Thesis Presentation - Rev JD 17July2016

Development of Scheduling, Path Planning and Resource
Management Algorithms for Robotic Fully-automated
Multi-story Parking Structure
Jayanta Kumar Debnath
20 July 2016
University of Toledo
Electrical Engineering and Computer Science Department
Master of Science in Electrical Engineering
(with concentration in Computer Science and Engineering)
Thesis Presentation

 Introduction
 Problem Statement
 Proposed Methodology
 Proposed Path Planning Algorithm
 Proposed Elevator Scheduling Algorithm
 Proposed Resource Management Algorithm
 Real-time Concurrent Simulation Model
 Simulation Results
 Conclusions and Future Study
Contents

IntroductionWhy Automated Parking?
• Create space
• Increase revenue
• Better customer security
• Green parking
50% less real-
estate than
traditional
parking lot!
No drive way
roads like
traditional
parking space!
Lower
deployment cost
plus more
revenue
generating space!
.
More security
for people and
their vehicles!
Increase green
space and reduce
traffic congestion
and carbon
footprint!
Promising and effective
solution for busy
metropolitan areas
parking challenge!

IntroductionCurrent Automated Parking Technology
Stacker Type Automated Parking Tower Type Automated Parking
• Require dedicated lane for stacker crane.
• Low space utilization.
• Do not require sophisticated AI Algorithms.
Stacker Crane
• Require one elevator.
• Low space utilization.
• Do not require sophisticated AI
Algorithms.
• Parking capacity is not scalable.

Chess Type Automated Parking Puzzle Type Automated Parking
• No dedicated driveway or lane required.
• Vehicles can be moved horizontally only.
• Multiple elevators.
• Maximum space utilization possible.
• Require sophisticated AI Algorithms.
• Parking capacity is highly scalable.
• Each cell require lifting mechanism.
• Vehicles can be moved both
vertically and horizontally.
• No elevator required.
• Space utilization less than chess type.
• Require sophisticated AI Algorithms.
• Parking capacity is highly scalable.
Puzzle parking
structure is similar to
chess parking except
there is no elevators!

Moving Vehicles using Roller Bed Mounted Pallets on Chess Type Parking!

Problem Statement
Motivation of this Thesis!
 Robotic and fully automated parking structures are becoming increasingly
feasible from the technology perspective.
 There is a lack of reported designs in literature for a computerized
management system for such structures.
 Artificial Intelligence is well suited for and can enhance efficiency,
scalability and mass level commercialization of robotic fully-automated
parking structures.
 Problem Statement: Design, develop and prototype in simulation an
integrated software implementation for a management system that can plan
multiple concurrent paths, schedule a group of elevators, and allocate
parking space and other related resources in real time with service times
acceptable to users.

Problem SpecificationRequirements
Ground Floor Layout (shown for 10×20 topology)
Vehicle Movement Directions
• No driving lanes on any floor of the multistory parking structure
• Number of parking spaces on a given floor and number of stories are variables.
• Minimum 80% utilization rate for parking on a given floor
• No more than 5 minutes waiting time for delivery or retrieval of a vehicle by drivers
• Multiple independent lifts (or elevators)
• Robotic carts or pallets move vehicles.
• Unlimited number of vehicles in motion throughout the structure at any given time
• Vehicle cart and elevator movements are modeled in compliance with physics.
V V V V V V V V V V V V
L L L L L L L L
E E EEE E EE
– Vehicle Exchange Bay ; – Elevator Cell ; – Elevator Load/Unload Bay ; – Storage CellV E L

Proposed MethodologyStorage Process
Storage Management Algorithm
assigns a storage location for a
Storage Request
Elevator Scheduling
Algorithm assigns an
elevator and informs
customer.
Customer leaves their vehicle
in the elevator and leave.
Elevator transport vehicle to
desired floor and unload the
vehicle.
Path Planning Algorithm
finds a path to storage
location and moves the
vehicle accordingly.
Storage and Retrieval
Request Entry Kiosk!
Elevator
Needed?
Select Vehicle
Exchange Bay and
notify customer
Customer drops off
their vehicle in the
Vehicle Exchange
Bay and leaves.
Yes
No
L L L L L L L L
E E EEE E EE

Proposed MethodologyRetrieval Process
Storage Management Algorithm
locates vehicle parked at a specific
location for a Retrieval Request.
Elevator Scheduling
Algorithm assigns an
elevator and notifies
customer.
Customer picks up the
vehicle and leaves.
Elevator transports vehicle to
ground floor.
Path Planning Algorithm
finds a path towards elevator
location and moves the
vehicle accordingly.
Storage and Retrieval
Request Entry Kiosk!
Elevator
Needed?
Select Vehicle
Exchange Bay and
notify customer
Path Planning
Algorithm finds a
path towards Vehicle
Exchange Bay
location and moves
the vehicle
accordingly.
Yes
No
L L L L L L L L
E E EEE E EE

Proposed MethodologyTheoretical Bounds
L L L L L L L L
E E EEE E EE
What is the
minimum
number of
elevators?
What is the
minimum
number of
blank cells?
Bounds on minimum number of elevators and blank cells are derived
applying Queueing Theory on Storage and Retrieval Processes.

L L L L L L L L
E E EEE E EE
Proposed Path Planning AlgorithmOverview
 D* Lite Algorithm
 Path Planning for storage and retrieval of vehicles on cart.
 Uniform Cost Search
 Locating blank cells
 Path Planning for blank cells
Immovable
Obstacle!
Movable
Obstacle!
Starting Cell
Destination
Cell
Dynamic
Environment
Unblock
Procedure

L L L L L L L L
E E EEE E EE
Neighbor Cell on
Planned Path
Unblock
Procedure

L L L L L L L L
E E EEE E EE
Nearest blank
cell located using
Uniform Cost
Search!
Unblock
Procedure

L L L L L L L L
E E EEE E EE
Neighbor cell on
planned path of
blank cell
Selected
blank cell
Unblock
Procedure

L L L L L L L L
E E EEE E EE
Selected
blank cell
moved!
Unblock
Procedure

L L L L L L L L
E E EEE E EE
Vehicle
moved!
Check for change of
immovable obstacle
topology!
Unblock
Procedure

L L L L L L L L
E E EEE E EE
No change in
immovable obstacle
topology.
Follow previously
planned path
Check for change of
immovable obstacle
topology.
Unblock
Procedure

L L L L L L L L
E E EEE E EE
Immovable obstacle
topology changed!!
Re-plan path
efficiently which is a
special feature of D*
Lite algorithm!!
Check for change in
immovable obstacle
topology.
Unblock
Procedure

L L L L L L L L
E E EEE E EE
No change in
immovable obstacle
topology.
Follow previously
planned path
Check for change in
immovable obstacle
topology.
Unblock
Procedure

Proposed Path Planning AlgorithmD* Lite Algorithm
D* Lite Algorithm is Heuristic Based and Incremental fast re-
planning search algorithm and very effective in a dynamic environment.
10 11 12 21 20 19
7 6
9 8 7 6
5 4
6 7 8 9
11 12 13 20 19 18
6 5
8 7 6 5
4 3
5 6 7 8
12 13 14 19 18 17 12 11 10 9 8 7 6 5 4 5 6 7
13 14 15 18 17 16 11 10 5 4 3 4 5 6
14 15 16 17 16 15 10 9 4 3 2 3 4 5
15 16 17 16 15 14 9 8 3 2 1 2 3 4
16 17 18 17 13 7 2 1 G 1 2 3
12 6 5 4 3 2 1 2 3 4
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 3 4 5
17 16 15 14 13 12 8 7 6 5 4 3 4 5 6
14 13 12 11 11 9
13 12 11 10 10 8
8 7
7 6
10 9 8 7
11 10 9 8
16 15 16 15 14 13 11 6 5 4 5 6 7
15 16 17 16 15 14 12 7 6 5 6 7 8
16 17 18 17 16 15 13 12 11 10 9 8 7 6 7 8 9
16 14 13 12 11 10 9 8 7 8 9 10
S 20 19 18 17 15 14 13 12 11 10 9 8 9 10 11
7 6
9 8 7 6
5 4
6 5
8 7 6 5
4 3
9 8 7 6 5 4
5 4 3 4
9 4 3 2 3 4
9 8 3 2 1 2 3
13 7 2 1 G 1 2
12 6 5 4 3 2 1 2 3
13 12 11 10 9 8 7 6 5 4 3 2 3 4
15 14 13 12 8 7 6 5 4 3 4
10 9 8 7
11 10 9 8
15 16 15 14 13 11 6 5 4
15 16 17 16 15 14 12 7 6
16 17 18 17 16 15 13 12 11 10 9 8
16 14 13 12 11 10
S 20 19 18 17 15 14 13 12
Uninformed breadth-first search Heuristic based D* Lite or A* search
Heuristic is good!
Grey cells are
explored
during path
planning.

Proposed Path Planning AlgorithmD* Lite Algorithm
D* Lite Algorithm is a Heuristic Based and Incremental fast re-
planning search algorithm and very effective in a dynamic environment.
A* search Incremental D* Lite search
Incremental search is able to effectively re-use partial path plan from previous search!
7 6
8 7 6
5 4
6 5
8 7 6 5
4 3
8 7 6
5 4
11 10 9 4 3 2
11 10 9 8 3 2 1 2
11 7 2 1 G 1
12 6 5 4 3 2 1 2
12 13 10 9 8 7 6 5 4 3 2
S 8 7 6 5 4
10 9 8 7
11 10 9 8
11 6
12
13 12 11 10
14 13 12
7 6
8 7 6
5 4
6 5
8 7 6 5
4 3
8 7 6
5 4
11 10 9 4 3 2
11 10 9 8 3 2 1 2
11 7 2 1 G 1
12 6 5 4 3 2 1 2
12 13 10 9 8 7 6 5 4 3 2
S 8 7 6 5 4
10 9 8 7
11 10 9 8
11 6
12
13 12 11 10
14 13 12
Obstacle
added! Obstacle
added!
Grey cells are
explored in
re-planning.

Proposed Path Planning AlgorithmUnblock Procedure
o o
o o L o
o o
S o
o o o o
o o
o
o o
o o
o o
o o o o o o
o o o o o
o o o o
Use uniform cost
search to locate nearest
blank cell

Uniform cost search
1st Iteration
o o
o o L o
o o
S o
o o o o
o o
o
o o
o o
o o
o o o o o o
o o o o o
o o o o
No blank cell
Found!

Uniform cost search
2nd Iteration
No blank cell
Found!
o o
o o L o
o o
S o
o o o o
o o
o
o o
o o
o o
o o o o o o
o o o o o
o o o o

Uniform cost search
3rd Iteration
No blank cell
found!
o o
o o L o
o o
S o
o o o o
o o
o
o o
o o
o o
o o o o o o
o o o o o
o o o o

Uniform cost search
4th Iteration
Blank cell
found!
o o
o o L o
o o
S o
o o o o
o o
o
o o
o o
o o
o o o o o o
o o o o o
o o o o

o o
o o L o
o o
S o
o o o o
o o
o
o o
o o
o o
o o o o o o
o o o o o
o o o o
Two blank cells!
Two possible
destination cells!
Find nearest blank cell – destination cell pair.

o o
o o L o
o o
S o
o o o o
o o
o
o o
o o
o o
o o o o o o
o o o o o
o o o o
Nearest blank
cell – destination
cell pair
Find nearest blank cell – destination cell pair.

Use D* Lite path planning to move blank cell towards destination cell
o
o o L o
o o
S o
o o o o
o o
o
o o
o o
o o
o o o o o o
o o o o o
o o o o

Proposed Elevator Scheduling Algorithm
Two-level Integer Programming Formulation
Problem Formulation
Vehicle Set: S
Elevator 1 Elevator j Elevator NE…... …...
Vehicle Subset Assigned
to Elevator j: Sj
Trip 1 Trip k Trip |Sj|…... …...
For a given
vehicle-to-elevator
assignment
High Level: Vehicle-to-Elevator
Assignment
Low Level: Vehicle-to-Trip
Assignment
Each trip will
serve one
vehicle!
HNPGA (Hybrid Nested
Partition and Genetic
Algorithm) used for High
Level Assignment!
FIFO used for Low Level
Assignment!

X X X ……. X X X
The Entire Feasible Region:
Most Promising Region
1 1 2 ….NE 1 2 1 1 2 ….NE 1 1 1 1 2 ….NE 1 3
Partitioning
Iteration 0:
Iteration k:
.
.
.
.
},...,4,3,2,1{ ENX 
)(:RegiongSurroundin k
)()(:RegiongSurroundin kbk 
||S
……
……
Depth: 0
Depth: d
Depth: d+1
Basic partitioning scheme
shown, where at each
iteration the assignment of
next 1 unassigned vehicle is
fixed.
1 X X ……. X X X 2 X X ……. X X X 3 X X ……. X X X NE X X ……. X X X……
Iteration 1:
)σ(1
.
.
.
)(:)(region,-subbestofregiongsurroundinWhole kbkb  
Depth: 1X X X X X X X X
X X
1 1 2 ….NE 1 2 5 X
X X X X 1 1 2 ….NE 1 NE X X
1 1 2 ….NE 1 2 1 X 1 1 2 ….NE 1 2 2 X 1 1 2 ….NE 1 2 NE X
1 1 2 ….NE 1 X X X
Iteration k-1:
Depth: d-1
)σ(k 1
σ(k)
1 1 2 ….NE 2 X 1 1 2 ….NE 3 X 1 1 2 ….NE NE X……X X X X X X
)(kb
at iteration k on depth d
Most Promising Region at iteration k-1 on depth
d-1. This would be most promising region at
iteration k+1 if backtracking occurs at iteration k.
at iteration 1 on depth 1
Selected best sub region of most
promising region at iteration k. This
would be most promising region at
iteration k+1 if globally verified.
Proposed Elevator Scheduling Algorithm
HNPGA : Select Next
Two steps at each iteration of HNPGA for selecting next Most Promising Region
Step 1: Select best sub region. Step 2: Global verification of selected
best sub region with Surrounding
Regions.
Both steps use Genetic Algorithm
Nested Partition Tree!

1 5 3
1 5 3 2 4 5 1 5 3 1 3 4 1 5 3 5 2 1…...
4 5 1 3 5 6
6 1 5 3 2 5
2 4 1 1 6 2
1 2 4 5 3 4
2 5 1 3 6 2
4 5 2 1 6 2
1 5 3
1 5 3
1 5 3
1 5 3
1 5 3
1 5 3
1 3 4 3 5 61 5 3
4 5 6 …... 3 1 4
Proposed Elevator Scheduling AlgorithmStep 1: Select Best
Sub Region
Total 10 vehicles;
Each field represents
vehicles to schedule
Initial populations of GA
After
evaluation
cycles!
Fittest of final populations
Crossover and
Mutation
Best sub region
found by GA!
Selected Most Promising
Region at first iteration.

1 5 3
1 5 3 2 4 51 5 3 1 3 4 1 5 3 5 2 1…...
1 3 4 3 5 6
1 3 4 3 2 5
2 4 1 1 6 2
1 2 4 5 3 4
2 5 1 3 6 2
4 5 2 1 6 2
1 5 3
1 5 3
1 5 3
1 5 3
1 5 3
1 5 3
2 1 3 1 4 4…...
6
5
2
4
Fixed values from
selected best sub
region
Uniform
Sampling
Values
other
than
(1,3,4)
Uniform Sampling
Values
other
than
(1,5,3)
Uniform Sampling
Proposed Elevator Scheduling AlgorithmStep 2: Global
Verification
Initial populations of GA uniformly taken from three region.
Selected
best sub
region!
Selected Most Promising
Region at first iteration.

Proposed Elevator Scheduling AlgorithmObjective Function
of GA
𝐽 =
𝑗=1
𝑁 𝐸
𝐽𝑗 =
𝑗=1
𝑁 𝐸
𝑡𝑗
𝑏
+
𝑖=1
|𝑆𝑗
𝑅
|
𝑡𝑖
𝑟𝑒
+ 𝑡𝑖
𝑙
+ 𝑡𝑖
𝑒
+ 𝑡𝑖
𝑢
+
𝑖=1
𝑆 𝑗
𝑆
𝑡𝑖
𝑙
+ 𝑡𝑖
𝑒
+ 𝑡𝑖
𝑢
+ 𝑡𝑖
𝑡𝑠
4 5 2 1 6 21 5 3
Each field or gene of
chromosome
represents vehicles to
schedule.
The value of each
field represents the
assigned elevator.
Total time required to complete storage
or retrieval process associated with
assigned vehicles.

Proposed Elevator Scheduling AlgorithmCrossover Operator
2 3 5 21 4
5 6 1 42 3
Chromosome 1:
Chromosome 2:
2 3
5 2
1 4
5 6
1 4
2 3
Chromosome 1:
Chromosome 2:
After Crossover
4p
C

2 3 5 21 4
5 6 1 42 3
Chromosome
After Mutation
Randomly generated Mutation
Point=4 and Randomly
Generated Elevator No =6
2 3 5 21 6
2 3 5 21 4
Randomly
Generated Mutation
Points = 2 & 6
2 2 5 31 4
After Mutation
First Mutation
Operator
Second Mutation
Operator
Proposed Elevator Scheduling AlgorithmMutation Operator

Theoretical Bounds on Resource NeedsQueueing Theory
Server - 01
Server - 02
Server - S
Mean Arrival
Rate, λ
Mean Service
Rate, μ
𝛌 < 𝛍 × 𝑺Steady State
Condition!
M/M/S Queue Model
Stochastic
Arrival Process
Stochastic
Service Process
Multiple Parallel
Servers
Without steady
state queue will
grow infinitely
large eventually.

Proposed Resource Management AlgorithmStatistical Models
Rush hour period
customer arrival
modeling
Morning Rush Hour
• 2 clock hour period from 6:30 AM to 8:30 AM
• 95% of requests are storage
• 5% of requests are retrieval
Evening Rush Hour
• 2 clock hour period from 4:00 PM to 6:00 PM
• 95% of requests are retrieval
• 5% of requests are storage
Inspired by busy
downtown
business districts
traffic pattern

Proposed Resource Management AlgorithmStatistical Models
0
20
40
60
80
100
120
0-5
5-10
10-15
15-20
20-25
25-30
30-35
35-40
40-45
45-50
50-55
55-60
60-65
65-70
70-75
75-80
80-85
85-90
90-95
95-100
100-105
105-110
110-115
115-120
NV,M,T
5-Minute Time Periods during rush hours
Distribution of Mean Arrival Rate during Rush Hours
(NV,M,max = 100)
Poisson Distributed Customer Arrivals with varying mean arrival rate!

Theoretical Bounds on Resource Needs
Bound on
Minimum Number
of Blank Cells
L L L L L L L L
E E EEE E EE
Modeled part of retrieval process at the beginning of evening rush hour
as M/M/S queue where blank cells act as multiple servers to transport
vehicles toward elevator load/unload bay!

Theoretical Bounds on Resource Needs
Bound on
Minimum Number
of Blank Cells
L L L L L L L L
E E EEE E EE
𝑁 𝐵,𝐹 =
𝑁 𝑉,𝑀,𝑚𝑎𝑥
12 × 𝑁 𝐹 × 3600
× (𝑑 𝐵+5𝑑 𝐸) × 𝑡 𝑚𝑜𝑣𝑒 + 1 + 𝑚𝑎𝑥
1≤𝑇≤12
𝑁 𝐵,𝐹,𝑇,𝑆
Applying 𝛌 < 𝛍 × 𝑵 𝑩,𝑭

Theoretical Bounds on Resource NeedsBound on
Minimum Number
of Elevators
L L L L L L L L
E E EEE E EE
L L L L L L L L
E E EEE E EE
Modeled part of storage/retrieval process as M/M/S queue where
elevators act as multiple servers to transport vehicles between floors!

Minimum Number
of Elevators
Speeding up
Starting Destination floor
Distance
,
2
2
.
Slowing
down
,
2
2
.
Traveling at
Constant
Speed
Starting floor Destination floor
Distance
𝑉𝐸
Slow down
Speed up
If, 𝐷 𝐻𝐻 ≤ 𝑉𝐸,𝑚𝑎𝑥
2
𝑎 𝐸 :If, 𝐷 𝐻𝐻 > 𝑉𝐸,𝑚𝑎𝑥
2
𝑎 𝐸 :
Elevator Dynamics

Minimum Number
of Elevators
Applying 𝛌 < 𝛍 × 𝑵 𝑭
1
2( 2𝐷 𝐹 𝑁𝐹 𝑎 𝐸 + 𝑇𝐸𝐷𝑂 + 𝑇𝐸𝐷𝐶) + 𝑇𝐿 + 𝑇 𝑈
× 𝑁 𝐸 >
3600
If, 𝐷 𝐻𝐻 ≤ 𝑉𝐸,𝑚𝑎𝑥
2
𝑎 𝐸 :
1
2
𝑉𝐸,𝑚𝑎𝑥
𝑎 𝐸
+
𝐷 𝐹 𝑁 𝐹
2𝑉𝐸,𝑚𝑎𝑥
+ 2(𝑇𝐸𝐷𝑂 + 𝑇𝐸𝐷𝐶) + 𝑇𝐿 + 𝑇 𝑈
× 𝑁 𝐸 >
3600
If, 𝐷 𝐻𝐻 > 𝑉𝐸,𝑚𝑎𝑥
2
𝑎 𝐸 :

Real-time Concurrent Simulation ModelUnified Modeling
Language
The overall functionality of simulation is modeled through five major
activity modules, which are (a) Automated Parking Lot, (b)
Automated Storage Controller, (c) Automated Retrieval
Controller, (d) Elevator Controller, and (e) Elevator Scheduler
Modular
Simulation
Architecture

Language
State machine diagram for Automated Retrieval Controller: moving
towards elevators

Language
State machine diagram for Automated Storage Controller: moving
from elevators

Language
State machine diagram for Elevator Controller : moving between
floors

Language
Busy-wait
Synchronization
Techniques used
to communicate
among concurrent
threads.
Timing diagram

Simulation StudyExperimental Setup
𝑵 𝑪 𝑵 𝑹 𝑵 𝑽,𝑴,𝒎𝒂𝒙 𝑵 𝑭
10 10 100 2
20 20 200 3
30 30 300 4
40 40 400 5
500 6
600 7
700 8
800 9
10
Space Utilization > 80%
The capacity of parking
lot needs to be fully
utilized within two
clock-hour period
43 Test Cases Found!
Generating
Test Cases
Number
of
columns
on each
floor
layout
Number
of rows
on each
floor
layout
Number
of floors
Maximum value of
mean arrival rate for
vehicle requests for
the entire parking
structure per hour
among all rush hour
time slots

Simulation StudySimulation Software
A software application with multithreading was
developed through the Unified Modeling Language
(UML) using Java and MATLAB programming
languages.
Simulation Software was run in Linux
environment for better multithreading
capability!

Simulation StudyRunning Simulation in 50X Speedup
Case No – 35 : 𝑁𝐹 = 4, 𝑁 𝑅 = 20, 𝑁𝐶 = 10,𝑁𝐸 = 6, 𝑁 𝑉,𝑀,𝑚𝑎𝑥= 700

Simulation StudySimulation Results
0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
Time(Minutes)
Test Case Number
Average Customer Waiting Time for Storage (WTS) Without Immovable Carts
With 10% Immovable Carts
0
1
2
3
4
5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
Time(Minutes)
Test Case Number
Average Customer Waiting Time for Retrieval(WTR)
Without Immovable Carts
Average customer waiting time within an impressive 5 minutes mark!

In most cases, average customer waiting time within an impressive 2 minutes mark!
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
ProbabilityDistribution
Waiting Time (Minutes)
Average Customer Waiting Time for Storage (WTS) Distribution for 43
Test Cases
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
ProbabilityDistribution
Average Customer Waiting Time for Retrieval (WTR) Distribution among
43 Test Cases

0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
Time(Minutes)
Test Case Number
Maximum Customer Waiting Time for Storage (WTS) Without Immovable Carts
0
5
10
15
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
Time(Minutes)
Test Case Number
Maximum Customer Waiting Time for Retrieval (WTR) Without Immovable Carts
For most cases, the maximum (worst case) customer waiting time is less than 5 minutes
although for a small number of cases it was between 10 to 17 minutes!

Extreme maximum values occur for very few test cases with
10% immovable carts. In general, maximum waiting times
are within the 6-minute mark.
0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
ProbabilityDensity
Maximum Customer Waiting Time for Storage (WTS) Distribution among
43 Test Cases
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
ProbabilityDensity
MaximumCustomer Waiting Time for Retrieval (WTR) Distribution
among 43 Test Cases
Low Probability!

Simulation Study
Simulation Results for Case #42 with 10%
Immovable Carts
0
0.01
0.02
0.03
0.04
0.05
0.06
1
23
45
67
89
111
133
155
177
199
221
243
265
287
309
331
353
375
397
419
441
463
485
507
529
551
573
595
617
639
661
683
705
727
749
771
793
815
837
859
881
903
925
947
969
991
1013
1035
ProbabilityDensity
Waiting Time (Seconds)
Customer Waiting Time for Retrieval (WTR) Distribution : Case No - 42
0
0.1
0.2
0.3
0.4
0.5
1
18
35
52
69
86
103
120
137
154
171
188
205
222
239
256
273
290
307
324
341
358
375
392
409
426
443
460
477
494
511
528
545
562
579
596
613
630
647
664
681
698
715
732
749
766
783
800
ProbabilityDensity
Waiting Time (Seconds)
Customer Waiting Time for Storage (WTS) Distribution : Case No - 42
Most of the customers experience average
waiting times; very few customers have to
wait more than the average value!
Frequency Distribution of
Waiting Times for
Individual customers for
Case #42
Considering 10% immovable carts
Considering 10% immovable carts

ConclusionsConclusions
In light of and within the context of the simulation
study presented, the design appears feasible for real
time deployment in an industrial-grade environment.
• Average Customer Waiting Time is not more than 5
minutes in most cases!
• Space Utilization for parking is more than 80% !
• Design supports customer arrival rates of up to 800
customers per hour!

Future StudyRecommendations
• In the current system, all the parking spots are the same size. Given that there
are different size vehicles (sedans, SUVs, mini vans, trucks, etc.) to park, the
size of a parking spot would have to match the largest car size. To maximize the
available real-estate space utilization rate and enhance the capacity, future
studies may consider the design other topologies which may have different size
parking spaces.
• Study of the effect of robotic cart failures could be extended further to
determine the adverse impact on performance more closely.
• We assumed, for the analysis based on the queueing theory, that customers
would not engage in balking or reneging in the waiting lines. In future studies
these and other similar complications can be injected into the statistical models
to determine their effects on performance.
The research could be extended in the future from the following aspects:

Publications
Debnath, Jayanta K., and Gursel Serpen. "Real-Time
Optimal Scheduling of a Group of Elevators in a Multi-
Story Robotic Fully-Automated Parking Structure."
Procedia Computer Science 61 (2015): 507-514.
J. Debnath and G. Serpen, Design of Multithreaded
Simulation Software through UML for a Fully
Automated Robotic Parking Structure, to appear in
proceedings of International Conference on Simulation
Modeling Practice and Theory, Las Vegas, Nevada, July
2016.

Thesis Presentation - Rev JD 17July2016

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