It's been a fair old while since the initial post about the Dublin bikes scheme, and in the intervening period I've been able to add new tools to enable us better understand bike schemes' behaviour. In advance of expanding the site to other cities, I'm going to take a look back at Ireland's capital for a more expansive exploration of its behaviour and performance. There's a bit to this post, so I've split it up into sections:

1. Animating Dublin
2. Day Profiles
3. Station Metrics
4. Estimating Commuting Journeys
5. Conclusions

1. Animating Dublin

While it hardly constitutes a statistical analysis, there is something about animating the daily activity of the scheme that makes the frenetic yet predicable daily pattern clearer than a set of tables or graphs. The animation below illustrates the population of stations over a one-week period of Jul 16th to 22nd 2018. It's rendered at 25 frames per second, with 5 minutes of elapsed time between frames.

Some points I gleaned from watching this too many times:

• Strikingly, the weekday commute seems to involve almost every bike in the scheme being washed back and forth on a tide of commuters.
• If you slow down the video (there's a cog for this in the bottom right), you'll notice some early morning activity starting around 5.30 AM. I believe this is the activity of the re-distributors teeing up the scheme to be in the best position to support the commute. More on this below.
• It appears that the stations newly introduced this year as part of an expansion of the scheme, mostly with a focus on the north side, have been well utilised: we see these stations filling up and emptying out during the daily commutes along with the general trend.
• We can see several stations, e.g in Portobello, empty out in the morning and clearly getting refilled by the re-distributors. This is clearly necessary, as they are rapidly emptied once again before the commute is finished.

2. Day Profiles

With the new Day Profiles tool, it's now possible to view the progression of a given metric (bikes in transit, empty stations, etc) over the course of a given day of the week, based on historical data. It's also possible to compare days of the week, to explore the maximum/minum values, and the see the 'spread' (standard deviation) of the data. The day profile information below is based on a 3-month period from May 1st to July 31st 2018.

2.1 Bikes in Circulation

Below is the mean values of estimated bikes in circulation for each day of the week over a 24-hour period:

Some observations:

• Weekdays follow the basic triad of Morning-Lunch-Evening commuting that was observed in the first blog post on Dublin, with daily maxima at approximately:
  • Morning: 08:50
  • Lunch: 13:25
  • Evening: Two close peaks at 17:20 & 17.50
• There is a small peak around 06:50 in the morning too - this is likely indicative of a redistribution effort on behalf of the operators, as it correlates with an improvement in the number of empty/full stations as outlined later in this article.
• Saturday and Sunday follow a different trend, with Sunday seeing a 30% lower number of bikes in transit in the afternoon.

Accounting for Monday

Mondays seem somewhat quieter, but there were two bank holidays during the 3 months in question which one would expect to bring down the mean. This is reflected when we plot the chart overlayed with a band showing +/- one standard deviation, comparing Monday and, for example, Thursday:

We can see that Monday's data is more broadly spread, implying on normal work days that it's as busy a day as any other. This is also clear when one turns on the 'show maxima/minima' function in the chart (not shown above), where we can see the trend for these public holidays adhear to that which we observe on a weekend.

The Evening Roll-Off

Following is the same chart but zoomed in for the period from 4-7pm, showing weekdays with their +/- 1 standard deviation band:

Three items of note here for me:

• Friday seems a fair bit quieter in the evenings. This seems reasonable - a lot of people might hang around town after work for longer than they would the rest of the week to socialise rather than use it to commute home.
• Despite late night shopping, Thursday does not seem to display any different behaviour from that of Tuesday or Wednesday. I guess people are wisely choosing not to attempt to bring that fancy new blender or bowler hat home on the basket!
• There seems to be a minor double peak, spaced by a half hour, between 17.20 and 17.50. This may be due to a some people clocking off around 5pm and others getting out of work a half hour later.

We can re-purpose the same machinary that brought us the charts above to similarly investigate the day profiles for the number of empty and full stations. So let's do just that.

2.2 Empty Station Weekday Profiles

A limiting factor in determining peak values on the road is how many stations become empty during commuting time, particularly before the peak is reached around 08:50. Here's the data for mean numbers of empty stations, with +/- one standard deviation overlayed:

Some inferences to be drawn include:

• Mornings:
  • Mondays start with significantly fewer stations with no bikes. This is likely due to a natural balancing effect from the more sporadic behaviour we witness at the weekend, whereby come Sunday evening the scheme is nicely spread out.
  • The number of empty stations plunges from around 05:30 each morning. I'd guess this is due to a manual re-balancing undertaken by the network operator (JC Deceux) in an effort to have maximim availability once the commute begins.
  • The worst time of the day for getting a bike from a station is at about 08:55, by which time the commuters of Dublin have managed to totally drain about 30-45 stations - about 25 - 40 percent of the total.
• Afternoons see a steady re-balancing taking place, likely due to the contributions both of manual re-balancing on the trucks and lunchtime errands bringing down the numbers
• Evenings:
  • The number of empty stations starts to climb early in the evening commute, with the numbers rising steadily from about 5pm onwards.
  • The rise in empty stations in the evening is more gradual than the mornings, likely due to the similar behaviour in terms of bikes in circulation, whereby the number of people cycling at once in the evening is slightly lower and tapers more slowly.

2.3 Full Station Weekday Profiles

The chart below illustrates the weekday profiles for the number of full stations.

Some notes on this data:

• Just as with the previous metric, the number of full stations plunges between 5:30 and 7 AM each morning. This suggests the manual risdistribution effort involves taking bikes from full stations and populating empty ones.
• Excluding early morning time, there are daily mean maxima of about 12 full stations each day - approximately 10% of the total. This is a third of the equilivent number for empty stations. One is, it would seem, three times more likely to encounter an empty station than a full one. Considering there about three times as many slots as bikes, this seems reasonable.

3 Station Metrics

This section makes use of the Metrics Map tool, presenting statistics based on the period of May 1st to July 31st.

3.1 Morning Redistributions

As mentioned before, there appears to be a manual re-distribution taking place early each weekday morning, between the hours of 05:30 AM and 07:00 AM. The following map illustrates the mean net change for each station over this period of the day. Stations in blue are losing bikes, and stations in red are gaining them.

We can see that the re-balancing effort involves taking bikes from stations that filled up the night before, and placing them in stations that emptied out during the same period. This leaves the scheme in a more balanced state before the commute begins.

3.2 Morning Commute

As identified earlier (see section 2.1), the morning commute results in a spike of bikes in circulation beginning at approximately 07:45 and ending at about 09:30. Let's see what this looks like in terms of station performance.

The Trend

The map below illustrates the mean net flow of bikes over the three months in question for the morning commute. Again, blue stations are losing bikes and red ones are gaining them:

Let's rank these into the top ten gainers and losers of bikes:

The draining of stations appears somewhat more diffuse than their filling up - this is reflected in the concentration we see in the map being focussed on only a couple of areas, with the stations around the Convention Centre being the most popular destinations.

Emptiest Stations

Let's try to get an idea of how much of the time stations are empty during this morning commuting period. Redrawing the map to display the metric 'Percentage of Time Empty', we get the following result:

Note that the two dark red stations in the South-East are closed (James Street East & Benson Street). These are excluded below.

Let's rank them. The following table is the bottom ten stations for this metric, meaning they spend the most time empty during the morning commuting time:

Time Spent Full

Lastly for the morning commute, let's see how much of the time stations spend full:

Ranking them in terms of those performing worst, here's the top 10. Again, those two stations in dark red are closed and are discounted:

We can see from the standard deviation figures that the pattern is rather fuzzy, however it does seem to be the case that for several of the stations above, one would be lucky to find a free stand for about a third to one quarter of the commuting period. Several of these stations are also the ones receiving the most bikes on average each morning, suggesting an expansion at these locations would be helpful.

3.3 Evening Rush Hour

As identified earlier (see section 2.1), the evening commute results in a spike of bikes in circulation beginning at approximately 16:30 and winding down by approximately 19:00.

The Trend

Here is the average net change in the number of bikes in each station during the evening commute:

Let's rank these into the top ten gainers and losers of bikes:

Emptiest Stations

The following map illustrates the percentage of time spent empty on average during the evening commute over the 3 month period:

As before, we must exclude the two closed stations in darkest red. Ranking these, we get the following top ten list:

Time Spent Full

Lastly for the evening commute, let's see how much of the time stations spend full:

As before, we must exclude the two closed stations in darkest red. Ranking these, we get the following top ten list:

4. Estimating Commuting Journeys

According to the Dublin Bikes website the average journey time as of August 21st 2018 is 15 minutes. Given we have the ability to estimate the number of bikes in circulation as outlined in the previous post, and also have day profiles to hand, we can combine these data together to estimate how many journeys are being made.

To do this, I integrate the area under the lines for the estimated bikes in circulation for the day profiles over the time periods of each commute. This area is the aggregate number of minutes bikes are spending out of their racks. We can then divide this area by the average journey time of 15 minutes to get an estimate of the number of journeys. Unfortunately, this is going to include bikes out on the lorry for manual redistribution, so it's not perfect. With that provisio, the results are as follows:

5. Conclusions

• As noted before, Dublin's bike scheme is used extensively for commuting with the central axis running from the north-west to south-east quadrents of the city centre in the mornings and returning each evening.
• A re-distribution effort appears to take place early each weekday morning, starting before 6AM. During this time, stations in the south-east, 'office-centric' area are somewhat re-populated with bikes and from north-west. This results in a very significant improvement in the number of empty and full stations before the morning commute commences.
• Excluding early morning and late night, the least 'balanced' time of a weekday, in terms of number of stations full and empty, is shortly after 9 AM. The number of empty stations reaches its peak at about this time, with the number of those full reaching their peak at about 9.30 AM. At this time of the day, at least 30 stations are empty on average and about 10 are full.
• Assuming 15 minutes journey time on average, it looks as though the number of commuting journeys is in the region of 2,000-2,500 in the morning commute (07:45 - 09:30 AM) and 2,600 to 3,100 in the evening commute (16:30 - 19:00 AM). It must be mentioned that this is an estimate and unavoidably includes those bikes transported on re-distribution trucks in this period.
• Several stations (greater than 10) spend the majority of their time empty in the morning commuting period, with the most affected being Blessington Street at 75 % of the time empty for the 3 month period studied. This is followed closely by nearby Hardwicke Street in the second spot and then Portobello Road in third.
• Expansion of the scheme into new stations, mostly on the northside east of Stoneybatter and the eastern end of North Circular road has resulted in new locations that fit into the commuting trend of surrounding pre-existing locations.