Mobility Sigma Accounting¶

PLMN-GraphSim treats mobility signaling as a per-handover byte counter, denoted \(\sigma\). The simulator does not replay packet-level protocol messages. Instead, each detected cell change is classified by depth, charged with the constant for that depth, and accumulated over the run.

The same handover stream feeds both architectures. The only difference is the per-event charge.

flowchart LR
    H[Same UE movement trace] --> C[Classify handover depth]
    C --> F5[5G sigma charge]
    C --> R[6G-RUPA sigma charge]
    F5 --> S[Accumulate Sigma]
    R --> S
    S --> A[Compare total signaling]

This page covers how to read the mobility scenario's output. The constants themselves are derived in The Signaling Cost Model, and the procedure behind each one is drawn out message by message in Handover Sequence Diagrams.

Constants¶

Event	5G charge	6G-RUPA charge	Simulator counters
\(d=1\): serving edge UPF unchanged	600 B	200 B	`sigma_5g_xn`, `sigma_rupa_intra`
\(d=2\): serving edge UPF or UL-CL changes, PSA pinned	1150 B	200 B	`sigma_5g_n2`, `sigma_rupa_inter`
\(d=3\): PSA relocation, SSC mode 2 or 3	2200 to 2700 B	200 B	not charged in routine SSC-1 runs
\(d=4\): roaming entry, deployed HR re-establishment	3250 B	450 B	`sigma_roam_5g`, `sigma_roam_rupa`
\(d=4\): roaming entry, idealized 5G border handover	1300 B	450 B	sensitivity mode

Routine intra-PLMN mobility uses SSC mode 1: the PSA is pinned for the PDU session lifetime. Crossing into another PSA region is therefore still a \(d=2\) event in the simulator; the cost surfaces as path stretch, not as PSA relocation. \(d=3\) is a policy decision rather than a geometric one, so it never fires on a routine run.

The counter names are historical, and they misname the classification

sigma_5g_xn and sigma_5g_n2 suggest that \(d=1\) means an Xn handover and \(d=2\) means an N2 handover. That is not what the simulator computes, and it is not how 3GPP works. Which RAN procedure runs (Xn or N2) and whether the serving UPF changes are independent axes. TS 23.502 Sec. 4.9.1.2.4 is an Xn handover that does relocate the intermediate UPF, and Sec. 4.9.1.3 step 5 is conditional, so an N2 handover may well keep it.

src/Simulation/Handover.jl classifies on the UPF, never on the RAN procedure:

handover_level(topology, old_upf, new_upf) = old_upf == new_upf ? 1 : 2

Read sigma_5g_xn as "depth-one bytes" and sigma_5g_n2 as "depth-two bytes". The numbers are unaffected; only the names are wrong. See Handover Sequence Diagrams Sec. 2 for the full taxonomy.

What Each Depth Charges¶

\(d=1\), serving edge UPF unchanged, 600 B. The user moves between base stations served by the same edge UPF. Only the N3 tunnel endpoint is rewritten, through one PFCP Session Modification. Realized by TS 23.502 Sec. 4.9.1.2.2 over Xn, or by Sec. 4.9.1.3 with the conditional UPF selection skipped.

\(d=2\), serving edge UPF or UL-CL changes, PSA preserved, 1150 B. The user crosses into another edge UPF's region. The old session is released, a new one established, and the path repointed at both ends, while the PSA and the UE's IP address stay pinned. Realized by TS 23.502 Sec. 4.9.1.2.4 over Xn, which is the common case since neighbouring gNBs usually do have Xn, or by Sec. 4.9.1.3 where there is no Xn.

6G-RUPA, 200 B at every depth. The moving node obtains a new location-dependent address synonym under an aggregate that already exists. Active flows survive because EFCP connections are keyed by connection-endpoint and port identifiers rather than by the address. Core forwarding state is untouched, so \(\Delta S_{\mathrm{core}} = 0\) whatever the depth.

The 200 B is flat in depth, not in flow count

\(\sigma_{\mathrm{RUPA}} = 50 + 150F\) for a node carrying \(F\) active flows: 50 B of address and local-routing metadata plus a 150 B rebinding exchange per flow. The 200 B headline is the \(F=1\) case of the modelled eMBB profile. 5G rewrites one tunnel per session however many flows it carries, so a node holding many concurrent flows narrows and eventually inverts the signaling comparison, at \(F \ge 4\) against \(d=1\) and \(F \ge 8\) against \(d=2\). Depth flatness is unaffected either way.

Roaming Entry¶

For deployed 5G Home-Routed roaming, the simulator models a border crossing as PLMN reselection plus a new HR PDU-session establishment: 3250 B, and the 5G flow breaks. The idealized connected-mode inter-PLMN handover, 1300 B with the session surviving, is kept as a sensitivity mode because 3GPP does specify it even though it is not the deployed default.

For 6G-RUPA, first entry into the internetwork layer costs 450 B, covering enrollment, renumbering, and one internetwork advertisement. Later moves return to the flat 200 B renumber, since enrollment is charged once rather than per event.

Both border semantics are reported, at 86.2 % and 65.4 % advantage respectively.

Output Interpretation¶

The reported signaling totals are cumulative byte counters, summed over depth:

\[ \Sigma_{5\mathrm{G}} = \sigma_{5\mathrm{G}}^{d=1} + \sigma_{5\mathrm{G}}^{d=2} + \sigma_{5\mathrm{G}}^{\mathrm{roam}}, \qquad \Sigma_{\mathrm{RUPA}} = \sigma_{\mathrm{RUPA}}^{d=1} + \sigma_{\mathrm{RUPA}}^{d=2} + \sigma_{\mathrm{RUPA}}^{\mathrm{roam}}. \]

In the output columns those three 5G terms are Sigma_5G_Xn, Sigma_5G_N2 and Sigma_Roam_5G, with the naming caveat above.

The advantage is computed from totals, not from a hard-coded percentage:

\[ A = 1 - \frac{\Sigma_{\mathrm{RUPA}}}{\Sigma_{5\mathrm{G}}}. \]

Because national intra-PLMN traces are dominated by depth-one handovers, the aggregate advantage stays near the depth-one ratio \(1 - 200/600 = 66.7\,\%\), rising slowly as the depth-two share \(\beta\) grows. \(\beta\) is a property of how the deployment cuts its regions, not of how fast the user travels, so a coarse UPF partition and a fine one produce different aggregates from identical mobility.

Results¶

The sweep in results/national-sweep.csv covers 27 operator fields across six countries, each run under pedestrian (5 km/h), urban (50 km/h) and highway (120 km/h) mobility, for 81 runs. Reproduce with julia --project=. runs/national_sweep.jl.

By Country¶

Country	Runs	Operators	gNBs (max)	Advantage \(A\)	\(\beta\) (depth-two share)	Path-length excess
Canada	18	3	20 077	67.15 to 68.03 %	1.59 to 4.67 %	0.00 to 0.54 km
France	24	4	116 993	66.91 to 67.56 %	0.79 to 3.00 %	0.12 to 2.80 km
Mexico	9	3	163 116	67.72 to 71.52 %	3.56 to 18.61 %	0.02 to 0.25 km
Portugal	9	3	7 350	67.07 to 67.85 %	1.32 to 4.02 %	0.04 to 0.46 km
Spain	9	3	46 396	66.85 to 67.30 %	0.60 to 2.12 %	0.10 to 5.09 km
USA	12	4	277 160	67.68 to 68.67 %	3.42 to 6.98 %	0.37 to 2.14 km

Across all 81 runs the advantage stays in a 4.7-point band, 66.85 to 71.52 %, with a mean of 67.76 %. The floor is the depth-one ratio of 66.7 %, which no deployment can go below, and the spread above it is entirely \(\beta\).

Mexico is the instructive outlier. Its \(\beta\) reaches 18.61 % where Spain's stays under 2.12 %, and its advantage rises with it to 71.52 %. That is a coarser UPF partition, not faster users: the same three mobility profiles run everywhere.

By Speed¶

Profile	Runs	Handovers per user-hour	\(\beta\)	Advantage \(A\)	Path-length excess
Pedestrian, 5 km/h	27	1.77 to 7.81	0.60 to 16.14 %	66.85 to 70.96 %	0.00 to 1.74 km
Urban, 50 km/h	27	16.88 to 59.30	0.93 to 17.09 %	66.95 to 71.18 %	0.00 to 2.80 km
Highway, 120 km/h	27	33.83 to 112.95	1.40 to 18.61 %	67.09 to 71.52 %	0.01 to 5.09 km

Speed moves the event rate by a factor of roughly 20 and the event mix almost not at all. The \(\beta\) ranges of the three profiles overlap almost completely, and each one spans the same width as the whole dataset, because within a profile the variation comes from which country the run is in. Speed sets how often you pay; the deployment's region partition sets what you pay.

Source Sensitivity¶

Three countries have an official national registry alongside the crowdsourced OpenCelliD field, which makes the source dependence measurable rather than assumed. Same operator, same mobility profile, different tower source:

Operator	Field	gNBs	Handovers per user-hour	Advantage \(A\)
Orange France	ANFR (official)	33 665	3.96	67.02 %
Orange France	OpenCelliD	116 993	7.81	66.91 %
Bell Canada	ISED (official)	10 643	2.12	67.22 %
Bell Canada	OpenCelliD	11 237	2.26	67.52 %

Pedestrian profile shown; the pattern holds at all three speeds.

This is the single most important caveat on the absolute numbers. OpenCelliD reports 3.5 times as many gNBs for Orange France as the national regulator does, and the handover rate very nearly doubles with it, from 3.96 to 7.81 per user-hour. Absolute handover rates are therefore not a defensible output of this simulator. The advantage moves by 0.11 points over the same swing, because it is a ratio of two totals charged against the same event stream, so whatever the tower density is, it cancels.

Core-State Churn¶

\(\Delta S_{\mathrm{core}}\) is counted per event alongside \(\sigma\), and it is the starkest of the three coordinates because one column is identically zero.

Field	Profile	Agents	5G core writes
T-Mobile USA	highway	274 700	8 532 032 000
Telcel Mexico	highway	103 175	5 825 549 000
AT&T USA	highway	274 700	5 809 667 000
Movistar Spain	urban	40 544	886 120 000
Movistar Spain	pedestrian	40 544	116 141 000

The 6G-RUPA column is zero in all 81 runs, across every country, operator, field and mobility profile. This is structural rather than empirical: a renumbering assigns an address under an aggregate the layer already advertises, so no core forwarding entry is added or removed. 5G writes per-session tunnel state at every move, so its column scales with the session population times the event rate.

Path-Length Excess¶

Under SSC mode 1 the anchor is pinned, so crossing into another PSA region lengthens the path instead of relocating anything. The measured excess over the optimal-anchor distance is small on national topologies:

Field	Profile	PSAs	Mean anchor distance	Optimal	Excess	PSA-region crossings
Orange Spain	highway	5	131.47 km	126.38 km	5.09 km	3 250
Free France	urban	5	102.50 km	99.70 km	2.80 km	1 292
AT&T USA	highway	5	504.06 km	501.93 km	2.14 km	5 322

Mean excess over all 81 runs is 0.65 km, worst case 5.09 km. Two things follow. The hairpin is real but small at national scale, so intra-PLMN path stretch is not where the argument lives. And the excess is a function of the anchor count, which operators do not publish, so this coordinate is swept rather than asserted: see results/anchor-sweep.csv and runs/anchor_sweep.jl. The same mechanism at the roaming border is what produces the large numbers, because there the pinned anchor is in another country.

Key Insights¶

The Advantage Is a Floor, Not an Average¶

No deployment in the sweep goes below 66.85 %, and the reason is structural: the aggregate is a mix-weighted blend of per-depth ratios, every one of which is at least \(1 - 200/600\). Deployments with coarser UPF regions land higher because they generate more depth-two events, each of which 5G charges 1150 B against the same flat 200 B. Improving 5G's mobility performance by making regions finer therefore lowers the measured advantage without changing anything about 6G-RUPA.

Ratios Survive Bad Input, Absolute Numbers Do Not¶

The OpenCelliD-versus-registry comparison is the cleanest demonstration in the dataset. A 3.5-fold error in tower count produces a 97 % error in handover rate and a 0.11-point change in advantage. Any claim this simulator makes about absolute event counts inherits the quality of the tower data; claims about the ratio do not.

Speed Sets the Rate, Geometry Sets the Mix¶

Pedestrian to highway moves handovers per user-hour by more than an order of magnitude while leaving \(\beta\) essentially untouched. This is what justifies separating the two in the cost model: the simulator supplies the mix, which is a deployment property, and the analysis supplies the per-event charge, which is a procedure property.