2. Introductrivia
• Population of Omaha? 408,958
• Population of Lincoln? 258,379
• Population of Bellevue? 50,137
• Capacity of UNL Memorial Stadium?
91,000
It is true that Memorial Stadium is the 3rd most crowded
city in Nebraska! …. How long does it take to evacuate?
3. Problem and assumptions
• Problem: Time to evacuate the fans from Memorial Stadium at full
capacity?
• Assumptions:
• The stadium is full
• Leave stadium=Out of the system
4. Objectives
• To model the UNL Memorial Stadium as a queueing system
• To compare the observed results with other simulation processes
• To discuss if the simulation times obtained are compliant with current
evacuation regulation
5. Data collection and assumptions (1)
148 blocks in total
91,000 fans
=> 615 fans per block
33 blocks, 7 gates
33 * 615 = 20295 fans
20295/7 = 2900 fans
per gate
Assumed capacity: 91,000 fans
6. Data collection and assumptions (2)
Side
#Blocks
Estimated #fans
Gates
Estimated
population
gate
South
31
19065
4
4767
North
33
20295
5
4059
East
33
20295
7
2900
West
51
31365
4
7842
Table 1: Estimated population per gate.
per
7. Data collection and assumptions (3)
Population = 4059/Gates
Population = 4767/Gates
GATES: 24,1,2,3
Population =2900/Gates
=
GATES: 4,6,8,10
Population= 7842/Gates
GATES: 11,12,14,15,16
GATES:17,18,19,
20,21,22,23
The big picture of
how our queues
look like
8. Data collection and analysis (4)
• How many fans arrive at a gate per minute:
• Uniform between 200 and 300 per minute
• How many fans exit a gate per minute:
• Constant 180 per minute
• Transfer time from seat to gate:
• Uniform between 1 and 10 minutes
Note: Observations were done on November 9th, Huskers vs
Wolverines. Does this look like an emergency evacuation? (Hint: how
did we win that match? )
9. Arena model construction
• We have 20 of these:
• Max arrival is different for each gate (based on population)
• Arrival rate, service rate and transfer time are the same for each
queue
Time for Arena demo!!!!!
11. Results
Simulation of each side of the stadium
Sides
South
West
North
East
Total Population Numer of gates Number of servers
4767
7842
4059
2900
4
4
5
7
6
6
6
6
Arrival rate
Service rate
Simulation time (minutes)
Uniform (0.2,0.3) seconds
Uniform (0.2,0.3) seconds
Uniform (0.2,0.3) seconds
Uniform (0.2,0.3) seconds
Constant (2 s)
Constant (2 s)
Constant (2 s)
Constant (2 s)
30.883
47.967
26.950
21.850
Arrival rate
Service rate per server
Simulation time (minutes)
Uniform (0.01.0.015) seconds
Constant (2 s)
48.4
Complete simulation
Gate
All
Total Poulation Number of gates Number of servers
91031
20
20*6
Evacuation Time
12. Validation
Direct Estimation:
Highest Population = 7842 (west Gate)
Service Rate = 30 minute *6 /fan
Total time for serving fan = 7842/180= 43.57 minutes
Considering walk time = 5.5 minutes (Uniform (1,10))
Total Time for evacuation = 43.57+5.5 = 49.57 minutes
Simulated evacuation time = 48.4 minutes
Percentage Error = (48.54-49.57)/49.57 = -2.08 %
13. Conclusions
• We found that:
• The evacuation time obtained from the simulation is 48 minute and 25
second
• The simulation result matches the estimation.
• Accomplishment of objectives:
• To model the UNL Memorial Stadium as a queueing system: Done!
• To compare the observed results with other simulation processes: Next week!
• To discuss if the simulation times obtained are compliant with current
evacuation regulation: Next week!
