Location Models For Airline Hubs Behaving as M/D/C Queues By: Shuxing Cheng

```Location Models For Airline Hubs
Behaving as M/D/C Queues
By:
Shuxing Cheng
Yi-Chieh Han
Emile White
Outline
Heuristic Procedure
 HLRA Model
 Computational Experience
Examples
 CAB data
 Solutions and Comparisons
Conclusions
M/D/C queue
HLRA1 Model
k
i
m
j
Heuristic Procedure
To solve the model, the procedure has two phases :
Construction phase:
Find the initial set of p (A fixed number of servers) locations by
using greedy heuristic model
Randomly chose one of the three best nodes but not the best and add
it to the set of locations
Improvement phase:
Use one-opt exchange heuristic and diversification step to find
optimum set of locations
Move location of each hub in initial solution to non-hub and
compare value before and after trade
Determine new set of locations with tabu search procedure until no
improvement is obtained, i.e. no less than minimum solution
Computational Experience
( 900 instances )
No.
of each
hub
k
i
j
Assumptions: 1) Traffic between nodes ~uniform[0,5]
2) Hub-to-hub transportation costs save 50%
3) Fixed costs of each hub are set to 10000, 25000 and 50000
4) Right-hand side of the capacity constraint is set to 1200, 1400 and 1600
Result: Fixed Cost of each hub
, average cost
, number of hubs
, 25 s
Model
Our model was evaluated on a set of 25 U.S. cities.
Different features of the model were changed to analyze the results:
Savings percentage: α = 0.25, 0.5, 0.75
Different fixed operating costs: 40,000 vs. 60,000
Different levels of total flow were analyzed
Results
As the savings percentage increased, so did the cost of the operation.
The number and location of hubs varies more for lower levels of α and for
lower initial fixed costs.
However, the number and location of hubs tends to stabilize as the level of α
increases.
Results
We can then choose a specific situation and analyze the statistics of each
individual hub airport.
We can then view each different airport hub in the system and determine
which airports are near capacity and which ones are relatively underused.
Can view amount of traffic that goes through one hub versus multiple
hubs.
Different Models
 This model differs when compared with previous models
without capacity constraints.
 Previous work on uncapacitated multiple hub models would focus
more traffic through certain hubs.
 This may have reduced costs overall, but it can lead to
overutilization in some hubs and underutilization of other hubs.
 In reality, this would cause overcrowding and delays that the hub.
 The new model sets capacity limits that distributes
passengers more evenly to different airports.
 This means less congestion in certain airports.
 To compare the two models, fixed costs were set to zero
and a new constraint was added that fixes the number of
hubs in the model.
Comparison
Comparison
This table shows the comparison of our two models.
We can see for the model from this paper (HLRA), the passenger
flow is more evenly spread among the different hubs.
The costs are a little higher, but this model potentially alleviates
congestion and overcrowding at certain hub airports that could lead
to delays that are not accounted for in the models.
Figure 2-5 show multiple assignment network with 20-node
problem for various values of  and 3 hubs using both
models.
As the value of  increases, the number of multiple
assignments in both UMAHMP and HLRAI models
increases.
Conclusions
 Compared to the existing models, the congestion at each
hub is considered in the new model.
 The key feature of this new model is the transformation of
the probabilistic constraint stating that the amount of
congestion in a hub cannot exceed a given threshold with a
given probability, into a deterministic linear constraint.
 Hubs are modeled as M/D/c queuing system.
 A novel procedure is developed to solve this system.
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