What is the ultimate schedule for a public bus system?

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One problem I have looked at is "what is the ultimate or best schedule scheme for a bus and a bus system?"

What are the functions that a schedule scheme should optimize?
  • Reduce the waiting time between transfers between one bus and another bus.
  • Provide "meets" during off hours so night time travelers are not marooned at a bus stop when a slightly early bus misses a transfer time with a slightly later bus.
  • Organize the rolling stock to carry the most people during rush hours.
  • Arrange for the driver to start and end his driving work at the bus terminal.
Topology provides some very useful ideas for organizing a route network.
  • Think of each bus route of a bus system as a loop.
  • Think of all the bus routes of a bus system as many loops with many loops crossing. Like a pile of rubber bands.
  • The place where s bus route crosses another route is called a node.
  • The length of bus route between nodes is called an edge.
  • As long as there are an even number of bus routes entering and exiting each node, there exists an Euler path.
  • An Euler path can be completely driven by a bus driving over each stretch of road (or edge) .
  • The Euler path is in honor of the famous problem solved by Leonard Euler called the "Seven Bridges of Konigsberg." A Wikipedia entry for Eulerian Path
What timing structure would work best with an Euler path bus network?

  • Suppose we look for a timing structure where there is the smallest wait time when transfering from one bus to a different bus.
  • If two buses on different routes arrive at the same time and wait for passengers to transfer from the other bus this is the shortest wait for all travelers.
  • If the travel time between system nodes is made the same then the most nodes will have the least transfer time in all directions.

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