Airport Escort System with Physical Background
by
Xixin Cheng
Dept. of Statistics and Actuarial Science, The University of Hong Kong,Hong Kong
Coauthors: Shuhao Cao(Dept. of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, USA) Yan Zhou(Dept. of Statistics and Finance,USTC)

In this paper, we bring forward our plan of an Airport Escort System (AES), which includes the theory of the network frame, the algorithm for the movement mode of the system, the analysis of the short and long term cost, a detailed guidance of how to apply theory to a specific airport, and three specific examples.

First, by analyzing the short term and long term cost formulae, we know why and when we should adopt the AES. Then we figure out our aim is to minimize the long term cost. Then we give a general path of our process to solve this optimization problem. And we point out the key to this problem is to find the relationship between extra delay time D and the number of wheel chairs and escorts N.

Secondly, after we settle down the network frame of AES, we compare AES to connecting vessels system, a common physical system in our daily life, and point out that AES is very similar to the connecting vessels system in all aspects, and the movement mode in connecting vessels system could provide us a way to develop an algorithm to determine the movement in AES.

By defining the wasted transition resource, a counterpart to the conception of potential energy in connecting vessels system, and some assumptions, we point out that the movement mode in AES should keep the wasted transition resource as few as possible. Following this idea, we construct an optimization model, and by solving this model, we obtain the detailed movement mode in AES, where should the wheel chairs go and how many of them should go.

Then with this system network frame and movement algorithm, we do the Monte Carlo simulation. With hundreds repeats of simulation results, we obtain the average extra delay time D under certain given N by statistical estimation. After that, by obtaining the estimations of average extra delay time corresponding to a range of different N , we are able to construct an exact regression model to get the functional relationship between D and N.

Holding the functional relationship between D and N, and some other information, we return to solve the very first long term cost optimization problem, and solve it by modern technology.

After a summary of our plan as the guidance of how to apply our method to specific airports, we simulate three airports with different sizes and different levels of traffic loads. The result suggest that AES works fine, but due to the inefficiency of wheel chairs, adding more work units into AES is not a good idea to further reduce the extra delay time. Thus we advise that the airport should utilize a more efficient transportation tool instead of wheel chair in AES in order to further shorten the delay and to face more and more escort demands in future.

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Date received: March 14, 2007