Improving Parking Garage Efficiency using Reservation Optimization Techniques

Improving Parking Garage Efficiency using Reservation Optimization Techniques By Arjun Rao Advisor : Dr. Ivan Marsic Committee Members : Dr. Joseph Wilder Dr. Manish Parashar

INTRODUCTION Ø Problems with Parking Garages • No reservation policy – Only display of rates and location – No reservation of parking spots • Ambiguity of information – Display of number of parking spots available creates ambiguity • Environmental concerns – 40% of total traffic (1) – 47000 gallons of gas was used up in a year in a business district of LA(1) • Lack of revenue management 2

OUTLINE • Goals • Proposed Solutions • Research Questions • System Architecture • Algorithms • Results • Conclusions and Future Work 3

GOALS Improve parking garage operation efficiency 1. Track car position for real-time monitoring 2. Improve reservation efficiency in garages using reservation defragmentation techniques 3. Improving revenue for parking garages using revenue management techniques 4

OUTLINE • Goals • Proposed Solutions • Research Questions • System Architecture • Algorithms • Results • Conclusions and Future Work 5

PROPOSED SOLUTIONS Ø What is Tracking of a car in a parking garage? • Knowing real-time position from entrance up to parking. • Obtaining knowledge of which parking spot has the car been actually parked in • Tracking is simulated based on real-world parameters 6

PROPOSED SOLUTIONS Ø What is Reservation Defragmentation? • Aim to free parking spots so as to accommodate more parking reservations • Re-arrangement of reservations to increase efficiency • Similar to disk defragmentation in principle. Reservations moved due to defragmentation Reservations not moved even after defragmentation 7

PROPOSED SOLUTIONS Ø What is Revenue Management? • Implemented Types: -Booking Limits: Classifying parking spots in garage based on fare to increase revenue -Overbooking: Permitting reservations beyond capacity of parking garage to account for noshows i. Spoilage Costs ii. Denied Parking Corporate Class Leisure Class Booking Limits Overbooking 8

OUTLINE • Goals • Proposed Solutions • Research Questions • System Architecture • Algorithms • Results • Conclusions and Future Work 9

RESEARCH QUESTIONS A) Tracking • • What method can be used to track cars? What metrics should be selected to show effectiveness of these algorithms? B) Reservation Defragmentation • • What methods can be used for packing more number of reservations into the garage? What metrics should be chosen to demonstrate efficiency of such algorithms? C) Revenue Management • • What techniques can be used for revenue management? Can these techniques from other industries be directly be ported over to the parking garages? 10

OUTLINE • Goals • Proposed Solutions • Research Questions • System Architecture • Algorithms • Results • Conclusions and Future Work 11

SYSTEM ARCHITECTURE Ø Overall System Tracking Sub-System Reservation Defragmentation Sub-System Parking Garage Entrance Console Database Remote Client Revenue Management Sub-System 12

SYSTEM ARCHITECTURE Ø Tracking System Parking Lot Functions _______ Simulator _______ -Mark entry -Track -Park - Provide new spot -Determine accuracy -Arrival Thread -Sensor detection -Path vectors - Modified spot generation Database (My. SQL)

SYSTEM ARCHITECTURE Ø Reservation Defragmentation Parking Lot Functions _______ -Make reservation -Defragmentation -Update reservations Simulator _______ -Reservation thread -Bitmap/Vector allocation -Defragmentation thread Database (My. SQL) 14

SYSTEM ARCHITECTURE Ø Revenue Management Database -Decide Parameters -Run Booking Limit Algorithm -Decide Parameters -Run Overbooking Algorithm Set Booking Limits Set Overbooking capacity

OUTLINE • Goals • Proposed Solutions • Research Questions • System Architecture • Algorithms • Results • Conclusions and Future Work 16

ALGORITHMS I. Tracking Ø Sensor details • Sensor action is simulated using real-world commercially available sensor data (cost and accuracy). • Ultrasonic sensors used for car detection (motion and occupancy) • Sensors are used for interfloor and intra-floor motion detection • All sensors are ceiling mounted Ultrasonic Sensor Prototype(2) Wiring up ultrasonic sensors(2) Example of a parking garage with ultrasonic sensors

ALGORITHMS I. Tracking a) Algorithm T 1 • More sensors used • High Accuracy/High cost • Algorithm tracks car based on sensor crossed • Features included – Track car path – Dynamic allocation Floor Exit Sensor Floor Entry Sensor 18

ALGORITHMS I. Tracking b) Algorithm T 2 • Fewer sensors used • Low Accuracy/Low cost • Algorithm tracks car based on sensor crossed • Features included – Track car path – Dynamic allocation Floor Exit Sensor Floor Entry Sensor 19

ALGORITHMS I. Tracking c) Performance metrics • Inaccurate Tracking - Fail to detect occupancy sensor OR - Fail to achieve the tolerance limit (10%, 50%, 75% ) • Example of 50% tolerance Number of sensor points Example of 75% tolerance

ALGORITHMS II. Reservation Defragmentation Ø Usage of bitmap Parking Spot Index 1 2 3 4 5 . . 500. . . 0000 1 1 1 0 0 0030 0 0 1 1 1 0100 0 0 1 1 1 • It is a matrix of 1’s and 0’s having ‘m’ rows each indicating ‘ 30 minutes’ of time and ‘n’ columns indicating parking spot index. • ‘ 1’ indicates ‘Reservation made’ and ‘ 0’ indicates ‘Free space’. Time (hours) • Bitmap indicates if reservation is made for that spot and time. : : : 2330 0 Bitmap matrix 21

ALGORITHMS II. Reservation Defragmentation Ø Bitmap Terminology Current Time Free Space Contiguous Free Time Slot for Spot 4 Slot Index Reservation Made 0 1 2 3 4 5 6 7 8 9 Contiguous Free Time Slot for Spot 4 0 1 2 3 Parking Spot Index 4

ALGORITHMS II. Reservation Defragmentation Ø Types of reservations used 1. Next Day Reservations 2. Current Day Reservations 23

ALGORITHMS II. Reservation Defragmentation Ø Basic Components First Fit Algorithm Defragmentation Algorithm 24

ALGORITHMS II. Reservation Defragmentation Parking Spot Index a) First Fit Algorithm(3) • Attempts to place the reservation in the first parking spot that can accommodate the reservation. Easy to implement. • Fast allocation • Inefficient allocation 1 2 3 4 5 6 0 1 Time slot Index • 0 1 2 2 5 6 8 3 4 3 5 9 6 11 10 4 7 12 7

ALGORITHMS II. Reservation Defragmentation Ø Implemented Algorithms 1. • Algorithm R 1 • Interval Scheduling 2. • Algorithm R 2 • Recursive First Fit 3. • Algorithm R 3 • Free Space Vector 26

ALGORITHMS II. Reservation Defragmentation b) Algorithm R 2: Recursive First Fit Decreasing(5) Sort Arrange • Sort reservations according to decreasing reservation duration • Re-arrange compatible reservations using first-fit algorithm. 27

28 ALGORITHMS II. Reservation Defragmentation • Algorithm R 2: Example Reservations sorted according to durations Sort 8 7 12 1 4 11 2 10 9 5 3 28

ALGORITHMS II. Reservation Defragmentation • Algorithm R 2: Example->Current Day Parking Spot Index 0 1 2 3 4 5 Parking Spot Index 6 0 8 4 3 5 9 7 4 0 10 1 11 12 2 3 4 5 2 5 6 7 1 2 1 Post. Defrag 6 0 11 1 3 6 6 Time slot Time Slot Index 2 2 Current Time 3 8 10 7 12 4 3 4 9 5 6 Time Slot Index 5 1 7

ALGORITHMS II. Reservation Defragmentation • Algorithm R 3: Example-> Current Day Parking Spot Index 0 8 4 3 5 9 7 4 10 12 2 Post. Defrag 3 4 5 6 7 0 11 1 3 6 6 2 5 Time slot Time Slot Index 2 2 1 1 6 11 1 8 3 9 7 4 10 2 3 4 12 5 6 Time Slot Index 5 1 0 Time slot Current Time

ALGORITHMS II. Reservation Defragmentation • Algorithm R 1: Example->Next Day Parking Spot Index 0 1 2 3 4 5 Parking Spot Index 6 7 Current Time 0 1 2 3 4 5 6 7 0 5 2 11 10 3 5 9 6 7 4 6 2 8 4 11 1 6 2 3 5 Time slot Time Slot Index 1 Post. Defrag 8 10 3 12 9 12 7 4 Time Slot Index 1

ALGORITHMS II. Reservation Defragmentation Ø Performance Metrics • Percentage Reduction in Free time slots = Number of empty time slots (Pre-defrag)-Number of empty time slots(Post-defrag) Number of empty time slots (Pre-Defrag) 100 • Percentage Decrease in Occupied Parking spots = Number of empty parking spots (Pre-defrag)-Number of empty parking spots(Post-defrag) Number of empty time slots (Pre-Defrag) 100

ALGORITHMS II. Reservation Defragmentation Ø Performance Metrics • Reduction in mean length of contiguous free time slot (say Mx) : – Calculate total number of free time slots per parking spot (say FTM) – Calculate number of sets of contiguous time slots per parking spot (say S) Mx = FTM / S • Percentage Increase in garage capacity = Total number of cars in garage( Post-defrag) - Total number of cars in garage (pre-defrag) Total number of cars in garage (Pre-defrag) 100

ALGORITHMS III. Revenue Management a) Booking Limits Algorithm(7) • Two fare class model (Leisure class and Corporate class • Booking Limit = C – Q* Where C = Capacity of garage Q* = Optimal Protection level • Calculate F(Q) where F(Q) is the cumulative probability of demand for the spot at the corporate class cost given that Q is the protection level. Traditionally, derived from historical data but in our case derived from simulation based on real- world values 34

ALGORITHMS III. Revenue Management a) Booking Limits Algorithm • Mathematical decision: If we protect Q+1 spots for the corporate class, then we should lower the protection to ‘Q’ as long as: (1 – F(Q)) (Rh) <= Rl ; F(Q) = Cumulative Probability Rh = Corporate class fare Rl = Leisure class fare 35

ALGORITHMS III. Revenue Management b) Overbooking Algorithm: Probabilistic/Risk Model(8) • Probability equation decides amount of overbooking to be done. • Overbooking (AU) on a garage [capacity (CAP)] such that we have a minimum number of customers denied parking. Basic Equation AU × (1 -NSR)* = CAP Overbooking • Gaussian no-show rate (NSR) for reservations. 36

ALGORITHMS III. Revenue Management c) Overbooking Algorithm: Probabilistic/Risk Model • Difference between airline and garage overbooking • Overbooking amount is calculated prior to reservations being made. • Overbooking done on entire garage capacity. Formula AU = _______CAP_______ (1 -NSR + 1. 645*STD) Where, AU = Total Overbooked Capacity (in 30 minute slots) CAP = Garage Capacity (in hours) NSR = No-show rate STD = Std. Deviation of NSR 37

Outline • Goals • Proposed Solutions • Research Questions • System Architecture • Algorithms • Results • Conclusions and Future Work 38

RESULTS I. Tracking Ø Simulation Parameters Sr. No. Parameter Value Garage Operator Parameters 1. Sensor failure 2%, 5%, 10%, 20%, 50% Yes 2. Speed Limit Max. limit of 30. 23 mph Yes 3. Arrival Distribution Poisson Distribution Yes 4. Customer Arrival Rate 100 cars per hour Yes 5. Garage Capacity 500 parking spots Yes 6. Performance Metric 10%, 50% and 75% tolerance Yes 39

RESULTS Tracking 100 90 Percentage Inaccurate Trackings I. Percentage inaccurate trackings for given tolerance 80 70 60 Algo. T 1 : 75% 50 Algo. T 2 : 75% 40 Algo. T 1 : 10% 30 Algo. T 2 : 10% 20 10 0 2 5 10 Sensor Failure Rate(in %) Capacity of garage = 500 spots 20 50 40

RESULTS Tracking 12 Average number of sensor points per car 10 Number of sensors whose data is recorded I. 8 6 Algorithm 1 Algorithm 2 4 2 0 2% 5% 10% Sensor Failure Rate 20% 50% 41

RESULTS I. Tracking Ø Conclusions • With increase in sensor failure rate, increase in inaccurate tracking is exponential • Algorithm T 2 is more inaccurate than Algorithm T 1 due to usage of fewer sensors • Higher the failure tolerance, lesser are the inaccurate readings Sensor Failure Rate Failure Tolerance Inaccurate tracking Inaccuracies observed

RESULTS I. Tracking Ø Conclusions • Information Provided 3 Algorithm T 1 • Implementation Costs Algorithm T 2 11 Algorithm T 2

RESULTS II. Reservation Defragmentation Ø Simulation Parameters Sr. No. Parameter Value 1. Garage Capacity 500 parking spots 2. Period of observation 24 hours 3. Duration of reservations 30 minutes to 22 hours 4. No-show rate 15% 5. Type of reservations Next-day reservations 6. Performance Metric 1 Time slots freed Performance Metric 2 Parking spots freed Performance Metric 3 Length of contiguous free time slots 44

RESULTS II. Reservation Defragmentation % decrease in fragmented free time slots 70 60 Decrease in fragmented free time slots after 15% random cancellation 50 40 Algorithm R 1 Algorithm R 2 30 Algorithm R 3 20 10 0 200 500 1000 Number of reservations made for the day 1750 Reservations 95% of maximum capacity 1750

RESULTS II. Reservation Defragmentation 20 18 Decrease in occupied parking spots after 15% random cancellation % increase in free parking spots 16 14 12 Algorithm R 1 10 Algorithm R 2 8 Algorithm R 3 6 4 2 0 200 500 1000 Number of reservations made in the day 1750 Reservations 95% of maximum capacity 1750 46

RESULTS II. Reservation Defragmentation 48 time slots (max. number of free time slots per parking spot) 47

RESULTS Mean Length of number of free time slots II. Reservation Defragmentation 48 time slots (max. number of free time slots per parking spot) 48 For 1750 reservations

RESULTS II. Reservation Defragmentation Conclusions (Next day) • Increase in number of reservations causes increase in percentage defragmentation • Algorithm R 2 provides best defragmentation in terms of metrics when random cancellation is carried out. • Algorithm R 3 provides improved parking garage spot occupancy when block cancellation is carried out. • Std. deviation for R 2 is lesser than R 1 and R 3 indicating more predictability of algorithm R 2. 49

RESULTS II. Reservation Defragmentation Ø Simulation Parameters Sr. No. Parameter Value 1. Garage Capacity 500 parking spots 2. Period of observation 24 hours 3. Duration of reservations 30 min to 22 hrs (exp. dist. ) 4. No-show rate 15% 5. Type of reservations Current-day reservations 6. Performance Metric Increase in garage capacity 50

RESULTS II. Reservation Defragmentation 6. 00% Percentage increase in maximum occupancy of parking garage Percentage Increase 5. 00% 4. 00% Algorithm R 1 3. 00% Algorithm R 2 Algorithm R 3 2. 00% 1. 00% 0. 00% 51

RESULTS III. Revenue Management Ø Simulation Parameters Sr. No. Parameter Value 1. Garage Capacity 500 parking spots 2. Fare classes Leisure Class and Corporate class 3. Leisure Fare/Corporate Fare 0. 166 -0. 75 (based on airlines) 4. Corporate Customer Arrival Distribution Poisson Distribution 5. Corporate Customer Arrival Rate 5 cars/hour to 500 cars/hour 6. Performance Metric Protection level and Booking Limit 52

RESULTS III. Revenue Management 53

RESULTS III. Revenue Management Ø Simulation Parameters Sr. No. Parameter Value 1. Garage Capacity 500 parking spots 2. Fare classes Leisure Class and Corporate class 3. Leisure Fare/Corporate Fare 0. 166 -0. 75 (based on airlines) 4. Corporate customer arrival distribution Binomial Distribution (used for heavy traffic with uniform distribution) 5. Corporate customer arrival Probability 10% - 90% 6. Performance Metric Protection level and Booking Limit 54

RESULTS III. Revenue Management 100 Booking Limits for Binomial Distribution 90 80 60 Rl/Rh 50 0. 166 40 0. 23 30 0. 33 20 0. 5 10 0. 666 0. 75 9 0. 8 0. 01 0. 70 0 00 00 60 0 0. 00 0 01 5 0. 4 0. 3 0. 2 0. 1 0 0. Percentage of spots reserved for Corporate Booking 70 Probability of customer entering to be a corporate customer Parking Garage Capacity = 500 spots 55

RESULTS III. Revenue Management Ø Conclusions • With Poisson arrival distribution, increase in corporate customer arrival rate and rate ratio leads to an exponential increase in protection level • For Poisson distribution, increase in arrival rate of corporate customers causes more proportional increase in protection level as compared with increase in ratio of leisure class to corporate class fare. • With Binomial distribution, as the probability of an entering customer to be a corporate customer increases, with increasing rate ratio, protection level increases almost linearly. • Hence, for optimum protection level, irrespective of arrival distribution, the parking garage should have a high corporate customer arrival and high Rl/Rh ratio.

RESULTS III. Revenue Management Ø Simulation Parameters Sr. No. Parameter Value 1. Garage Capacity 500 parking spots 2. No-show distribution Gaussian 3. No-show rate 10% - 50% 4. Std. Dev. Of No-show rate 0. 01 - 0. 5 4. Customer Arrival Distribution Poisson 5. Performance Metric Overbooking Capacity 57

RESULTS III. Revenue Management 58

RESULTS III. Revenue Management Ø Conclusions • For low values of standard deviation of no-show rate, overbooking is useful since we can afford to book more reservations than the maximum capacity of parking garage. • For high values of standard deviation of no-show rate, overbooking is futile since we are not even able to reach capacity booking • For high values of no-show rate, we see higher values of overbooking as compared with low values of no-show rate. . 59

Outline • Goals • Proposed Solutions • Research Questions • System Architecture • Algorithms • Results • Conclusions and Future Work 60

CONCLUSIONS I. Discussion of Research Questions • A suitable tracking metric was developed Accuracy Duration [Tolerance] Trackin g Metric [Inaccurate trackings] Total Freed parking spots Total Freed time slots Defrag Metric Increase in capacity of garage Contiguous free time slots • A suitable reservation defragmentation metric was developed 61

CONCLUSIONS I. Discussion of Research Questions • Suitable modifications were made to obtain booking limits for parking garages. Existing formulae Booking Limits for Parking Garages Suitable Parking distributions Airline [Airline Seats] Overbooking Parking Garage [Hours of Parking] • Modification of overbooking for parking garage led to a suitable metric 62

FUTURE WORK • Usage of a prediction model which would give some prior knowledge about the future usage of system which would enable allocating spots to users in a more efficient manner. • Explore feasibility of n-fare booking limits for parking garage • Perform overbooking only on certain booking classes • Look into implementation of overbooking with reservation defragmentation 63

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