liao , Nikolaos Pappas This is my paper

Pith reviewed 2026-05-25 17:17 UTC · model grok-4.3

classification 💻 cs.NI
keywords service chainingNFVMECqueueing modelperformance analysisend-to-end delayvirtual network functions
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The pith

A queueing model for service-chained virtual network functions yields analytical expressions for end-to-end performance metrics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models an end-to-end system with MEC servers and core network servers hosting virtual network functions under service chaining constraints. It develops a queueing network that accounts for both processing and transmission flows to derive analytical expressions for metrics such as delay and throughput. The same method applies to larger extended systems, producing a stochastic model whose predictions align with simulations. This enables evaluation under different scenarios to inform traffic flow control decisions.

Core claim

The authors construct a queueing model for a communications system consisting of MEC servers and a core network server with different types of virtual network functions. They propose a method to derive analytical expressions for performance metrics of interest for both the base system and an extended larger system, resulting in a stochastic model. Simulation results coincide with the analytical predictions.

What carries the argument

A queueing network model capturing processing at virtual network functions and transmission flows between them in a service chaining setup.

If this is right

  • Closed-form expressions for performance metrics allow rapid evaluation of system behavior without running simulations.
  • The model supports analysis of larger systems through the same derivation method.
  • Insights from different scenarios guide decisions on traffic flow control and its effects on latency and throughput.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such models could help optimize the placement of virtual functions across edge and core to meet latency targets.
  • The queueing approach might extend to performance analysis in other distributed computing chains like microservices.
  • Validation across more realistic traffic patterns would strengthen applicability to IoT scenarios.

Load-bearing premise

The actual distributed system of virtual network functions with service chaining behaves like the proposed queueing network in terms of processing and transmission flows.

What would settle it

Running simulations or measurements on a physical MEC deployment with service chaining and comparing the observed end-to-end delays against the paper's analytical formulas under varying arrival rates and chain lengths.

Figures

Figures reproduced from arXiv: 1906.10549 by Emmanouil Fountoulakis, Nikolaos Pappas, Qi Liao.

Figure 1
Figure 1. Figure 1: System model: Blue dashed lines group the queues located in the same server. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Two dimensional Markov chain for the subsystem consisting of [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Markov chain for Q5. below P3 =              λ¯ 5 λ5 λ¯ 5µ5 λ5µ5 + λ¯ 5µ¯5 λ5µ¯5 λ¯ 5µ5 λ5µ5 + λ¯ 5µ¯5 λ5µ¯5 . . . . . . . . . λ¯ 5µ5 λ¯ 5µ¯5 + λ5              . We denote the steady state distribution of Subsystem 3 by π (3) = h π (3) 0 , π (3) 1 , . . . , π (3) M5 i . To derive π (3), we solve the following linear system of equations, π (3)P3 = π (3) , π (3)1 = 1. Using balance … view at source ↗
Figure 4
Figure 4. Figure 4: Markov chain for Q6. by λ6 = λ6,2 + λ6,5. We model the system as a Markov chain as shown in [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Two user devices transmit tasks to two primary MEC servers (locating at base stations) [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Effect of routing decision on the system performance. [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Effect of routing decision on the system performance. [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Objective: To maximize the system throughput. [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Objective: To minimize the system delay. [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Performance region. µ3 = µ4 = µ5 = µ, µ6 = 1, p = 0.8. Mi = M for 1 ≤ i ≤ 5, M6 = 100. 10a, the performance region is shown. We generate the region by selecting different parameters of the system. In particular, we vary the service rates and the capacities of Q1 −Q5, and we take the corresponding points as shown in the diagram. Each horizontal line is created by fixing the service rates and varying the ca… view at source ↗
Figure 11
Figure 11. Figure 11: System throughput vs system delay. µi = 0.6 for 1 ≤ i ≤ 5 and 7 ≤ i ≤ 11. µ = 1. M6 = 100, Mi = 50, for 1 ≤ i ≤ 5 and 7 ≤ i ≤ 11. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 50 100 150 200 250 (a) Performance of BS1. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0 20 40 60 80 100 120 (b) Performance of BS2 and the effect of high traffi… view at source ↗
Figure 12
Figure 12. Figure 12: Throughput vs delay performance. p2 = 0.5, µi = 0.5, ∀i, Mi = 50 for 1 ≤ i ≤ 5 and 7 ≤ i ≤ 11. M6 = 100 [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Throughput vs delay performance. p1 = 0.7. µi = 0.5 for 1 ≤ i ≤ 5 and 7 ≤ i ≤ 11. µ6 = 1, Mi = 50 for 1 ≤ i ≤ 5 and 7 ≤ i ≤ 11. M6 = 100. by comparing the analytical and simulations results. The routing decisions for all the cases are equal to 0.5. In [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Stochastic model of the server in the core. [PITH_FULL_IMAGE:figures/full_fig_p027_14.png] view at source ↗
read the original abstract

Future mobile networks supporting Internet of Things are expected to provide both high throughput and low latency to user-specific services. One way to overcome this challenge is to adopt Network Function Virtualization (NFV) and Multi-access Edge Computing (MEC). Besides latency constraints, these services may have strict function chaining requirements. The distribution of network functions over different hosts and more flexible routing caused by service function chaining raise new challenges for end-to-end performance analysis. In this paper, as a first step, we analyze an end-to-end communications system that consists of both MEC servers and a server at the core network hosting different types of virtual network functions. We develop a queueing model for the performance analysis of the system consisting of both processing and transmission flows. We propose a method in order to derive analytical expressions of the performance metrics of interest. Then, we show how to apply the similar method to an extended larger system and derive a stochastic model for such systems. We observe that the simulation and analytical results coincide. By evaluating the system under different scenarios, we provide insights for the decision making on traffic flow control and its impact on critical performance metrics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims to develop a queueing model for end-to-end performance analysis of a communications system consisting of MEC servers and a core-network server hosting VNFs, with both processing and transmission flows under service chaining. It proposes an (unspecified) method to derive analytical expressions for performance metrics, extends the same method to derive a stochastic model for larger systems, and reports that analytical and simulation results coincide. The work also evaluates different scenarios to yield insights on traffic-flow control decisions.

Significance. If the derivations are correct and the queueing-network representation is faithful, the paper would supply a useful analytical framework for joint processing/transmission performance in NFV/MEC environments with chaining constraints—an area of practical importance for low-latency IoT services. The reported match between analysis and simulation plus the explicit extension to larger systems would be genuine strengths; the absence of free parameters or self-referential fitting is also positive.

major comments (2)
  1. [Abstract] Abstract (and model-development paragraph): the central claim that 'analytical expressions' exist, match simulation, and extend to larger systems is asserted without any derivation steps, arrival/service process assumptions, independence conditions, or error bounds. This renders the soundness of the performance-metric formulas unverifiable from the supplied text.
  2. [Abstract] Abstract (weakest-assumption paragraph): the model fidelity claim—that a real distributed VNF chaining system can be faithfully captured by the proposed queueing network—is stated but not supported by any concrete mapping of hosts, routing, or resource-sharing details to queueing primitives, leaving the applicability of the derived expressions untested.
minor comments (1)
  1. The abstract could explicitly name the performance metrics (e.g., end-to-end delay, throughput) and the queueing disciplines employed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. Below we provide point-by-point responses to the major comments.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and model-development paragraph): the central claim that 'analytical expressions' exist, match simulation, and extend to larger systems is asserted without any derivation steps, arrival/service process assumptions, independence conditions, or error bounds. This renders the soundness of the performance-metric formulas unverifiable from the supplied text.

    Authors: The abstract is intended as a concise summary. The full derivations, including arrival and service process assumptions (Poisson arrivals and exponential service times for processing and transmission), independence conditions allowing for product-form solutions, and error bounds via simulation validation, are detailed in the model development and analysis sections of the manuscript. We will revise the abstract to include a short statement on the key assumptions and method to improve verifiability. revision: yes

  2. Referee: [Abstract] Abstract (weakest-assumption paragraph): the model fidelity claim—that a real distributed VNF chaining system can be faithfully captured by the proposed queueing network—is stated but not supported by any concrete mapping of hosts, routing, or resource-sharing details to queueing primitives, leaving the applicability of the derived expressions untested.

    Authors: The manuscript provides a concrete mapping in the system model section, where MEC servers are represented as queues for VNF processing, the core network server as a queue for both processing and transmission, and service chaining as probabilistic routing between these queues. Resource sharing is incorporated by modeling server capacities. We will update the abstract to briefly describe this mapping to strengthen the fidelity claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper constructs a standard queueing network model for joint processing and transmission flows in a service-chaining NFV/MEC system, then applies an (unspecified) derivation method to obtain performance metrics. Validation consists of matching these expressions to independent simulation runs. No load-bearing step reduces by construction to a fitted parameter, self-citation, or self-definitional relation; the derivation chain is presented as following from classical queueing principles and remains externally falsifiable via simulation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed from abstract only; full parameter list, axioms, and any invented modeling constructs are not visible. The central modeling premise is the applicability of queueing theory to the joint processing-transmission flows.

axioms (1)
  • domain assumption The end-to-end system with distributed virtual network functions can be represented as a queueing network whose processing and transmission components admit closed-form or tractable performance expressions.
    This premise underpins the proposed derivation method and the claim that analytical results coincide with simulation.

pith-pipeline@v0.9.0 · 5735 in / 1279 out tokens · 37370 ms · 2026-05-25T17:17:46.379301+00:00 · methodology

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Reference graph

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