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The article focuses on models of fleet routing and scheduling problems for transportation systems, which are formulated as integer linear programs with 0-1 variables. The topics discussed in this paper are concerned with important operational problems confronting the management of the competitive air transportation system. Some of these problems are significant for other transportation systems, including those with public-service rather than profit objectives. The problems are those connected with fleet utilization, fleet size, routing, and scheduling. Work that is related to some of these problems has been carried out by operations researchers and has been limited because, when optimal solutions were sought, computation times were excessive. The principal method of attack has been dynamic programming, which usually involves a very large state space for any real-life transportation system. The basic models are of the discrete-time rather than of the continuous-time variety. This property permits the formulation of the optimization problems as integer linear programs. The aim is to formulate a realistic model and to obtain its optimal solution

Investigations of motorist delays at the intersection of a major and minor road have involved variations of one or the other of two merging strategies: (i) MILLER'S[8] model that assumes that a minor-road motorist makes consecutive decisions consistently, and (ii) that of WEISS AND MARADUDIN[7] that assumptions that a different, independent decision is made for each headway. In this paper we show that results for both models may be obtained easily, using the results of queuing theory, if certain reasonable assumptions are made. Simple expressions for the Laplace-Stieltjes transforms and means of the delays are derived in the case of independent major-road headways with a common, general distribution. For exponential headways, a numerical study shows the mean Miller delay to increase with the variation in the merge times, while the mean Weiss-Maradudin delay decreases. To illustrate the application of the expressions obtained, we investigate the reduction in the delay achieved by inserting a traffic island between two streams of major-road traffic. [ABSTRACT FROM AUTHOR]