Airport Landside Analysis and Modeling

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Purpose of the Discussion

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To review and understand the basic airport terminal concepts

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To discuss modeling techniques applicable to primary and secondary .ows inside the airport terminal

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Discussion of challenges in airport terminal modeling

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Passenger behavior modeling

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Shopping activities inside airport terminals

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Security implications

 

Basic review of Terminal Concepts

Goals in the design of airport terminals:
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Walking distances (keep them short)

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Pleasing environment (helps the traveler)

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Services (well located and available)

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Security (minimize threat potential)

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Cost effective (typically includes concessions)

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Aesthetics (good waiting environment)

 

Sometimes these goals contradict each other (i.e., like the cost effectiveness vs. aesthetics)
Airport Terminal Concepts

Horizontal Distribution
1) Linear
2) Pier-Finger
3) Satellite
4)Transporter

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Combinations of these are possible

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In fact, most airport terminals evolve over time from one concept to another one (i.e., linear to pier and then to satellite or transporter)

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Landside con.gurations have either centralized or decentralized services

 

 

Linear Centralized Terminal (Advantages)

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Short walking distances if check-in facilities are decentralized (and not many transfer passengers)

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Good for passenger orientation

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Provides generous curb length

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Easy and cheap to construct

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Requires simple baggage conveying/sorting systems (reduces the procurement and operation cost of the baggage conveyance system)

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Good for separation of arriving and departing passengers

Linear Centralized Terminal (Disadvantages)

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Decentralization requires duplication of services

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Potentially long walking distances for transfer
passengers or with centralized services

 

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More expensive logistics for handling transfer baggage

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Reduced compatibility of building/apron geometry and future very large capacity aircraft development (i.e., 85-90 m wingspan)

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If a decentralized terminal concept is adopted extensive .ight information system is display is required

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Examples: Mexico City, Kansai, London Heathrow
Terminal 4, Munich, etc.

 

Compact Module with Semi-Centralized

 

Terminal

 

Compact Module (Advantages)

A special variation of the linear concept

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Saves some space compared to straight linear terminal

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Provides short walking distances is properly designed (see sketches of Kansas City Airport) for terminating passengers

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Increased curb length

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It has been implemented in some of the largest airports

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Charles de Gaulle Airport Terminal 2 (Paris)

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Dallas-Fort Worth Airport (Dallas, Texas)

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Kansas City Airport (extreme case of compactness)

 

Compact Module (Disadvantages)

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Can be confusing to the passenger (due to rounded shape

-disorienting)

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Requires a very extensive .ight information service

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Requires some sort of people mover to transport passengers between terminals (see the solution adopted at DFW)

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Man power requirements might be higher due to duplication of services at each compact terminal

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Usually long walking distances result for transfer passengers

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Transfer of baggage between terminals is also a problem

 

Example of Compact Module Terminal (MCO)

 

Pier/Finger Concept (Advantages)

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Centralization of services (less costly)

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Reduces the number of airline and government staff employees to manage the facility (due to the high level of centralization)

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Use of simple .ight information services (due to the centralization)

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The best concept for passenger control (security viewpoint)

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Examples: Amsterdam Schiphol, London Heathrow Terminal 3, San Francisco Intl. Terminal, Chicago O’Hare terminals A, B, E, F

Pier/Finger Concept (Disadvantages)

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Potentially long walking distances (specially for long piers)

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The curb length is generally insuf.cient (congestion is possible)

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Limited expansion capability of the main terminal

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Reduced aircraft maneuverability (instances where the piers are not parallel)

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Separation of arriving and departing passengers should be executed at different levels (3 level .nger)

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High capital cost for passenger moving and baggage conveyance systems

 

Example of a Pier Terminal (SFO Intl.)

 

Satellite Concept (Advantages)

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Allows centralization of airline and government staff

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Capability of good concession areas near the gates (preferred by passengers)

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Simple .ight information system

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Good expansion capability (provided land is available)

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Good to control passenger movement (excellent for security)

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Examples: Atlanta, Denver, Charles de Gaulle Terminal 1 (Paris), Tokyo Narita Terminal 2

Satellite Concept (Disadvantages)

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High capital and maintenance cost of the passenger moving system

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High capital and maintenance cost of the baggage conveyance system (could be very complex)

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Curbside is usually small and provides an opportunity for congestion

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Transfer passengers require larger connecting times

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Limited expansion capability of the main terminal

 

Example of Satellite Concept (Denver)

 

Transporter Concept with Centralized

 

Transporter Concept (Advantages)

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Good concept for small to medium size airports (<10 million enplanements)

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Good for aircraft maneuvering

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Simple and smaller main terminal

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Separation of arriving and departing passengers is possible

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Reduced walking distances

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Easy to expand provided land is available

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Examples: Dulles (Washington, DC) and Mirabel (Canada)

 

Transporter Concept (Disadvantages)

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The concept is impractical when the volume of traf.c surpasses 10 million due to transporter delays and frequencies needed

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Larger connection times

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High capital cost and maintenance of transporters

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Curbside might prove insuf.cient (possible congestion)

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Complexity in the airside to manage transporters and aircraft

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Additional cost of for larger number of ground vehicles

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Creates demand surges due to limited frequency of transporters

 

One Floor Airport Terminal

 

One Floor Airport Terminal Characteristics

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Simple and easy to implement (low cost)

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Good for passenger orientation

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Provides good amount of curb space

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Limited (or no) capability to use boarding gates

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Generally only apply to small airports

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Passenger .ows can be easily controlled (separation inside the terminal)

One and a Half Level Airport Terminal

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Provides a single level curbside (arriving and departing passengers processed at grade)

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Two level terminal building

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Departure lounges on the second level (boarding gates)

 

One and a Half Level Airport Terminal

 

One and a Half Level Terminal (Departures)

 

Departing Passenger Flows

Source: IATA Airport Development Reference Manual
Two-Level Airport Terminal

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Good for separating arriving and departing .ows inside the airport terminal

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Provides increased curb space

 

 

Two Level Airport Terminal (Departures)

 

Source: IATA Airport Development Reference Manual

Level of Service Standards

 

Proposed by IATA to provide airport terminal design standards. These are static LOS values.
Table 1. IATA Level of Service Standardsa.

Level of Service (m2 per occupant) 
A  B  C  D  E  F 
Check-in Queue Area  1.8  1.6  1.4  1.2  1.0  N/A 
Wait / Circulation  2.7  2.3  1.9  1.5  1.0  N/A 
Hold Room  1.4  1.2  1.0  0.8  0.6  N/A 
Baggage Claim Area (excludes claim service)  2.0  1.8  1.6  1.4  1.2  N/A 

a. Source: IATA Airport Development Reference Manual.

 

Interpretation of LOS Standards (IATA, 1995)

Table 2. Interpretation of Level of Service (IATA).

Legend  Remarks 
A  Excellent service; free .ow conditions; excellent level of comfort 
B  High level of service; condition of stable .ow; very few delays 
C  Good level of service; stable .ow; few delays 
D  Adequate level of service; condition of unstable .ow; acceptable delays 
E  Inadequate level of service; condition of unstable .ow; unacceptable delays 
F  Unacceptable level of service; condition of cross .ows; system breakdown 

LOS Design Criteria

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Level of service C is perhaps a good design tradeoff for most airport terminals

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LOS B is an excellent design practice if the budget allows it

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Level of service A is too expensive and prohibitive to implement

 

Personal Space Preferences

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Human factors studies suggest the human body can be approximated using a personal ellipse (personal sphere) of dimensions: 330 mm by 580 mm (depth by shoulder breadth). This however works only well in crowded mass transit vehicles where standees tolerate crowding.

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Some port authorities in the US employ body ellipses of 18 by 24 in for mass transit studies (crowding inside trains)

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Given that passengers at airports carry baggage it is

desirable to increase these dimensional standards to at least 5-10 ft2. This will imply a circle of approximately 760 mm (30 in) which is consistent with the single lane walking criteria used by most airport authorities.
Space for Movement

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Provide a minimum of 760 mm (30 in) of lateral spacing between each lane of pedestrians

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Longitudinal spacing for normal walking to avoid con.icts should be on the order of 2.5 to 3.0 m (8-10 ft)

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The resulting net area per pedestrian is then 2-3 m2 (20-30 ft2) for free .ow

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When queueing is allowed (not pedestrian .ow) personal spaces of 0.5-1.0 m2 (5-10 ft2) are tolerated

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Stairway spaces are smaller because the presence of treads. Typically, personal spaces of 1-2 m2 (10-20 ft2) are needed for unimpeded stair .ow

Predestrian Walking Speeds

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Pedestrian speed varies according to pedestrian density and other factors such as age, gender, personal disabilities, environmental factors and trip purpose

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Typical speeds are 85 m/min (270 ft/min)

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College students are known to walk faster than average populations

Principles of Pedestrian Flow

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Uses a hydrodynamic analogy to model pedestrian .ow

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The basic pedestrian traf.c .ow equation is,

 

f = s -
(1)
a
where:

f is the pedestrian volume measured in pedestrians per
foot or meter width of traf.c way per minute (pr/m-min)
s is the average pedestrian .ow speed (m/min)
a is the average are per pedestrian (m2/pr)

Principles of Pedestrian Flow

Note that this equation is analogous to that used to model traf.c .ows on highways. The term a  is just the inverse of the .ow density ( ) typically employed in highway
k
traf.c modeling.
Application constraints of Equation (1):

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The pedestrian .ow has to be steady (no interruptions)

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Uniform and continuous pedestrian movement

 

Interpretation of Walkway LOS

 

Table 2. Walkway LOS Standards (Source: Fruin)

LOS  f Pedestrian Flow pr/m-min (pr/ft-min)  a Average Area m2/pr (ft2/pr)  Description of Flow Conditions 
A  <23 (<7)  >3.3 (>35)  Free .ow 
B  23-33 (7-10)  2.3-3.3 (25-35  Minor con.icts 
C  33-49 (10-15)  1.4-2.3 (15-25)  Crowded but .uid, passing is restrictive 
D  49-66 (15-20)  0.9-1.4 (10-15)  Signi.cant con.icts, passing and speed restrictions 
E  66-82 (20-25)  0.5-0.9 (5-10)  Shuf.ing walk, passing and cross.ows very dif.cult 
F  Variable Flow  <0.5 (<5)  Frequent stops, contacts 

Example 1edestrian Flow Equations

 

Chicago O’Hare has two terminals as show in the .gure below.

Application of Pedestrian Flow Equations

2) Compare with LOS B and A 3) Find the average .ow speed under the given conditions
Application of Pedestrian Flow Equations

1) 2,500 pedestrians in 15 minutes is equivalent to 166.7 pedestrians per minute (pr/min)
. Looking at the basic walkway LOS curve (on page 43 of this handout) we observe that for LOS C this corresponds to an expected .ow of,
f = 10 pr/ft-min

This implies a corridor or 17 ft (for passenger .ow) plus 4 ft to account for 2 boundary layers on each side of the passageway. The total corridor width should be 6.5 m (21 ft) for LOS C.
Application of Pedestrian Flow Equations

2) For LOS B the width would be 8.5 m (28 ft) wide
For LOS A (assuming 5 pr/ft-min as the design standard) would yield a corridor 11.7 m (33.8 ft) wide
Note that airport terminal construction cost in the US is around $2000-3000 per square meter (regular space not underground).
In our example, a 350 m corridor would have implied a cost difference of 5.5 million dollars at $3,000 per square meter (comparing LOS A vs. LOS C)
3) The resulting speed in the corridor would be about 67 m/min (220 ft/min)
Fundamental Pedestrian Flow Relationships
25
20
15
10 5 0

 

Desi gn Point 

 

0 1020 30 40 5060 70 Area per Pedestrain (sq. ft)

 

 

 

Pedestrian Flow (pr/ft-min)

Fundamental Pedestrian Speed-Area and
Speed-Density Relationships

0 1020 30 40 5060 70 Area per Pedestrain (sq. ft)

 

Stairway Pedestrian Flows

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Pedestrian .ows decrease in stairways for two obvious reasons:

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Restricted .ow movement (bottleneck effect)

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Large energy expenditure while negotiating steps (specially true upwards)

 

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Ascending speeds vary from 15 to 90 m/min (50-300 ft/ min) with an average speed of 30.5 m/min (100 ft/min)

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For a single lane motion in stairways use 760 mm width (30 in)

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Use 1520 mm (60 in) minimum for .uid two-way movement

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Design stairway spaces at multiples of 760 mm

 

Interpretation of Stairway LOS

 

Table 3. Stairway LOS Standards (Source: Fruin)

LOS  f Pedestrian Flow pr/m-min (pr/ft-min)  a Average Area m2/pr (ft2/pr)  Description of Flow Conditions 
A  <5 (<16)  >1.9 (>20)  Free .ow 
B  16-23 (5-7)  1.4-1.9 (15-20)  Minor con.icts 
C  23-33 (7-10)  0.9-1.4 (10-15)  Crowded but .uid, passing is restrictive 
D  33-43 (10-13)  0.7-0.9 (7-10)  Signi.cant con.icts, passing and speed restrictions 
E  43-56 (13-17)  0.4-0.7 (4-7)  Shuf.ing walk, passing and cross.ows very dif.cult 
F  Variable Flow  <0.4 (<4)  Frequent stops, contacts 

Queueing LOS

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These standards are similar to IATA criteria for queueing

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However, these have been primarily derived from studies of mass transit systems and thus do not include baggage

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These standards are static but can be computed in simulation models by computing the instantaneous state of the system and then taking an average of area available to serve pedestrians.

 

Interpretation of Queueing LOS

Table 4. Queueing LOS Standards (Source: Fruin)
LOS  a Average Area m2/pr (ft2/pr)  Interpersonal Spacing m (ft)  Description of Flow Conditions 
A  >1.2 (>13)  >1.2 (>4)  Standing, circulation within queueing 
B  0.9-1.2 (10-13)  1.1-1.2 (3.5-4)  Standing, partially restricted circulation 
C  0.7-0.9 (7-10)  0.9-1.1 (3-3.5)  Standing, restricted circula-tion 
D  0.3-0.7 (3-7)  0.6-0.9 (2-3)  Standing without contact; long term waiting discom-fort 

Table 4. Queueing LOS Standards (Source: Fruin)

Walking Distances at Airport Terminals

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Numerous surveys in urban studies suggest 400 m. is the maximum walking distance accepted in the U.S. (used in mass transit studies)

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Unfortunately few studies have been conducted to understand how much distance is acceptable at airports terminals

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It is not uncommon today to walk 300-450 m inside large airport terminals and thus passenger seem to accept this fact

Time-Space Analysis of Holding Areas at
Airports

 

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Pedestrian .ow equations are limited to instances where the .ow of passengers is uniform and continuos

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There are numerous instances where this analysis is of little us when pedestrians traverse areas inside a terminal where they are forced to stop brie.y (i.e., security check-in stations)

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In these circumstances the Time-Space approach provides an alternative to estimate sizes of elements inside a terminal for a given level of service

Time-Space Approach

This approach assumes that the area provided per pedestrian in an element of the airport terminal is the quotient of the Total Supply (TS) and the Total Demand (TD)
TS

a = --------(5)
TD

The interpretations of TS and TD are as follows: TS = T × S (6) TD = n × t (7)
Time-Space Approach

where:T is the total period of analysisS  is the total area available at the airport terminal site
considered

t  is the predicted occupancy (or dwell) time per passenger inside the airport terminal element consideredn  is the total number of passengers occupying the airport
terminal element considered

Example 2: Time-Space Approach

The airport shown in the next .gures has two security checkpoints for all passengers boarding aircraft. Each security check point has two x-ray machines. A survey reveals that on the average a passenger takes 45 seconds to go through the system (negative exponential distribution service time).
The arrival rate is known to be random (this equates to a Poisson distribution) with a mean arrival rate of one passenger every 25 seconds.
In the design year (2010) the demand for services is expected to grow by 60% compared to that today.
Relevant Operational Questions

a) What is the level of service provided with two x-ray machines?
b) If four x-ray machines are installed in the horizon year .nd the new level of service.
Airport Terminal Layout

 

Security Check Point Layout

 

Solution

Since the Time-Space approach requires details about the size of the space provided at the security check point we need to either .nd this information or assume some reasonable values based on typical security counter spaces.
One good source for typical spaces at airports is IATA’s
Airport Development Reference Manual (IATA, 1995)

A typical x-ray security layout is shown in the next page

TS Approach Example

.
From the previous diagram an area of 3 by 12 meters is needed for each one of the x-ray stations (so S = 36 sq. meters per station)

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The queue area is actually treated as a ‘black box’ where the passenger time in the system is the sum of both the service time and the queueing time

.
Note that since the queue length is not known according to this naive model, some estimate of the passage time, t, is necessary. Running the steady-state stochastic model for two servers we obtain an average time in the system of 4 minutes (3.95 min) and thus 4.5 minutes is a reasonable estimate that includes walking time through the black box.

TS Approach Example

TS TS1hr × 72 m 22
×

a = -------= -----------= --------------------------------------------= 6.7 m -
TD nt144 pr ×

× 0.075 hr pr
Looking at the table of walkway levels of service this space would have an equivalent LOS of A
Note that this model requires an estimate of the transit times across the terminal section being analyzed (something that is not always possible)
Other Applications of the TS Approach

The same method has been used to estimate the width of corridors where there is .ow interruption activities. For example, window shopping.
Let S = wl  be the space available for an activity inside an airport terminal. Here w is the width of the are in question and l  is the length of the area in question. Then,
ant

w = --------(8)
Tl

Application of TS to Corridor Design

Using example 1 (Chicago O’Hare underground
passageway) and compare the answers using the TS
method.

.
The corridor length is 1,100 ft (l)

.
At 220 ft/min it takes 5 minutes to traverse this corridor at LOS C speed (previously computed)

.
Assume LOS C (use the same 25 ft2/pr as before)

.
Read the value of a from the chart (20 ft2/pr)

.
2,500 passengers in 15 minutes (n)

 

TS Approach to Corridor Design

Applying equation (8),
ant 25 × 2500 × 5
w = --------= ---------------------------------= 18.8ft
Tl 15 × 1100

Note that just like before we need to add 2 ft on each side to account for boundary layers at the corridor edges.
The resulting corridor according to this method is then
22.8 ft (or 6.95 m).

Pedestrain Flow Uses in Terminal Airport
Models

 

All simulation languages can extract the instantaneous
values of state variables of the system:

.
Queue lengths

.
Delays (or waiting times)

 

.
These state variables (or statistical metrics in some models) should have en effect in the future (at time t + .t in the simulation) behavior of temporary entities of the model

.
If passengers are modeled individually de.ne an attribute (to each passenger) that changes the delay times of future activities (such as moving through a congested corridor)

LOS Modeling in Airport Terminal Models

.
Simulation models are much more re.ned that current methods to estimate levels of service and as such, they describe dynamically a situation that static models such as the TS approach cannot

.
Sometimes, however, is necessary to compare the outputs of airport terminal simulation models with LOS standards such as those stated in the literature (Fruin, IATA, etc.)

.
One approach to obtain concurrent LOS statistics in your models is to de.ne resources that have physical size attributes associated with them. Once this is done you can compute LOS statistics such as passengers per unit area during the entire simulation.

 

 

Multiserver Stochastic Queueing Equations

Assume an in.nite source queue with constant λ and μ

.
Poisson arrivals with parameter λn

.
Probability function of service completions is negative exponential with parameter μn

.
Only one arrival or service occurs at a given transition

For more information on queueing models consult any Operations Research textbook (i.e., Hillier and Lieberman, 1996)
Multi-server Queueing Equations (I)

ρ= λ.sμ  utilization factor Probabilities of zero and nentities in the system
.s– 1 .(λμn (λμs. 1 .
.).)

P= 1 .. -----------------+ --------------------------------------------. (1)
0
∑n! s! .1 – (λ.sμ).
..
n= 0
. )
n.(λμ0 ≤≤ns
.-----------------P
. n! 0

Pn = (2)
. ≥
(λμ. )ns
.-----------------nP
ns
–
. s! s 0

Multi-server Queueing Equations (II)

Expected no. of entities in system
λs
..
ρP0 -

..
μλ

L = -----------------------2 + -
(3)
s!(1 – ρ)μ
Expected no. of entities in queue
λs
..
ρP0 -

..
μ

Lq = -----------------------2 (4)
s!(1 – ρ)
Multi-server Queueing Equations (III)

Example 3: Level of Service at Airport
Terminal Security Checkpoints

 

The airport shown in the next .gures has two security checkpoints for all passengers boarding aircraft. Each security check point has two x-ray machines. A survey reveals that on the average a passenger takes 45 seconds to go through the system (negative exponential distribution service time).
The arrival rate is known to be random (this equates to a Poisson distribution) with a mean arrival rate of one passenger every 25 seconds.
In the design year (2010) the demand for services is expected to grow by 60% compared to that today.
Relevent Operational Questions

a) What is the current utilization of the queueing system (i.e., two x-ray machines)?
b) What should be the number of x-ray machines for the design year of this terminal (year 2010) if the maximum tolerable waiting time in the queue is 2 minutes?
c) What is the expected number of passengers at the checkpoint area on a typical day in the design year (year 2010)?
d) What is the new utilization of the future facility?
e) What is the probability that more than 4 passengers wait for service in the design year?
Airport Terminal Layout

 

 

Security Check Point Solutions

a) Utilization of the facility, ρ. Note that this is a multiple server case with in.nite source.
ρ = λ / (sμ) = 140/(2*80) = 0.90

Other queueing parameters are found using the steady-state equations for a multi-server queueing system with in.nite population are:
 Idle probability = 0.052632 Expected No. of customers in queue (Lq) = 7.6737 Expected No. of customers in system (L) = 9.4737 Average Waiting Time in Queue  = 192 s Average Waiting Time in System  = 237 s b) The solution to this part is done by trail and error (unless you have access to design charts used in queueing models. As a .rst trial lets assume that the number of x-ray machines is 3 (s=3).

s – 1 (λμ2 (λμs 1 .
.).).
Finding Po, P0 = -----------------+ --------------------------------------------
∑n! s! .1 – (λ.sμ).
n = 0

Po = .0097 or less than 1% of the time the facility is idle

Find the waiting time in the queue,

 

Wq = 332 s

Since this waiting time violates the desired two minute maximum it is suggested that we try a higher number of x-ray machines to expedite service (at the expense of
cost). The following .gure illustrates the sensitivity of Po and Lq as the number of servers is increased.

Note that four x-ray machines are needed to provide the desired average waiting time, Wq.

Sensitivity of Po with S
Note the variations in Po as S increases.

Po 0.06
0.05
0.04
0.03
0.02
0.01 0

34
Po - Idle Probability
56
S - No. of Servers

78

Sensitivity of L with S

L 25
20
15
10
5
0

34
L - Customers in System
56
S - No. of Servers

78

 

 

Security Check Point Results

c) The expected number of passengers in the system is (with S = 4),
λs
..
ρP0 -

..
μλ
L = -----------------------+ -

s!(1 – ρ)2 μ

L = 4.04 passengers in the system on the average design year day.
d) The utilization of the improved facility (i.e., four x-ray machines) is
ρ= λ/ (sμ) = 230/ (4*80) = 0.72

e) The probability that more than four passengers
wait for service is just the probability that more

than eight passengers are in the queueing system, since four are being served and more than four wait.
8
Pn8)= 1 – ∑Pn
(>
n= 0
where,
(λμ. )
P= -----------------nP0 if ns
n ≤
n!
(λμ. )
P= -----------------nP if ns
n 0 >
–
s!sns

from where, Pn > 8 is 0.0879. Note that this probability is low and therefore the facility seems properly designed to handle the majority of the expected traf.c within the two-minute waiting time constraint.

 

 

Numerical Estimation of Queueing Parameters

Rates

 

Time

Deterministic Queue Parameters

.
The queue length, Lt , (i.e., state of the system)

corresponds to the vertical distance between the
cumulative demand and supply curves

 

.
The waiting time, Wt , denoted by the horizontal distance

between the two cumulative curves in the diagram is the individual waiting time of an entity arriving to the queue at time tin

.
The total delay is the area under bounded by the cumulative demand and supply curves

.
The average delay time is the quotient of the total delay and the number of entities processed

 

Differential Equation Representation

Most continuous simulations can be expressed as a set of .rst order differential equations. The previous state equation for Lt implies:
dLt = (λ– μ)
dt tt

This equation can be solved numerically (integrating forward with respect to time) if expressed in .nite difference form,
L= L+ (λ– μ).t
tt – 1 tt

A Word About Integration Algorithms

Several techniques can be implemented to solve a set of .rst order differential equations:
Euler Method - Simplest representation of rate variables (assumes rate variables are constant throughout the integration step size)
Runge- Kutta Methods - Several variations exist of these methods (3rd, 4th, 5th order). Uses a weighted average rate to estimate state variables every integration step. More accurate but more demanding computationally.
Example 5 - Airport Layout

 

This example assumes all service areas (ticket counters, security checks, etc.) to be equally spaced inside the airport terminal)

Mathematical Description of the Problem

λ = 1500 for 0 < t < 1
λ = 500 for t > 1

where, λ is the arrival function (demand function) and t is the time in hours. Estimate the following parameters:
.
The maximum queue length, L(t) max

.
The total delay to passengers, Td

.
The average length of queue, L

.
The average waiting time, W

.
The delay to a passenger arriving 30 minutes hour after the terminal closes for repairs

Problem Solution (I)

The demand function has been given explicitly in the statement of the problem. The supply function (μ)as stated in the problem is,
μ = 1000 if t < 2
μ = 1500 if t > 2

Plotting the demand and supply functions might help understanding the problem
Problem Solution (II)

Demand and supply functions for the sample problem

Time (hrs)

Problem Solution (III)

 

Sample table simulation using a spreadsheet approach

Simulation Time (hr)  State Variable (Lt)  Rate Variable (λt)  Rate Variable (μt)  Sum of Rates (λt -μt)  (Sum of Rates) .t 
0  0.0  1500.0  1000.0  500.0  100.0 
0.2  100.0  1500.0  1000.0  500.0  100.0 
0.4  200.0  1500.0  1000.0  500.0  100.0 
0.6  300.0  1500.0  1000.0  500.0  100.0 
0.8  400.0  1500.0  1000.0  500.0  100.0 
1.0  500.0  500.0  1000.0  -500.0  -100.0 

This procedure uses Euler’s Method to estimate state variables (i.e., rates λt and μt are assumed constant throughout every numerical integration interval).
Problem Solution (IV)

Cumulative .ow plots can help visualize the problem
1: Passengers In  2: Passengers Served
1: 2000.00
2:
1: 1000.00
2:
1:
2: 0.00

0.00  0.50 1.00 1.50 2.00 Time 7/7/93
Problem Solution (V)

The average queue length (L) during the period of interest, we evaluate the total area under the cumulative curves (to .nd total delay)
Td = 2 [(1/2)(1500-1000)] = 500 passengers-hour
a) The maximum number of passengers in the queue, L(t)
max,
L(t)max = 1500 - 1000 = 500 passengers at time t=1.0
hours
Find the average delay to a passenger (W)

Problem Solution (VI)

Td
W =  -----= 15 minutes
Nd

where, Td is the total delay and Nd is the number of passengers that where delayed during the queueing incident.
L = ----T-d = 250 passengers
tq

where, Td is the total delay and td is the time that the queue lasts.
Problem Solution (VII)

Now we can .nd the delay for a passenger entering the terminal 30 minutes after the partial terminal closure occurs. Note that at t = 0.5 hours 750 passengers have entered the terminal before the passenger in question. Thus we need to .nd the time when the supply function, μ(t), achieves a value of 750 so that the passenger “gets serviced”. This occurs at,
μ(t + .t)= λ()t= 750

therefore .t is just 15 minutes (the passenger actually leaves the terminal at a time t+.t equal to 0.75 hours). This can be shown in the diagram on the next page.

Problem Solution (VIII)

Demand and supply functions for example problem

1: Passengers In  2: Passengers Served
1: 2000.00
2:
1: 1000.00
2:
1:
2: 0.00

0.00  0.50 1.00 1.50 2.00 7/7/93

Time (hrs)

Handling Complex Time-Varying Behaviors

The methodology described in previous pages can be
extended to understand complex airport time-varying
behaviors.

Examination of the basic state equation,
L= L+ (λ– μ).t
tt – 1 tt

reveals that as long as the arrival and service .ow rates (i.e., λt and μt  are known functions of time - regardless
their mathematical complexity - the process of .nding the state, Lt, is simple using numerical integration.

People Conveyance Systems

.
At airports it is necessary to implement people conveyance systems such as electrical escalators, moving sidewalks (or power walks), and Automated People Movers (APM)

.
The general goals of these systems are:

.  
Reduce connection times

.
Changes in vertical .ows (2-level terminals)

.
Reduce the actual walking distances for passengers

.  
Improve the level of service (indirectly the image of the airport)

.
Move large volumes of passengers per unit of time

 

Electrical Escalator Capacities

 

Electrical escalators come in various widths and tread speeds. Shown below are some standard escalators used in the US.
Table 7. Typical Characteristics of Electrical Escalators (Fruin).

Width at Hip mm (in)  Width at Tread mm (in)  Theoretical Capacity (pr/hr)  Practical Capacity (pr/hr) 
813 (32)  610 (24)  5,000  2,040a 
6,700  2,700b 
1219 (48)  1016 (40)  8,000  4,080 
10,700  5,400 

a.90 ft/min linear speed
b.120 ft/min linear speed

Moving Sidewalks

.
Mechanical-electrical systems used to reduce walking distance at many airports

.
Share similar performance characteristics with electrical escalators

.
Given the horizontal disposition of movinf sidewalks add 10% to the practical capacity of an escalator

 

APM Fundamentals

Automated People Mover (APM) Systems:

1.
 Fully automated

2.
 No drivers

3.
 Operating on a guideway

4.
 Exclusive right-of-way

5.
 Expensive (15-40 Million per mile)

6.
 Link between airport terminal activities

7.
 Link to other transportation modes (i.e., mass transit)

 

APM Background

Tampa International Airport
.  
In 1971

.
First APM system

City of Miami
.  
In 1986

.  
First DPM in the United States

 

Today, about 19 airports have APM systems in the United States including:
.  SEATAC, Atlanta, Chicago, Dallas-Forth Worth, Denver, Orlando, etc.
APM Systems

 

 

APM Capacity Estimation

The basic equation for APM capacity usually predicated in terms of a minimum headway, hmin
h
min  is usually dictated by APM station capacity since stops at stations would require between 30-45 seconds of stopped time under demanding .ow conditions
h
min  should be the least of station headway and guideway headway (this last one dictated by safety considerations) to make sure two TUs do not collide even if the leading TU stops instantaneously - brick wall analogy
APM Capacity Analysis

3600Cn
v
C = ---------------------
h
min
where:

C  is the hourly capacity of the APM system (passengers
per hour)
C is the capacity of each vehicle (passengers per vehicle)

v

n is the number of vehicles per transit unit (in the APM) and hmin  is the minimum headway (seconds)

 

References

 1) Lin,Y. A Simulation Model of an Automated People Mover at Airports. M.S. Thesis. Virginia Polytechnic Institute and State University, Blacksburg, VA 24061.
2) Kulkarni, M. Development of a Landside Terminal
Simulation Model. M.S. Thesis. Virginia Polytechnic
Institute and State University, Blacksburg, VA 24061.

3) Fruin, J.J. Designing for Pedestrians. in Public Transportation Systems. Hoel and Gray: Editors. John Wiley and Sons, New York, 1993.
4) IATA. Airport Development Reference Manual: 8th Edition. International Airline Transport Association, Montreal, 1995.

 

 

redche

good points