In recent years, the reliability of transport systems has been widely recognised as a key issue in transport planning and evaluation. To analyse the level of reliability we need information about the distribution of travel times. Transport analysts are in a serious need for tools to estimate this distribution in hypothetical scenarios, but there are currently few such tools. In this paper we raise the question of whether it is possible to look at the outputs of each single run of a traffic microsimulation model as estimates of traffic conditions on a single day, while accounting for the fact that randomness and heterogeneity are in the nature of traffic phenomena. If it is possible to establish an analogy between a single run and a single day, then the distribution of outputs between runs can be used as an estimate of the respective distribution in the real network. Investigating this issue is vital since many practitioners wrongly assume that such analogy can be taken for granted. We discuss here methodological, statistical and computational aspects that this question brings in, and illustrate them in a series of experiments, where a special procedure for calibrating the microsimulation model has a key role.