Path planning under 2D map is a key issue in robot applications. However, most related algorithms rely on point-by-point traversal. This causes them usually cannot find the strict shortest path, and their time cost increases dramatically as the map scale increases. So we proposed RimJump to solve the above problem, and it is a new path planning method that generates the strict shortest path for a 2D map. RimJump selects points on the edge of barriers to form the strict shortest path. Simulation and experimentation prove that RimJump meets the expected requirements.

Due to the limitations of the existing methods (for example, the route binary tree method) that can only automatically generate routes based on a single chart, a method for automatically generating the shortest distance route based on an obstacle spatial database is proposed. Using this proposed method, the route between two arbitrary points at sea can be automatically generated. First, the differences in accuracy and updating time of charts are quantitatively analysed. Next, the mechanism for updating obstacles is designed, an obstacle spatial database is constructed, and the obstacle data extracted from multiple charts are fused. Finally, considering the effect of efficiency on the amount of obstacle data, a route window and an improved R-tree index are designed for quickly extracting and querying the obstacle database. The experimental results demonstrate that compared with existing methods, the proposed method can generate the shortest distance between two arbitrary points at sea and eliminates the limitation of the area of the chart. In addition, with data from multiple charts, the route generated by the proposed method is more reliable than that of the existing methods, and it is more efficient.

Classical Jackson networks are a well-established tool for the analysis of complex systems. In this paper we analyze Jackson networks with the additional features that (i) nodes may have an infinite supply of low priority work and (ii) nodes may be unstable in the sense that the queue length at these nodes grows beyond any bound. We provide the limiting distribution of the queue length distribution at stable nodes, which turns out to be of product form. A key step in establishing this result is the development of a new algorithm based on adjusted traffic equations for detecting unstable nodes. Our results complement the results known in the literature for the subcases of Jackson networks with either infinite supply nodes or unstable nodes by providing an analysis of the significantly more challenging case of networks with both types of nonstandard node present. Building on our product-form results, we provide closed-form solutions for common customer and system oriented performance measures.

We find the joint distribution of the lengths of the shortest paths from a specified node to all other nodes in a network in which the edge lengths are assumed to be independent heterogeneous exponential random variables. We also give an efficient way to simulate these lengths that requires only one generated exponential per node, as well as efficient procedures to use the simulated data to estimate quantities of the joint distribution.

In a car navigation system the conventional information used to guide drivers in selecting their driving routes typically considers only one criterion, usually the Shortest Distance Path (SDP). However, drivers may apply multiple criteria to decide their driving routes. In this paper, possible route selection criteria together with a Multi Objective Path Optimisation (MOPO) model and algorithms for solving the MOPO problem are proposed. Three types of decision criteria were used to present the characteristics of the proposed model. They relate to the cumulative SDP, passed intersections (Least Node Path – LNP) and number of turns (Minimum Turn Path – MTP). A two-step technique which incorporates shortest path algorithms for solving the MOPO problem was tested. To demonstrate the advantage that the MOPO model provides drivers to assist in route selection, several empirical studies were conducted using two real road networks with different roadway types. With the aid of a Geographic Information System (GIS), drivers can easily and quickly obtain the optimal paths of the MOPO problem, despite the fact that these paths are highly complex and difficult to solve manually.

Individual items of flow in a telecommunications or a transportation network may need to beseparated by a minimum distance or time, called a “headway”. If link dependent, such restrictions in general have the effect that the minimum time path for a “convoy” of items to travel from a given origin to a given destinationwill depend on the size of the convoy. The Quickest Path problemseeks a path to minimise this convoy travel time.A closely related bicriterion problem is the Maximum Capacity Shortest Path problem. For this latter problem,an effective implementation is devised for an algorithm to determine desired sets of efficient solutions which in turn facilitates the searchfor a “best” compromise solution. Numerical experience with the algorithm is reported.

Consider the Delaunay graph and the Voronoi tessellation constructed with respect to a Poisson point process. The sequence of nuclei of the Voronoi cells that are crossed by a line defines a path on the Delaunay graph. We show that the evolution of this path is governed by a Markov chain. We study the ergodic properties of the chain and find its stationary distribution. As a corollary, we obtain the ratio of the mean path length to the Euclidean distance between the end points, and hence a bound for the mean asymptotic length of the shortest path.

We apply these results to define a family of simple incremental algorithms for constructing short paths on the Delaunay graph and discuss potential applications to routeing in mobile communication networks.

The Algorithm in this paper is designed to find theshortest path in a network given time-dependent cost functions. It hasthe following features: it is recursive; it takes place bath in abackward dynamic programming phase and in a forward evaluation phase; itdoes not need a time-grid such as in Cook and Halsey and Kostreva andWiecek's "Algorithm One”; it requires only boundedness (above andbelow) of the cost functions; it reduces to backward multi-objectivedynamic programming if there are constant costs. This algorithm has beensuccessfully applied to multi-stage decision problems where the costsare a function of the time when the decision is made. There are examplesof further applications to tactical delay in production scheduling andto production control.

This paper proposes a navigation system for a non-holonomic mobile robot. The navigation is based on a “look and move” approach. The aim is to define intermediate points called sub-goals through which the robot must pass. This algorithm is particularly suitable for navigation in an unknown environment and obstacle avoidance. Between two successive sub-goals, a shortest path planning solution is adopted. We have adopted the “Dubins' car” because of the environment perception sensor, a 180° laser scanner. In order to minimize the calculation time, the theoretical results of shortest path are approximated by simple equations. The navigation algorithm proposed can be used either in a structured or unstructured environment. In this context the local map construction is based on the segmentation of a structured environment; so for an unstructured environment, a suitable algorithm must be used instead.