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This research was prompted by work undertaken by the author on the efficiency of shipping operations in the Suez Canal. The physical limitations of the Canal allow only one-way movement of ships for the greater part of its length, and thus ships are organised in convoys. These convoys have fixed starting times, with normally just one convoy per day operating in each direction. When traffic is heavy in the southbound direction, a second (smaller) relief convoy is organised to reduce waiting times which can otherwise exceed 24 hours. The process can be analysed by means of a bulk-service queueing model, where convoys of ships correspond to service batches of customers.

The model has application in the many other fields of transport where relief services are supplied. For example, a coach or train operator will often provide a relief service when customer demand is high. The process may be extended to cover cases where relief is provided for the relief service, resulting in a “cascade” of relief service queues.

A method is derived for estimating a discrete choice model incorporating heteroscedasticities to reflect repeated measurement problems. Heterogeneity of each observation is characterised by a specific scale function and individual heterogeneity is introduced in the random utility choice model. This research proves that the unobserved influences affecting a specific individuals' mode choice are correlated from one of his or her selections to the next repeated questions. This research also suggest a strong evidence of learning effect, implying variances would be decrease as the responses faces repeated questions.

This contribution discusses a continuum model of large discrete networks in planar domains. For this model, the Kirchhoff law, boundary conditions and capacity constraints lead in a system optimisation approach to a infinite dimensional constrained optimisation problem and to “mixed” variational inequalities. Mixed finite element methods can be formulated for these variational inequalities such that computable discretizations of the continuum problem are obtained.