The Scheduling of Activities in Sparse Networks

The Scheduling of Activities in Sparse Networks


J Laird, R Batley, ITS, University of Leeds, UK


We extend Small?s analysis of activity scheduling to one of sparse networks with infrequent services, and rationalise it against the concept of scheduling costs ? arising from scheduling constraints. A ferry service case study is used for context.


The need for effective scheduling of trips is perhaps never more pertinent than in peripheral regions. Among the more isolated regions of Europe are the populated islands of Scotland; wherein the activity schedules of both inhabitants and visitors are dictated by spatially sparse road networks, and a spatially and temporally sparse network of ferry and air services. It is not unusual for such communities to be served by a single scheduled service per day, and even where services are more frequent, it is commonplace for their operation to cease at the end of the working day. An added complication is that peripheral regions may often be associated with extreme environments; the operation of even the few available transport services may therefore be unreliable. The provision of transport infrastructure and services in such regions is rarely a trivial matter, both technically and financially, and the regulatory support of government may often be crucial. Hence the importance of understanding trip scheduling in peripheral regions, and promoting accurate economic appraisal of any enhancements to their transport provision.

Travel research appears to have reached reasonable consensus as to the means of analysing trip scheduling, which is to defer to Small?s (1982) analysis. Small adopts earlier works on time allocation by Becker (1965) and Johnson (1966), and introduces the additional consideration of scheduling both to the representation of utility, and to the associated constraints. In the context of sparse networks, however, the applicability of Small?s analysis might be questioned. Small appeals particularly to urban car commuting, offering an infinite resolution of departure time options, albeit with the possibility of (predictable) congestion. In comparison to Small?s context, departure time options in peripheral regions are apparently fewer, more rigidly constrained, as well as more uncertain. Several subsequent papers have proposed extensions to Small?s (1982) analysis, some of which would appear useful to the present context; these include Noland and Small?s (1995) analysis of travel time variability, and Bates et al.?s (2001) interest in fixed interval public transport services.

Notwithstanding the original contributions of Small, as well as the embellishments of the subsequent researchers, we believe that the theoretical representation of trip scheduling may be further enhanced to appeal to the context of sparse networks. The contribution of our paper, therefore, is to formalise two substantive extensions to Small?s analysis, as follows. First, we develop Bates et al.?s analysis further to consider a markedly more discrete resolution of the public transport service interval, reinterpreting notions of schedule delay for service frequencies of a single journey per day. Second, and following from the first, we reconcile Small?s notion of schedule delay with the concept of scheduling costs (Wilson, 1989); the latter representing the inherent inconvenience of scheduling constraints. Moreover we believe that, in sparse networks, the benefits of improvements to low frequency public transport services may arise through both the ability of individuals to re-organise their activities to something more desirable than before, and their ability to minimise transport related schedule delay.

Following our theoretical exposition of these extensions, we offer illustration by means of a case study of improvements to ferry services in the Western Isles of Scotland. This illustration carries the implication that scheduling costs may be significant, and that failure to consider them may constitute a serious omission of economic appraisal.


Association for European Transport