The travel time variability may significantly influence the driver's route choice. Estimating travel 2 time reliability is thus really appealing to urban infrastructure managers. This could provide 3 better information to drivers, encourage their reassignment on the network, and optimize its 4 use. In this paper, we study any arterial in under-saturated conditions with known fixed-time 5 traffic signals. The kinematic wave model is chosen to simply represent traffic dynamics. A semi-6 analytical (grid-free) method is applied to determine the separation between vehicle groups at 7 each signal of the arterial. The main contribution of this paper is to present an aggregated 8 diagram that describes the functioning of this arterial. It graphically provides the direct 9 assessment of vehicle travel times with respect to their departure and the traffic flow. This tool 10 only depends on signal settings and is cyclic and invariant for fixed-time signals. We show how 11 to use this diagram to generate probabilistic travel time distributions when some input 12 parameters are uncertain. Furthermore, this diagram appears insightful when the traffic flow is 13 not accurately known.