A Polynomial Estimate of Railway Line Delay

Railway service may be measured by the aggregate delay over a time horizon or due to an event. Timetables for railway service may dampen aggregate delay by addition of additional process time, either supplement time or buffer time. The evaluation of these variables has previously been performed by numerical analysis with simulation. This paper proposes an analytical estimate of aggregate delay with a polynomial form. The function returns the aggregate delay of a railway line resulting from an initial, primary, delay. Analysis of the function demonstrates that there should be a balance between the two remedial measures, supplement and buffer. Numerical analysis of a Copenhagen Sbane line shows that the polynomial function is valid even when theoretical assumptions are violated.