The paper is concerned with scheduling the two-way traffic between two stations connected by a single-track railway with a siding. It is shown that if, for each station, the order in which trains leave this station is known or can be found, then for various objective functions an optimal schedule can be constructed in polynomial time using the method of dynamic programming. Based on this result, the paper also presents a polynomial-time algorithm minimising the weighted number of late trains.
Foreword to the thematical issue devoted to the seventieth anniversary of Academician V.S. Tanaev
We consider a sequence of Markov chains that weakly converge to a diffusion process. We assume that the trend contains a linearly growing component. The usual parametrix method does not apply since the trend is unbounded. We show how to modify the parametrix method in order to get local limit theorems in this case.
In this paper, we consider the minimizing total weighted completion time in preemptive equal-length job with release dates scheduling problem on a single machine. This problem is known to be open. Here, we give some properties of optimal schedules for the problem and its special cases.