1. A method, implemented in a computer readable and executable program on a computer processor, simulating, controlling, and optimizing dynamic global models of transport systems, the method comprising: combining a multidimensional Monotonic Lagrangian Grid (MLG) algorithm with algorithms for separation assurance and updating trajectories of a plurality of moving nodes within transport systems: storing into a structure of the multidimensional MLG algorithm, by the computer processor, physical locations describing the plurality of moving nodes, sorting and ordering the plurality of moving nodes on a grid structure in real space and indexing space, causing a monotonic mapping between indices of the grid structure and locations describing the plurality of moving nodes, and repeating sorting until the grid structure is monotonic, updating trajectories of the plurality of moving nodes; and determining in real time, by the computer processor, separation assurance between each node of the plurality of moving nodes in dynamic global models of transport systems, resulting in avoidance of blockages in transport paths, and avoidance of collisions of each node of the plurality of moving nodes in transport systems, wherein determining separation assurance further includes automatically controlling collision avoidance, conflict detection and resolution maneuvers for separation assurance to maintain an adequate separation distance between each node of the plurality of moving nodes, by: executing by the computer processor a fast nearest-neighbors search algorithm for each node, executing an interaction algorithm, and executing a tracking algorithm for a primary collision avoidance conflict resolution maneuver and, a group of subsequent collision avoidance conflict resolution maneuvers for each node of the plurality of moving nodes, and wherein executing the tracking algorithm includes simulator operations as follows: reading by the computer processor, a travel path plan for each node of the plurality of moving nodes into computer memory; assigning each node of the plurality of moving nodes an ID, an initial x-, y-, z-location, a final x-, y-, z-location, a set of waypoints between the initial x-, y-, z-location, the final x-, y-, z-location, and an average speed; calculating a first velocity vector for each node of the plurality of moving nodes; inputting a plurality of data in a data structure of the multidimensional MLG algorithm, wherein the plurality of data include a node ID and a current x-, y-, z-location for each node of the plurality of moving nodes characterized as: 
 (multi-D) MLG( i,N ), where i= 1,. .. ,4  (10), 
 i= 1: x -location  (3), 
 i= 2: y -location  (4), 
 i= 3: z -location  (5), and 
 i= 4: a node ID  (8), wherein the data structure of the multidimensional MLG algorithm in Cartesian coordinates is defined by a plurality of constraints: 
 x ( i,j,k )≦ x ( i+ 1 ,j,k ) i= 1 ,. .. ,Nx− 1 ; j= 1 ,. .. ,Ny; k= 1 ,. .. ,Nz, 
 y ( i,j,k )≦ y ( i,j,+ 1 ,k ) i= 1 ,. .. ,Nx; j= 1 ,. .. ,Ny− 1 ; k= 1 ,. .. ,Nz 
 z ( i,j,k )≦ z ( i,j,k+ 1) i= 1 ,. .. ,Nx; j= 1 ,. .. ,Ny; k= 1 ,. .. ,Nz− 1,  (1), wherein i, j, and k are grid indices (in i-j-k space) of each node of the plurality of moving nodes, wherein Nx, Ny, and Nz are a number of nodes of the plurality of moving nodes in each direction, wherein the plurality of constraints mean that each grid line in each spatial direction is forced to be a monotone index mapping, wherein, 
 N=Nx×Ny×Nz (9), is a total number of nodes of the plurality of moving nodes, and wherein each node of the plurality of moving nodes can represent one of an individual vehicle, particle, object, node and platform in transport systems, performing qualitative diagnostics checking operations of the multidimensional MLG algorithm; calling one or more algorithms to perform operations of conflict detection and resolution, and updating positions and trajectories of each node of the plurality of moving nodes; calculating a second velocity vector for each node of the plurality of moving nodes; incrementing time; and one of returning to sorting each node of the plurality of moving nodes using the multidimensional MLG algorithm, based on the x-, y-, z-locations and ending execution of the tracking algorithm.