Section 4 : More Interworking and The Peaks

Differential Running Times

All the timetables that have been looked at so far have had the same running times throughout the day.  In reality, running times may vary to reflect different traffic conditions at different times of the day. 

Look at service number 13 which runs between Town Centre and Hopton.

The running time in each direction is 22 minutes and minimum layover is 3 minutes.  During the day the service operates to a 10 minute headway and in the evening the headway is 15 minutes.

Step 1, as always, is to work out the number of buses need for the two headways.

22 + 22 + 3 + 3 / 10 = 50 / 10 =  5 buses

22 + 22 + 3 + 3 / 15 = 50 / 15 =  4 buses + 10 minutes

When the 10 minute headway applies there is no excess layover which means that any extra running time must result in an extra bus being involved if the headway, running time and minimum layovers are retained.

When the 15 minute headway is in operation there are 10 excess minutes of layover time, which means that any extra running time up to 10 minutes in total can be accommodated with the existing number of buses.   But in the evening rather than increasing running time it may be possible to reduce it.  So how much running time needs to be taken out in order to save a bus?

It’s quite simple. Apply the following formula:

Headway – Excess Layover = reduction in round journey time needed

This gives 15 – 10 meaning that the require reduction is 5 minutes.  This could be achieved by reducing running time by 5 minutes, or reducing total round journey time by adjusting both running times and layover to the tune of 5 minutes.  In this case 4 minutes will be taken off the running time and 1 minute from minimum layover.

20 + 2 + 20 + 3 / 15 = 45 / 15 = 3 buses

Let’s turn now to the period where traffic conditions require extra running time to be allocated.   The journeys most affected are those leaving Town Centre on the outward journey, whilst those returning from Hopton are not affected quite so much because they operate against the peak traffic flow.  For that reason 5 minutes is added to the outward running time only.

27 + 3 + 22 + 3 / 10 = 55 / 10 = 6 buses + 5 minutes

Clearly an extra bus is needed to accommodate the extra running time.

Supposing, however, the decision is to run the service with the existing number of buses – 5. What affect will that have on the timetable?

The following formula tells us:

Round journey time / Number of Buses = Headway

Which gives:

55 / 5 = 11 minutes

The options are

1. abandon clock face headways and run every 11 minutes using the same number of buses.
2. maintain the frequency and clock face headways by adding an extra bus into the cycle

Option 1

Bus No	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5	1	2	3	4	5	1	2	3	5	2	3
Town Centre	1500	1510	1520	1530	1540	1550	1600	1611	1622	1633	1644	1655	1706	1717	1728	1739	1750	1801	1812	1823	1834	1845	1900	1915	1930	1945
Hopton	1522	1532	1542	1552	1602	1612	1627	1638	1649	1700	1711	1722	1733	1744	1755	1806	1816	1826	1836	1846	1856	1905	1920	1935	1950	2005
Hopton	1525	1535	1545	1555	1605	1615	1630	1641	1652	1703	1714	1725	1736	1747	1758	1809	1819	1829	1839	1849	1849	1907	1922	1937	1952	2007
Town Centre	1547	1557	1607	1617	1627	1637	1652	1703	1714	1725	1736	1747	1758	1809	1820	1831	1841	1851	1901	1911	1921	1927	1942	1957	2012	2027

The first journey to have the extra 5 minutes running time is the 1600 departure from Town Centre.  This widens the headway on one occasion at Hopton where the headway becomes 15 minutes from 1615 to 1630.

If the 1834 journey took the full peak running time of 27 minutes it would arrive Hopton at 1901 returning to Town Centre at 1904 which would mean that it was only 3 minutes ahead of the next departure at 1907.  To avoid this, the 27 minutes peak running time is reduced by 1 minute per journey from 1750 inwards until it resumes the original running time of 22 minutes with the 1834 departure from Town centre.   The 1845 journey takes the evening off peak running times and layover.

Bus 4 and bus 1 drop out at 1901 and 1921 respectively.

Option 2

This retains the 10 minute headway but to enable this to happen an extra bus has to be introduced into the cycle at 1650.

Bus No	1	2	3	4	5	1	2	3	4	5	1	6	2	3	4	5	1	6	2	3	4	5	6	3	5	6	3
Town Centre	1500	1510	1520	1530	1540	1550	1600	1610	1620	1630	1640	1650	1700	1710	1720	1730	1740	1750	1800	1810	1820	1830	1845	1900	1915	1930	1945
Hopton	1522	1532	1542	1552	1602	1612	1627	1637	1647	1657	1707	1717	1727	1737	1747	1757	1806	1815	1824	1833	1842	1850	1905	1920	1935	1950	2005
Hopton	1525	1535	1545	1555	1605	1615	1630	1640	1650	1700	1710	1720	1730	1740	1750	1800	1809	1818	1827	1836	1845	1852	1907	1922	1937	1952	2007
Town Centre	1547	1557	1607	1617	1627	1637	1652	1702	1712	1722	1732	1742	1752	1802	1812	1822	1831	1840	1849	1857	1906	1912	1927	1942	1957	2012	2027

Bus 1, bus 2 and bus 4 drop out at 1831, 1849 and 1906 respectively.