Traffic congestion, the bored game

Play the game

• Take one Monopoly board
• Space out the tokens for the players evenly around the squares of the board
• N.B. There are 40 squares and, typically, 8 tokens

For each player

• Roll two dice then calculate their sum minus two
• Take the minimum of that number and the number of empty squares clockwise before the next token

When all players have rolled they then move their token clockwise by the number calculated. Note that there is no overtaking or pulling level with another player.

Repeat the rounds until thoroughly bored. To enhance the experience play "The Road to Hell" by Chris Rea, a song inspired by driving around the M25 in congestion.

The fundamental diagram of traffic flow

The traffic flow may be calculated as the speed times the density. The density is the number of tokens for the 40 squares so, as it increases to 40 the speed and the flow both go to zero due to congestion. For this game it results in

Constant speed

Instead of rolling the dice use a constant speed of 5 moves for a really dull game.

Nagel-Schreckenberg model

Determine the number of moves by

• If the last number of moves was less than 6 then increase by one
• If that causes a collision then reduce to the number of spaces in the gap
• If not stationary roll one die. If the result is 1 or 2 then reduce the number moved by 1