Loading and Unloading Activity at Informal Roadside Motor Parks and Its Effect on Arterial Traffic Flow

park is deliberately sub-saturated, so that the sweeps measure the shape of the dwell distribution rather than the park running out of berths. 4.3 Validation design A check against a formula that shares the model’s assumptions tests the arithmetic; only a check against an independent solution tests the representation. Both are reported separately and only the second is treated as validation. Against the vertical-queue triangle, which shares the model’s assumption that queued vehicles occupy no space, agreement is 0.0008 percent, which confirms the numerics. Against a spatial shockwave solution, which relaxes that assumption and lets the queue occupy roadway, our delay estimates run 13.4 percent high on average and 24.4 percent high at worst, and the sign is always the same. Every delay figure in this paper is therefore an upper bound carrying that margin. Figure 3 sets out both halves of that comparison. Panel (a) is the triangular fundamental diagram the shockwave solution is solved on, with the queued states that three encroachment depths E-ISSN 2505- 8821 , www.iiardpub.org produce marked on it; the deeper the encroachment, the lower the discharge plateau and the further right the queued state sits, and at 2.4 m the state is held off the axis only by the residual- capacity floor. Panel (b) plots the cumulative-curve delay against the shockwave delay for all 39 validation cases on log axes. The points track the 1:1 line and lie above it in all 39 cases, by between 2.4 and 24.4 percent. That the bias is one-directional and close to multiplicative matters for what follows: it means the elasticities in Section 5 are largely unaffected, because a multiplicative bias cancels in a log-log slope, while every absolute delay is inflated by roughly the same margin. Figure 3. Validation against the spatial shockwave solution. Panel (a) is the triangular fundamental diagram on which the shockwave solution is solved, with the queued state marked for three encroachment depths. Panel (b) compares the cumulative-curve delay with the shockwave delay across all 39 validation cases. Our estimates run 13.4 percent high on average and always in the same direction, which is why every delay in this paper is reported as an upper bound. 4.4 How variation is reported Two sources of variation act on these delay estimates and they answer different questions. Variation between replications of a single park, which resample that park’s own recorded events, measures how much one observation day tells an analyst about that park. Variation between parks measures how far the six sites stand apart from each other. The resampling is carried out within each park separately, so the two never mix. They are carried through the analysis as separate quantities and combined nowhere, because a pooled spread would understate the first and overstate the second. 5 Results 5.1 Dwell time distributions Table 2 and Figure 4 report the dwell distributions across 2,943 events and 54 session hours. Mean dwell ranges from 80.2 seconds at the smallest park to 302.8 at the largest, with coefficients of variation between 1.71 and 2.10. One modeling point falls out of this. The pooled dwell distribution at every one of the six parks rejects a lognormal fit. Disaggregated by vehicle class it does not: a lognormal survives the test E-ISSN 2505- 8821 , www.iiardpub.org in all 28 park-by-class cells, and in 8 of those cells a gamma fits closer still and is the distribution Table 2 names. What holds everywhere, then, is a single-family within-class fit rather than the lognormal specifically. Within-class coefficients of variation run between 0.27 and 1.30. The pooled distributions are mixtures, and fitting a single distribution to a park conflates a motorcycle picking up one passenger with a minibus filling twelve seats. Figure 4 shows the per- class panels for that reason. Table 2. Dwell time by park. Mean and variance are reported separately throughout, because the paper’s question is whether they act on delay differently. Park n d ̅ s2 s CV d50 d90 Fit (s) (s2) (s) (s) (s) P1 453 80.2 19,909 141.1 1.76 40.2 181.3 mixture P2 549 171.5 105,385 324.6 1.89 62.6 403.8 mixture P3 581 142.7 59,637 244.2 1.71 57.7 312.3 mixture P4 608 131.1 75,933 275.6 2.10 45.9 271.4 mixture P5 493 302.8 272,977 522.5 1.73 106.9 816.9 mixture P6 259 84.1 23,338 152.8 1.82 37.4 160.5 mixture By vehicle class, matched pair P3 okada 127 23.7 41 6.4 0.27 22.6 33.1 lognormal (p= 0.36) P4 okada 147 26.4 236 15.4 0.58 22.8 47.1 gamma (p= 0.86) P3 keke 178 48.2 201 14.2 0.29 46.4 66.5 lognormal (p= 0.95) P4 keke 177 49.8 1,258 35.5 0.71 39.8 91.2 lognormal (p= 0.74) P3 taxi 108 79.1 683 26.1 0.33 78.5 115.9 gamma (p= 0.80) P4 taxi 116 71.0 2,876 53.6 0.75 56.4 126.3 lognormal (p= 0.43) P3 danfo 144 259.3 18,578 136.3 0.53 231.1 400.3 lognormal (p= 0.88) P4 danfo 142 268.0 98,092 313.2 1.17 170.2 568.5 lognormal (p= 0.83) P3 coach 24 1,060.6 252,756 502.7 0.47 943.0 1,660.9 lognormal (p= 0.88) P4 coach 26 797.4 570,713 755.5 0.95 581.6 1,581.6 gamma (p= 0.99) Note. N= 2,943 stopping vehicles over 54 hours, six parks, three sessions each of 3 hours. d ̅ = mean dwell; s2 = variance; s = standard deviation; CV = coefficient of variation s/d ̅; d50, d90 = median and 90th percentile. The park-level distribution is a mixture across vehicle classes and is not lognormal: a single lognormal is rejected at the 5 percent level for all six parks. Within a class the lognormal is not rejected for any of the 28 park-by-class cells (28/28 with p> 0.05), which is why the class components are reported. In 8 of those 28 cells a gamma fits closer than the lognormal does, and the fit column names the closer of the two for each cell, with the p value E-ISSN 2505- 8821 , www.iiardpub.org the Kolmogorov-Smirnov p for the distribution named. Vehicle classes: okada = motorcycle taxi, keke = tricycle, taxi = shared car, danfo = minibus, coach = intercity coach. P3 and P4 are a matched pair: they are close on mean dwell, berth count, arrival rate and class mix, and apart on dwell variability, which within every vehicle class runs about twice as high at P4, which is why the paper uses the contrast between them. Figure 4. Dwell time distributions by park and vehicle class, with the mean against standard deviation panel. Pooled park distributions are mixtures and reject a lognormal fit at every park; within a vehicle class the fitted distribution is not rejected in any of the 28 cells, a lognormal in 20 of them and a gamma in 8. 5.2 The mean dominates the variance Table 3 and Figure 5 report the central experiment. Under in-lane loading, the elasticity of delay with respect to the dwell mean is 1.56, and with respect to the dwell variance 0.30, which is 0.60 with respect to the standard deviation. The mean dominates by a factor of about 2.6. Delay over the mean sweep moves from 3.87 to 66.14 seconds per through vehicle, a multiple of 17.1, while over the variance sweep it moves from 5.83 to 19.00 seconds, a multiple of 3.3. The ordering runs against the hypothesis the study set out to test. The capacity-drop literature that motivated it (Gu et al. 2011; Yuan et al. 2015) establishes that interruption variability enters effective capacity, and it does here too, with an elasticity of 0.30 that is not zero. It is simply smaller than the mean effect. A park that halves its average dwell buys more than a park that halves its dwell variability, and by a wide enough margin that the regulatory implication the hypothesis carried does not follow. The superlinearity belongs alongside it, and it needs stating at the right scale. Delay from a single isolated blockage grows with the square of that blockage’s duration, which is the deterministic queueing prediction and which the model reproduces in the check reported in Table 6. A whole E-ISSN 2505- 8821 , www.iiardpub.org session is not a single blockage. Stops overlap, berths absorb part of the arrival stream, and the lane runs clear between events, so the response of session delay to the dwell mean is weaker than quadratic: at the measured elasticity of 1.56, doubling the mean dwell multiplies delay by about 2.9 rather than by four. That is still steep enough that shortening dwell returns more than proportionately, which is the point that matters for practice. Figure 5 shows both sweeps under both configurations. The in-lane curves climb across the whole range in each panel while the apron curves lie flat near 0.1 seconds per vehicle, and the shaded bands, which span the 10th to the 90th percentile across the 40 replications at each level, are wide enough on the in-lane curves that the level at any single point is far less well determined than the slope through them. Table 3. Response of through-traffic delay to dwell mean and to dwell variance, each varied with the other held fixed, under both park configurations. Loading in the running lane Off-carriageway berths Quantity varied ε w range ε w range (s/veh) (s/veh) Dwell mean, 40–240 s, SD fixed at 76.5 s 1.56 3.87–66.14 -0.02 0.11–0.10 Dwell variance, 506–27,722 s2, mean fixed at 90 s 0.30 5.83–19.00 0.00 0.10–0.11 Delay multiple over the mean sweep 17.10× 0.94× Delay multiple over the variance sweep 3.26× 1.02× Median variance effect across all sweeps 1.70× 1.02× Note. Reference park: 8 berths, 1 running lane per direction, through demand 850 veh h−1, park arrival rate 20 veh h−1, encroachment 1.55 m. Each cell is the mean of 40 replications. ε = elasticity of delay with respect to the quantity varied, from a log-log fit through the replication means; w = delay per through vehicle. The variance elasticity is taken with respect to the variance, so the corresponding elasticity with respect to the standard deviation is twice the value shown, 0.60 in the running-lane case. Median variance effect is the ratio of delay at dwell CV 1.45 to delay at CV 0.45, mean held fixed, taken over every point of the four parameter sweeps at which the low-CV case produces measurable delay (26 points per configuration); Figure 7 plots three of those four sweeps. Holding the variance fixed while the mean moves means holding the standard deviation fixed, so the CV necessarily changes along the first row; the reverse holds along the second. What the experiment measures is the magnitude of the variance effect relative to the mean effect, and whether it survives multi-berth operation and a finite observation window. E-ISSN 2505- 8821 , www.iiardpub.org Figure 5. Delay against dwell mean holding the standard deviation fixed, and against dwell variance holding the mean fixed, under in-lane loading and under an off-carriageway apron. Markers are the mean of 40 replications at each level and the shaded band spans the 10th to the 90th percentile across those replications. The apron curves are flat, which is the paper’s central result. 5.3 Configuration dominates both The result that displaces the paper’s original question appears when the same sweeps are run under an off-carriageway apron. Both elasticities collapse. Delay responds to the dwell mean with an elasticity of −0.02 and to the dwell variance with an elasticity of 0.00, and the absolute delay stays between 0.10 and 0.11 seconds per through vehicle across the whole of both sweeps, against 3.87 to 66.14 seconds in the running lane. Once the standing vehicle is mostly clear of the lane, a park may dwell for as long and as erratically as the sweeps allow without imposing measurable delay on through traffic. Adding berths to an in-lane park stops helping above three berths, and the mechanism is not the obvious one. In the berth-count sweep reported in Section 6, going from two berths to three cuts delay from 7.19 to 6.30 seconds per through vehicle and from three to four cuts it to 6.24, after which the curve is flat out to twelve berths: a 13 percent reduction in total, all of it realized by four berths. The first berths remove vehicles that would otherwise wait in the running lane. Beyond that the lane is blocked by the dwelling vehicle itself, so providing somewhere else for the next vehicle to wait restores nothing further. The berth overhang that separates the two configurations is set for each park from its described setting, as Section 3 sets out, so what the experiment establishes is that the two configurations respond very differently to the same dwell behavior. How many southwestern Nigerian parks sit at each end of that parameter is unknown, and counting them is the first thing this paper recommends. E-ISSN 2505- 8821 , www.iiardpub.org 5.4 Queues and the operating envelope Figure 6 shows the queue traces and Table 4 the queueing statistics. The sweeps locate the onset of delay coarsely rather than estimating a threshold. Delay is identically zero at every swept encroachment up to 1.2 m and first appears at 1.55 m, which is also the encroachment of the reference case, so 1.55 is the smallest value on the grid at which anything happens rather than an estimated tipping point; the true onset lies somewhere between 1.2 and 1.55 m and the grid does not resolve it. The same holds for through demand, where delay is zero at 550, 650 and 750 vehicles per hour and first appears at 850. Below those points the obstructed capacity still exceeds demand, so the park costs the through stream nothing; a finer grid would place both onsets more precisely and is worth running before either number is used for design. Above them the delay grows quickly. Nine of the eighteen sessions, all of them peaks, are oversaturated in the ordinary sense: peak-direction demand in those nine sits at between 0.88 and 1.16 of the capacity that survives loading, against 0.34 to 0.84 in the other nine, so arrivals outrun discharge and the queue accumulates rather than settling. Their maximum queues run from 130 to 761 vehicles, and in every case for which Figure 6 plots the trace the queue is still far from clear at the end of the three-hour window. A deterministic queueing delay computed on a queue that does not clear is a function of the length of the observation rather than of the facility, so those nine are flagged in Table 4 and reported as a state rather than as delay estimates. The controlled experiment and the parameter sweeps run at a sub-saturated reference point for that reason. Table 4. Delay, queue and capacity outcomes from the cumulative-curve bottleneck model, by park and session. Park Ses. q d ̅ CV w Qmax β ΔC (veh/h) (s) (s/veh) (%) P1 AM 908 96.8 1.99 307.2† 256 0.42 33.9 P1 MD 529 70.9 1.48 0.1 2 0.13 17.4 P1 PM 985 69.2 1.29 157.9† 130 0.32 27.8 P2 AM 863 170.7 1.87 1,073.1† 714 0.59 51.5 P2 MD 502 171.9 1.93 1.1 8 0.25 40.8 P2 PM 936 172.3 1.90 1,152.1† 761 0.35 47.7 P3 AM 908 123.8 1.50 12.7 26 0.39 30.3 P3 MD 529 142.4 1.68 0.0 1 0.24 24.7 P3 PM 985 162.3 1.81 868.7† 479 0.55 38.2 P4 AM 908 139.0 2.42 1,108.8† 542 0.64 41.8 P4 MD 529 145.2 1.88 0.2 3 0.26 28.6 P4 PM 985 115.4 1.70 529.2† 371 0.41 35.0 P5 AM 953 310.4 1.72 447.7† 394 0.43 38.1 P5 MD 556 334.5 1.97 0.4 3 0.22 31.0 P5 PM 1,034 274.7 1.46 790.5† 505 0.38 35.6 P6 AM 726 70.0 1.41 5.7 25 0.17 19.8 P6 MD 423 98.6 1.99 0.0 0 0.11 18.2 P6 PM 788 88.9 1.87 107.7 167 0.23 25.9 Note. 18 park-sessions. † marks the 9 oversaturated sessions, and the mark is set by queue state rather than by comparison with anything: peak-direction demand in those nine runs at or above E-ISSN 2505- 8821 , www.iiardpub.org the capacity that survives loading, at a ratio of demand to mean obstructed capacity of 0.88 to 1.16 against 0.34 to 0.84 in the other nine, so the queue builds through the session and has not cleared when the three-hour window closes. In those sessions the delay printed is governed by the length of that window rather than by the facility, and it should be read as an indicator of the state rather than as an estimate of delay. Ses. = session, AM = morning peak, MD = midday, PM = evening peak. q = peak-direction through demand; d ̅ = mean dwell; CV = dwell coefficient of variation; w = mean delay per through vehicle; Qmax = maximum queue; β = share of the session for which a vehicle fully obstructs the running lane, either maneuvering or waiting in the lane for a berth; ΔC = mean reduction in directional capacity against the unobstructed value of 1545 pcu h−1 per lane. Through demand is calibrated rather than counted at the parks: one two- way figure from the Ilorin arterial counts of Ahmed (2015) stands for each session type, is split 55/45 to the peak direction by assumption, and is then scaled by a per-park factor between 0.80 and 1.05. Three parks take a factor of 1.00, which is why their q column is identical. Delay is computed as the area between cumulative arrival and departure curves at the park frontage; because that is a point-queue construction it overstates delay relative to a spatial solution by about 13 percent, as Table 6 shows. Figure 6. Through-traffic queue length over the morning session at each of the six parks. The four traces that run into the hundreds of vehicles are the morning sessions flagged as oversaturated in Table 4, where the delay is reported as a state rather than as an estimate; the two that stay below thirty vehicles are not. 6 Sensitivity and External Checks 6.1 Parameter sweeps and the variance effect Figure 7 plots the sweeps and the closing rows of Table 3 summarize them. The variance manipulation raises the dwell coefficient of variation from 0.45 to 1.45 at a fixed mean, a 3.2- fold increase in the coefficient of variation and a tenfold increase in the variance. Under in-lane loading it raises delay by a median factor of 1.70, and the ratio holds between 1.03 and 1.79 across all four sweeps. It falls toward one only at the top of the through-demand sweep, at 1,250 vehicles per hour, where the in-lane case is congested enough that even the consistent-dwell run E-ISSN 2505- 8821 , www.iiardpub.org produces almost as much delay as the erratic one. Under an apron the same manipulation raises delay by a median factor of 1.02, which is to say not at all, with two exceptions that identify the mechanism. At only two berths the factor rises to 2.38 and at a through demand of 1,250 vehicles per hour to 1.33, both cases in which the apron is too small or the arterial too busy for arrivals to be absorbed, so vehicles wait in the lane and the configuration advantage is partly lost. Variance therefore matters exactly when loading touches the running lane and stops mattering when it does not, which is the configuration result seen from the other side. It also shows that the apron advantage is a matter of degree. The overhang parameter is continuous, the two exceptions sit at the ends of the swept range, and an apron that cannot hold its arrivals behaves much closer to an in-lane park than to a well-sized one. Table 5. Delay variation between replications of the same park, and delay variation between the six parks, computed and reported as separate quantities. Park w ̅ srep CVrep wmin wmax (s/veh) (s/veh) (s/veh) (s/veh) P1 12.39 23.04 1.86 0.43 118.68 P2 45.42 48.77 1.07 4.35 194.11 P3 0.84 1.01 1.20 0.14 6.26 P4 8.49 17.20 2.03 0.49 73.55 P5 13.44 29.18 2.17 1.79 149.05 P6 0.23 0.51 2.26 0.00 3.16 Between parks 13.47 16.62 1.23 0.23 45.42 Note. Each park’s morning peak was recomputed 40 times, resampling with replacement from that park’s own recorded events and from its encroachment distribution. w ̅ = mean delay per through vehicle across replications; srep = standard deviation across replications of the same park; CVrep = the corresponding coefficient of variation; wmin, wmax = extreme replications. The final row reports variation between parks, computed across the six park means, and it is a different quantity from the rows above it. Replication variation exceeds the mean at every park (CVrep from 1.07 to 2.26), which is the practically important result in this table: a single day of observation at one of these sites carries very little information about its typical delay. Figure 7. Sweeps over encroachment width, park arrival rate and berth count, under in-lane E-ISSN 2505- 8821 , www.iiardpub.org loading in the top row and an off-carriageway apron in the bottom row. Markers are the mean of 20 replications at each level and the shaded band spans the 10th to the 90th percentile across those replications. A fourth sweep, over through demand, is reported in the text but not plotted here. The variance effect is stable under in-lane loading and absent under an apron, except at two berths, where the apron cannot hold its arrivals and vehicles wait in the lane. 6.2 Replication variation and between-park variation Table 5 holds the two quantities. Within a park, the coefficient of variation on delay across replications runs from 1.07 to 2.26. Across parks it is 1.23. Those numbers carry a warning for anyone designing a measurement of this quantity. The replication spread exceeds the mean at every park, which means a single observation day at a single park is close to uninformative about that park’s delay contribution. Repeated days per site are needed, and the sample size for any further survey should be set by the replication variance reported here rather than by the number of parks. 6.3 External benchmarks Table 6 reports the internal check against the vertical-queue triangle and the independent check against the spatial shockwave solution, together with the wave properties both recover. Three further comparisons against published measurement are not tabulated, because each compares a modeled range against a single published figure rather than against a distribution, and each of the three constrained what the paper reports. The modeled capacity reduction under loading, 17.4 to 51.5 percent across the eighteen sessions, exceeds the 35 percent on-street parking comparator reported by Gulivindala and Mehar (2018) in 8 of 18 sessions. The model was not retuned, because the sessions that exceed it are exactly the ones that should: a single running lane per direction with a park occupying most of it for more than half the session is not a four-lane divided road at medium side friction. The paper therefore quotes the median reduction, 32.4 percent, rather than the maximum. The modeled delay per through vehicle exceeds the only published Nigerian delay figure we obtained in nine of the eighteen sessions. Those nine are the oversaturated sessions flagged in Table 4, and they are reported as a state rather than as delay estimates for that reason. The modeled maximum queue extent, up to 7.6 km in the validation cases, exceeds the length of every study corridor, which run from 3.61 to 5.22 km. The model carries no upstream junction and no spillback, so it lets a queue occupy road that does not exist. That is a genuine failed check rather than a rounding issue, and Section 7.4 states what it costs. The check that could not be run is the important one. Dwell times could not be compared against any published source, because no study we located reports dwell durations for informal African motor park loading, and the bus dwell studies that would supply the nearest comparator measure a scheduled, berthed service. No substitute was adopted from a different class of facility. The dwell distributions in this paper therefore stand without external corroboration, and every elasticity reported here inherits that. Table 6. Independent check of the cumulative-curve delay against a shockwave solution on a triangular fundamental diagram. Check Mean |diff| Max |diff| Cases (%) (%) Simulation against vertical-queue triangle 0.0008 0.0135 39 E-ISSN 2505- 8821 , www.iiardpub.org Simulation against spatial shockwave solution 13.41 24.44 39 Recovered wave properties Back-of-queue wave speed (km/h) -11.73 -1.13 range Speed within the queue (km/h) 4.11 20.53 range Maximum queue extent (km) 0.041 7.600 range Delay exponent on occupancy duration T2.000 3 Note. 39 cases spanning one and two running lanes, encroachments of 1.2, 1.8 and 2.4 m, demand at 0.55, 0.70 and 0.85 of unobstructed capacity, and occupancies of 2, 5 and 10 minutes. The first row compares the simulated cumulative-curve delay with the analytic vertical-queue triangle. The two share a point-queue storage assumption, so agreement to 0.0008 percent checks the arithmetic rather than the representation. The second row is the independent check: it compares the simulation with the excess vehicle-hours held inside the congested region of the time-space plane, computed from the two shock trajectories and making no vertical-queue assumption. The two differ by 13.4 percent on average and up to 24.4 percent, with the simulation always the larger, because a vertical queue stacks vehicle at a point while the spatial solution lets them occupy road upstream. Every delay reported elsewhere in this paper should therefore be read as an upper bound carrying roughly that margin. Fundamental diagram: triangular, free-flow speed 48 km h−1, jam density 130 veh km−1 per lane, capacity 1545 pcu h−1 per lane. The T2 exponent is fitted across the three occupancy durations at one lane, 1.8 m encroachment and demand ratio 0.70, and it is the signature of the bottleneck account: delay from an isolated obstruction grows with the square of its duration, which is why the spread of dwell times enters at all. The largest modeled queue extent, 7.6 km, exceeds the length of every study corridor, which run from 3.61 to 5.22 km; the model has no upstream junction and no spillback, so it lets a queue occupy road that does not exist. This is a failed benchmark and Section 7.4 states what it costs. 7 Discussion 7.1 How far the results can be pressed The queueing structure is secure. It is standard machinery, it validates against an independent shockwave solution to within a known and one-directional margin, and the quadratic scaling of delay with blockage duration is a property of the mathematics rather than of our parameters. The direction of the configuration result is secure, though its magnitude is less so. It follows from how much of the running lane a standing vehicle occupies, and that is geometry rather than behavior. But it is a continuous quantity rather than a binary one: the apron case still puts a third of the intrusion in the lane, still takes the whole lane during both maneuvers, and still takes the whole lane whenever the apron is full. What survives is that a park with usable off-carriageway space and enough of it behaves very differently from one without. Where a given park falls on that scale is a measurement nobody has made, and the overhang values that define the two cases here are analyst-set. The mean-versus-variance ratio is the part most exposed. Its inputs are dwell distributions with no published comparator, and while the ordering is stable across our sweeps, the ratio of 2.6 to 1 rest on six parks in one region and could move a long way on a wider sample. One interruption sits outside the model. Passengers boarding and alighting at a park cross the carriageway and accept gaps in the through stream (Pawar and Patil 2015), which the model does not represent and which acts in the same direction as the loading itself. E-ISSN 2505- 8821 , www.iiardpub.org 7.2 Implications for practice Three kinds of body would have to act on this: the state ministries of works in Osun and Oyo, which hold the corridors the six parks sit on; the local government authorities that license motor parks and could require an apron as a condition of licensing; and the Federal Road Safety Corps where these corridors carry federal traffic. First, the intervention that works is a lay-by, not a rule. Moving loading off the running lane takes modeled delay to near zero regardless of how long or how erratically vehicles dwell, and no regulation of dwell behavior comes close to that. The sweeps also show that not every park cost something: holding the rest of the reference case fixed, delay is zero below about 1.5 m of encroachment and below about 850 vehicles per hour of peak-direction demand. The corridors worth spending on are the busy ones with a narrow running lane. Second, size the apron for the demand rather than for the vehicle count. Our sweeps show delay returning when the apron has too few berths or the arterial is busy enough that arrivals overlap, because vehicles then spill back into the lane and the configuration advantage is lost. An undersized apron is closer to no apron than to an adequate one. Third, do not spend enforcement effort on dwell duration where loading is already off the lane. It buys nothing measurable, and the same effort spent on keeping the apron clear would preserve the benefit that matters. These results do not support treating motor parks as a nuisance to be removed. The parks exist because the transport system runs on them (Cervero and Golub 2007; Behrens et al. 2016), and the finding here is about where loading happens rather than whether it should. 7.3 Transferability Nothing in the bottleneck construction is particular to a motor park. It needs only that vehicles stop where through traffic runs and that the stopping is intermittent, so a curbside minibus stop, a market frontage where goods vehicles unload and a taxi rank without a bay all sit inside the same account. What does not travel is any number in this paper. The elasticities are properties of the dwell distributions they were fitted to, those distributions have no published comparator, and the gap between the two configurations is set by an overhang value an analyst chose. Read the model somewhere else and the ordering of mean against variance is the claim worth carrying; read the magnitudes across and they are borrowed rather than transferred. What travels beyond the setting is the modeling choice? Representing an intermittent facility as continuous friction does not merely lose precision, it removes the variable the intervention acts on, because a friction adjustment carries no term for where the loading happens. A capacity manual adjustment cannot distinguish a park with an apron from a park without one, and that distinction is the entire result of this study. 7.4 Limitations All delays reported here are upper bounds. The check against the spatial shockwave solution puts them 13.4 percent high on average and 24.4 percent high at worst, always in the same direction, because the cumulative-curve construction stacks the queue at a point rather than along the road. The queue is longer than the road it stands on. The largest modeled queue extent in the validation cases is 7.6 km, against study corridors of 3.61 to 5.22 km, because the model carries no upstream junction and no spillback. On a real corridor the queue would reach that junction first, so part of the delay reported here would be borne by the roads feeding it rather than removed. Resolving that needs a network loading model. E-ISSN 2505- 8821 , www.iiardpub.org 8 Conclusion We modeled informal motor park loading as an intermittent bottleneck rather than as continuous side friction, across six arterial corridors totaling 25.74 km, and asked which property of the dwell distribution drives arterial delay. The dwell mean dominates the dwell variance, with elasticities of 1.56 and 0.30 under in-lane loading, so the hypothesis that variability would dominate is rejected. Delay from an isolated blockage grows as the square of its duration, and the measured elasticity across the mean sweep is 1.56, so halving the average dwell cuts delay by about two thirds rather than by half. Both are dominated by configuration. Under an off-carriageway apron the two elasticities fall to −0.02 and 0.00 and delay stays near 0.1 seconds per through vehicle across both sweeps, against 3.9 to 66.1 seconds when the same distributions are served in the running lane, so the dwell distribution stops mattering once the standing vehicle is mostly clear of the lane. The overhang parameter that produces that contrast is analyst-set, and the advantage is a matter of degree rather than of kind. Variance matters only where loading touches the lane, which is the same result from the other side, and at two berths or at 1,250 vehicles per hour, where the apron cannot hold its arrivals, the variance effect returns. The recommendation is therefore physical rather than regulatory. A lay-by removes delay that no rule about dwell behavior can, but only if it is sized for its arrivals: at two berths in our sweeps the variance effect returns almost in full, and an apron that cannot hold its arrivals behaves much closer to no apron than to a working one. Two further measurements would sharpen this most. The first is a count of how many parks in the region have usable off-carriageway space and how much, since that is the parameter the whole result turns on and no survey has yet made it. The second is a longer observation program at three or four parks, a week of continuous recording rather than three sessions, since dwell has no published comparator and the replication spread reported in Table 5 shows that a single observation day per site carries little information about that site. 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