From Roader's Digest: The SABRE Wiki
Multiplex is unofficial terminology created by SABRE for a section of road where two numbered routes meet, share the same piece of road for a distance then go their separate ways again.
The term is much used on SABRE but is not in general use by professional road engineers or administrators. Normally it is officially the case that each section of road has only one number, and the existence of a multiplex in a particular location is more of an inference rather than an indisputable fact. Indeed, some people reject the entire concept of a multiplex, though it does make sense to think of a multiplex as belonging to both routes that use it and some multiplexes are signed as such. Also, the 1935 Road numbering revision recognises the concept of a multiplex, though it uses the term merger to describe it.
In North America, the term concurrency is used, though not in all areas; whilst in parts of Australia such as Victoria, the term is combined route.
Multiplexes are often used in areas where geography proves challenging, resulting in multiple roads using a single corridor. Mid-Wales, for instance, has a large number of multiplexes (some examples including A483 and A470, A470 and A44, A489 and A470). They are also commonly used in city or town centres, especially where the construction of a Ring Road has caused roads in the city or town centre to be downgraded. An example is the A1309 in Cambridge, where inside the city's ring road other routes take precedence.
There is no hard and fast rule or convention for signposting multiplexes though there are occasions where roads in a multiplex have been signed as equal partners, that is, two road numbers separated by a slash. Examples of this include the A40 and A449 in Monmouthshire and Herefordshire; and the A6 and A591 south of Kendal.
On some occasions, on signs indicating distances to major destinations on route, two multiplexed road numbers are shown in a pair where the "dominant" road number comes first and the "recessive" number is shown in brackets after it. Examples of this convention being used include the A10 and A1122 east of Downham Market and the A5 and A483 between Shrewsbury and Wrexham. Usually at junctions and roundabouts, the recessive number is shown in brackets by default as an indirect route to a destination, such as can be seen east of Ely where the A10 and A142 share a short section of road between two roundabouts.
Most frequently, however, road signs and maps only use the dominant number in a multiplex. This is particularly the case for shorter multiplexes where it is easy for drivers to make the connection between two sections of road that exclusively belong to a particular number.
Rarely, a multiplex may run in only one direction. An example is between the former B1507 and B1512 in the centre of Downham Market. This is due to the town's one way systems meaning the B1512 ran southwards along the B1507, but not northwards.
Frequency of Multiplexes on UK and Irish Roads
In the original 1922 road numbering scheme, multiplexes (or discontinuous routes) were avoided whenever possible, though some short lengths were created, including the A74 and A702 in Lanarkshire. Now, there are numerous multiplexes up and down the United Kingdom. Notable examples include the A1/A1(M) and A66 between Scotch Corner and Darlington; M60 northwest of Manchester (with M62 being the junior partner); the M9 and M876 near Falkirk; and the M6 Toll and M42 to the northeast of Birmingham. The last three of these are the only examples of a multiplex between two motorways.
In the Republic of Ireland renumbering of the network since the 1970s has resulted in only a very few instances of this phenomenon: those involving National roads / Motorways include the N13 and N14 near Letterkenny, the M6 and N52 between Mullingar and Tullamore, and the N11 and N31 (now a 'useless multiplex') to the south of Dublin / west of Dún Laoghaire.
A so-called 'useless multiplex' (list) is a special type of multiplex where the dominant signed route in the multiplex ends, and the recessive road continues on. The name is wrong, as actually they are useful - used where a major route would otherwise end on a more minor one not far from another major road. The classic example given is that of the A303 and A30 between Andover and Basingstoke, where heading eastbound the dominant A303 simply terminates at the M3 junction, and the recessive A30 continues eastwards.