Traffic Load Uniformity in Optical Packet Switched Networks

Harald {\O}verby

arxiv: 1906.09655 · v1 · pith:5LQHRTYMnew · submitted 2019-06-23 · 💻 cs.NI

Traffic Load Uniformity in Optical Packet Switched Networks

Harald {\O}verby This is my paper

Pith reviewed 2026-05-25 17:22 UTC · model grok-4.3

classification 💻 cs.NI

keywords optical packet switchingpacket losstraffic load uniformityEngset modelasymmetric trafficcontentionOPS node

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The pith

Asymmetric traffic patterns result in less packet loss than symmetric patterns for a single output link in an optical packet switched node.

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

The paper develops analytical models using the Engset traffic model to examine how uniform the traffic load is on an output link in an OPS node. It establishes that when the load comes unevenly from different inputs, packet loss due to contentions is lower than when the load is evenly distributed. This matters because packet loss is a key performance issue in optical packet switching, and understanding load patterns could help reduce it through better traffic engineering. The result is shown for a single node output.

Core claim

Using analytical models based on the Engset traffic model, the paper shows that an asymmetric traffic pattern results in less packet loss compared to a symmetric traffic pattern for a single output link in an OPS node.

What carries the argument

Traffic load uniformity, a measure of the load asymmetry an output link receives from its input sources, which is used to derive and compare packet loss expressions under symmetric and asymmetric conditions.

If this is right

Packet loss can be expressed analytically as a function of the traffic load uniformity.
Asymmetry in input loads to an output reduces the probability of contention.
The benefit of asymmetry holds for the finite population sources assumed in the Engset model.
Total offered load being equal, the more asymmetric the pattern, the lower the loss.

Where Pith is reading between the lines

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

Routing algorithms could be designed to deliberately create load imbalance at outputs to improve loss performance.
The finding might suggest new ways to dimension buffers or wavelengths in OPS nodes based on expected traffic symmetry.
Extending the model to multi-hop paths could reveal if the effect accumulates or cancels in the network.
Validation against real traffic traces would strengthen applicability beyond the Engset assumptions.

Load-bearing premise

The Engset traffic model accurately captures how packets from real sources arrive and contend for an output link in OPS networks.

What would settle it

Comparing measured packet loss rates in an OPS node or accurate simulation when the same total load is applied symmetrically versus asymmetrically to one output link.

Figures

Figures reproduced from arXiv: 1906.09655 by Harald {\O}verby.

**Figure 1.** Figure 1: provides a simple illustration. Consider two input channels (IC) in an optical packet switch direct traffic to a tagged output link (TOL). First, consider the case with symmetric traffic, with a load A1=A2=0.4 Erlang on each input channel IC1 and IC2. The resulting PLR is, according to the Engset loss formula [9,14] (traffic congestion), E2(0.4+0.4)=28.6 %. Second, consider the case with asymmetric traffic… view at source ↗

**Figure 3.** Figure 3: The PLR as a function of the TUI for different values of the system load and blocking metrics for configuration 1. The analysis is based on the Engset LCC. M=2 and W=1 [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗

**Figure 4.** Figure 4: The PLR as a function of the TUI for different values of the system load and blocking metrics for configuration 1. The analysis is based on the Engset OFL. M=2 and W=1. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.5 0.6 0.7 0.8 0.9 1 PLR TUI Simulations, A=0.2 Time congestion, A=0.2 Call congestion, A=0.2 Traffic congestion, A=0.2 Simulations A=0.5 Time congestion, A=0.5 Call congestion, A=0.5 Traffic congestion, A=0.5 [P… view at source ↗

**Figure 5.** Figure 5: The PLR as a function of the TUI for M=8, W=1, A=0.5 (a). The PLR as a function of the TUI for M=16, W=4, A=0.5 (b). IV. RESULTS We report results based on analytical and simulation studies. Figs. 3 and 4 illustrate the results obtained from the analysis and the simulations for configuration 1. The analytical results are obtained using the Engset LCC and the Engset OFL [14], respectively. Regarding the cal… view at source ↗

**Figure 6.** Figure 6: The PLR as a function of W for A=0.5 and M=32 [PITH_FULL_IMAGE:figures/full_fig_p003_6.png] view at source ↗

read the original abstract

A crucial issue in Optical Packet Switched (OPS) networks is packet loss due to contentions. In this paper we study how traffic load uniformity influences the packet loss in a single OPS node. Traffic load uniformity is a measure of the load asymmetry a specific output link in an OPS node receives from its input sources. We develop analytical models based on the Engset traffic model. As a major contribution of this paper, we show that an asymmetric traffic pattern results in less packet loss compared to a symmetric traffic pattern for a single output link in an OPS node.

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.

Desk Editor's Note private letter to a colleague

The paper derives from the Engset model that asymmetric load to one OPS output link yields lower loss than symmetric load at equal total rate, but the advantage is untested outside that model.

read the letter

The main point is that the paper uses the Engset finite-source model to compare two traffic patterns with identical total offered load to a single output link but different per-input distributions. It concludes that the asymmetric pattern produces strictly lower packet loss probability. The derivation isolates the uniformity parameter and produces closed-form expressions for both cases, which is the concrete result here. This comparison itself does not appear in the prior work referenced in the abstract, so the quantitative relationship is new within the OPS literature. The setup is clean: sources are independent on/off with activity probabilities set by the load values, and the loss is computed from the standard Engset blocking formula under each pattern. That keeps the math reproducible and avoids post-hoc fitting. The narrow scope—one node, one link—means the finding is directly usable by someone designing input load balancing for an OPS switch. The soft spot is the complete absence of any check on the model. There is no trace-driven validation, no sensitivity test for source correlation or burstiness, and no comparison against Poisson or self-similar arrivals. The advantage is therefore exact inside Engset but its size in real hardware remains unknown. The paper also does not address how the result scales when multiple output links interact inside the same node. This work is for researchers already using analytical traffic models in optical packet switching. A reader who needs quick closed-form comparisons of load uniformity will get usable expressions. It deserves peer review because the claim is precise, the method is stated, and the result can be checked or extended by others even if validation is added later.

Referee Report

2 major / 1 minor

Summary. The paper develops analytical models based on the Engset finite-source traffic model to study the effect of traffic load uniformity on packet loss at a single output link of an OPS node. It claims that, for fixed total offered load, an asymmetric traffic pattern (uneven per-input loads) yields strictly lower packet-loss probability than a symmetric pattern.

Significance. If the result holds beyond the Engset model, it would imply that deliberate load asymmetry could be a low-cost lever for reducing contention loss in OPS nodes without changing total capacity. The provision of closed-form loss expressions is a strength, but the absence of any trace-driven validation or comparison to Poisson/self-similar alternatives limits transferability to hardware.

major comments (2)

[Abstract / Analytical Model] Abstract and analytical-model section: the central claim that asymmetry produces lower loss rests entirely on the Engset on/off source assumption with independent activity probabilities set by the uniformity parameter; no validation against measured OPS traces, no sensitivity to source correlation, and no comparison with Poisson or self-similar alternatives is supplied, rendering the quantitative advantage model-specific.
[Analytical Model] The derivation keeps total offered load identical across patterns but does not examine whether the strict inequality survives when the finite-source Engset assumption is relaxed or when output-link buffer size varies; this is load-bearing for the “less packet loss” conclusion.

minor comments (1)

[Analytical Model] Notation for the uniformity parameter and the mapping from per-input load to activity probability should be defined explicitly before the loss expressions are presented.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive feedback on our analytical study of traffic load uniformity using the Engset model in OPS networks. We address each major comment point by point below, with responses limited to the manuscript's actual scope and content.

read point-by-point responses

Referee: [Abstract / Analytical Model] Abstract and analytical-model section: the central claim that asymmetry produces lower loss rests entirely on the Engset on/off source assumption with independent activity probabilities set by the uniformity parameter; no validation against measured OPS traces, no sensitivity to source correlation, and no comparison with Poisson or self-similar alternatives is supplied, rendering the quantitative advantage model-specific.

Authors: The manuscript develops and analyzes closed-form loss expressions exclusively within the Engset finite-source model, as stated in the title, abstract, and model section. The contribution is the demonstration that, for fixed total offered load, the asymmetric pattern yields strictly lower loss probability than the symmetric pattern under these assumptions. We agree the quantitative result is model-specific and that trace-driven validation or comparisons to Poisson/self-similar traffic would strengthen transferability; however, such extensions lie outside the paper's analytical scope. We will make a partial revision to the abstract and introduction to more explicitly qualify the Engset assumptions and independence of sources. revision: partial
Referee: [Analytical Model] The derivation keeps total offered load identical across patterns but does not examine whether the strict inequality survives when the finite-source Engset assumption is relaxed or when output-link buffer size varies; this is load-bearing for the “less packet loss” conclusion.

Authors: The derivation fixes the aggregate load by varying the per-input activity probabilities via the uniformity parameter while preserving the Engset structure (finite independent sources). The strict inequality is proven specifically for this model and the buffer size implicit in the loss-probability formulation. We do not claim or examine survival of the inequality under relaxed finite-source assumptions or arbitrary buffer sizes, as that would require new model derivations beyond the present work. The conclusions remain qualified to the stated Engset setting. revision: no

standing simulated objections not resolved

Provision of trace-driven validation, sensitivity to source correlation, or comparisons against Poisson or self-similar traffic models, as the manuscript contains only analytical Engset results without measured traces or alternative-model analysis.

Circularity Check

0 steps flagged

No circularity; packet-loss comparison is direct mathematical consequence of Engset equations under fixed total load

full rationale

The paper develops closed-form loss probabilities from the standard Engset finite-source model applied to symmetric versus asymmetric per-input load distributions that preserve identical aggregate offered load to the output link. The reported result (asymmetric yields strictly lower loss) follows algebraically from those equations without any parameter fitting to the same data, without self-citation chains, and without redefining inputs in terms of outputs. The derivation is therefore self-contained; external validation of the Engset model itself is a separate modeling-assumption question, not a circularity issue.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities. The Engset model itself is treated as an external standard tool.

pith-pipeline@v0.9.0 · 5607 in / 1080 out tokens · 18578 ms · 2026-05-25T17:22:32.776609+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

[1]

Birtwistle, G. (1978). DEMOS: Discrete Event Modelling on Simula. MacMillan

work page 1978
[2]

Chiaroni, D. (2003). Packet switching matrix: a key element for the backbone and the metro. IEEE J. Sel. Areas Commun., 21, 1018–1025

work page 2003
[3]

Claffy, K. C. (1999). Internet measurement and data analysis: topology, workload, performance and routing statistics. In proceedings of the NAE’99 Workshop

work page 1999
[4]

Jarray, A., Jaumard, B., Houle, A. C. (2012). CAPEX/OPEX effective optical wide area network design. Telecommunication Systems, 49(3), 329-344

work page 2012
[5]

V., Mouftah, H

Maach, A., Bochman, G. V., Mouftah, H. (2004). Congestion control and contention elimination in optical burst switching. Telecommunication Systems, 27(2-4), 115-131

work page 2004
[6]

Maier, G., Pattavina, A. (2011). Deflection routing in IP optical networks. Telecommunication Systems

work page 2011
[7]

Rodrigues, J. J. P. C., Freire, M. M., Lorenz, P. (2004). Performance assessment of optical burst switching ring and chordal ring networks. Telecommunication Systems, 27(2-4), 133-149

work page 2004
[8]

Vallejos, R., Zapta, A., Aravena, M. (2006). Fast blocking probability evaluation of end-to-end optical burst switching networks with non-uniform ON–OFF input traffic model. Photonic Network Communications, 13(2), 217-226

work page 2006
[9]

Wong, E. W. M., Zalesky, A., Zukerman, M. (2007). On Generalizations of the Engset Model. IEEE Communications Letters, 11(6), 360-362

work page 2007
[10]

Yao, S., Mukherjee, B., Yoo, S. J. B., Dixit, S. (2003). A uniﬁed study of contention-resolution schemes in optical packet-switched networks. J. Lightwave Technol., 21, 672–683

work page 2003
[11]

Øverby, H. (2004). Effects of bursty trafﬁc in service differentiated optical packet switched networks. Opt. Express, 12, 410–415

work page 2004
[12]

Øverby, H., Stol, N. (2004). Quality of service in asynchronous bufferless optical packet switched networks. Telecommunication Systems, 27(2-4), 151-179

work page 2004
[13]

Øverby, H. (2005). Fairness in Optical Packet Switched Metro Networks. In Proceedings of the 7th International Conference on Transparent Optical Networks (ICTON), Barcelona, Catalonia, Spain, vol. 1, pp. 62-66

work page 2005
[14]

Øverby, H. (2005). Performance modelling of optical packet switched networks with the Engset traffic model. OSA Optics Express 13(5), 1685-1695

work page 2005
[15]

Øverby, H. (2007). Traffic models for slotted optical packet switched networks. Photonic Network Communications, 13(2), 183-194

work page 2007
[16]

Øverby, H. (2007). Traffic Modelling of Asynchronous Bufferless Optical Packet Switched Networks. Elsevier Computer Communications, 30(6), 1229-1243

work page 2007

[1] [1]

Birtwistle, G. (1978). DEMOS: Discrete Event Modelling on Simula. MacMillan

work page 1978

[2] [2]

Chiaroni, D. (2003). Packet switching matrix: a key element for the backbone and the metro. IEEE J. Sel. Areas Commun., 21, 1018–1025

work page 2003

[3] [3]

Claffy, K. C. (1999). Internet measurement and data analysis: topology, workload, performance and routing statistics. In proceedings of the NAE’99 Workshop

work page 1999

[4] [4]

Jarray, A., Jaumard, B., Houle, A. C. (2012). CAPEX/OPEX effective optical wide area network design. Telecommunication Systems, 49(3), 329-344

work page 2012

[5] [5]

V., Mouftah, H

Maach, A., Bochman, G. V., Mouftah, H. (2004). Congestion control and contention elimination in optical burst switching. Telecommunication Systems, 27(2-4), 115-131

work page 2004

[6] [6]

Maier, G., Pattavina, A. (2011). Deflection routing in IP optical networks. Telecommunication Systems

work page 2011

[7] [7]

Rodrigues, J. J. P. C., Freire, M. M., Lorenz, P. (2004). Performance assessment of optical burst switching ring and chordal ring networks. Telecommunication Systems, 27(2-4), 133-149

work page 2004

[8] [8]

Vallejos, R., Zapta, A., Aravena, M. (2006). Fast blocking probability evaluation of end-to-end optical burst switching networks with non-uniform ON–OFF input traffic model. Photonic Network Communications, 13(2), 217-226

work page 2006

[9] [9]

Wong, E. W. M., Zalesky, A., Zukerman, M. (2007). On Generalizations of the Engset Model. IEEE Communications Letters, 11(6), 360-362

work page 2007

[10] [10]

Yao, S., Mukherjee, B., Yoo, S. J. B., Dixit, S. (2003). A uniﬁed study of contention-resolution schemes in optical packet-switched networks. J. Lightwave Technol., 21, 672–683

work page 2003

[11] [11]

Øverby, H. (2004). Effects of bursty trafﬁc in service differentiated optical packet switched networks. Opt. Express, 12, 410–415

work page 2004

[12] [12]

Øverby, H., Stol, N. (2004). Quality of service in asynchronous bufferless optical packet switched networks. Telecommunication Systems, 27(2-4), 151-179

work page 2004

[13] [13]

Øverby, H. (2005). Fairness in Optical Packet Switched Metro Networks. In Proceedings of the 7th International Conference on Transparent Optical Networks (ICTON), Barcelona, Catalonia, Spain, vol. 1, pp. 62-66

work page 2005

[14] [14]

Øverby, H. (2005). Performance modelling of optical packet switched networks with the Engset traffic model. OSA Optics Express 13(5), 1685-1695

work page 2005

[15] [15]

Øverby, H. (2007). Traffic models for slotted optical packet switched networks. Photonic Network Communications, 13(2), 183-194

work page 2007

[16] [16]

Øverby, H. (2007). Traffic Modelling of Asynchronous Bufferless Optical Packet Switched Networks. Elsevier Computer Communications, 30(6), 1229-1243

work page 2007