The trial will see if using the road, instead of the M6, benefits businesses.
Lorries have been given permission to use the M6 toll road for free for a month.
Two lorry drivers killed in an eight-vehicle pile-up on the M6 in south Cumbria have been named.
The government is consulting on charging tolls to motorists, following on from the existing M6 toll road.
Stoke-on-Trent City Council said it would lobby government for a stop near junction 16 of the M6.
The UK's only toll motorway is the 27-mile (43km) M6 Toll north of Birmingham which opened in 2003.
On Tuesday evening, the M6 was closed in both directions between Newton-le-Willows and the Croft interchange near Warrington.
BBC: Snow and ice leads to travel delays and school closures
Police closed part of the M6 near Carlisle after a HGV trailer was left hanging over a bridge.
The crash happened on the southbound carriageway of the M6 on 27 November, between junctions 4a and 4.
The Freight Transport Association said while the M6 closures would cause disruption, it was needed to improve congestion.
The favoured option seems to be a toll road similar to that on the M6 in the Midlands.
BBC: Has the time come to ease the A14's traffic congestion?
Two lanes of the northbound M6 and the road passing under the bridge were closed for the recovery operation.
Heavy snow during rush hour in Warwickshire caused long delays on the M6.
Plans for a major road-building project linking Heysham and Morecambe to the M6 have been approved by the government.
Hundreds of drivers were stranded overnight on the M6 motorway in Greater Manchester.
David Morris, the Conservative MP for Morecambe and Lunesdale, was stuck on the M6 for more than three hours.
And yet, overall, the M6's design adds up: This is one big, sleek, prepossessing automobile, very mature and epically cool.
WSJ: 2013 BMW M6 Coupe Review: A Hurtling Flume Ride on Dry Land | Rumble Seat by Dan Neil
The road links the container port at Felixstowe in Suffolk with the M1 and M6 motorways via Cambridgeshire and Northamptonshire.
Two people have been killed and a number of others injured in a collision on the M6 in south Cumbria.
Motorist Ryan Murray was stuck for seven hours on the M6 in Lancashire as he made his way from Aberdeen.
The M6 was hardest hit as several lorries jack-knifed between Wigan and Standish, bringing traffic to a standstill for hours.
The road opened in 2003 and links junction 11a of the M6 near Cannock, Staffordshire, to Junction 3a at Coleshill, Warwickshire.
The accident happened at Coleshill, Warwickshire, near junction T1 on the northbound carriageway of the M6 Toll just before 18:30 BST.
The A14 links the country's largest container port in Felixstowe, Suffolk, with the M1 and M6 motorways via Cambridgeshire and Northamptonshire.
David Cameron told the BBC he understood people's "frustrations" about the road, which links the East coast to the M1 and M6.
The Highways Agency said it had treated the M6 overnight with salt.
Hundreds of drivers were stranded on the M6 around Wigan overnight as the motorway was closed in both directions between junctions 25-27.
The M6 was blocked in both directions between junctions 25 and 27 in Lancashire after more than 30cm (12ins) of snow fell.
The accident closed the M42 northbound between junction 7A and junction 9, and the M6 Toll northbound between junction T1 and the M42.
The M6's top speed is electronically limited to either 155 mph or 186 mph (the higher limit comes with the "M Driver" package).
WSJ: 2013 BMW M6 Coupe Review: A Hurtling Flume Ride on Dry Land | Rumble Seat by Dan Neil
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