UCLA 2012 Commencement Ceremonies So Young Kim

Order of Presentation I.Introduction II.Mathematical Modeling III.Network System 3.1. Overall Data Description 3.2. Network Shortest Path Flow Model Min-Cost Flow Model Network Interdiction 3.3. Assumptions IV. Results 4.1. Overall Results on the Shortest Path Flow 4.2. Overall Results on the Min-Cost Flow 4.3. Impact of Time Factor in Min-Cost Flow Interdiction (conversion vectors = 1 vs. 5) V. Conclusion and Limitations

I. Introduction “This year, UCLA will host over 60 degree-conferring ceremonies, receptions and celebrations” on June 15 (Fri), June 16 (Sat), and June 17 (Sun) “Total attendance at UCLA's various Commencement ceremonies has been estimated at 90,000 guests annually.” Number of lodging facilities (hotels and motels) = 345 around the UCLA. Starting room rates range from $42 to $ Simultaneous large amount of vehicle movement will result in severe traffic congestion in addition to the normally heavy LA traffic, accidents, and constructions.

Goals 1.Efficient distribution of ceremony guests to the lodging facilities near UCLA 2.Vulnerability of the network against a possible set of failures to address problems arising in such contexts 3.Interrelationship between Shortest Path Flow and Min-Cost Flow & Impact of Time Factor

II. Mathematical Modeling: 2.1. Shortest Path Flow

II. Mathematical Modeling: Shortest Path Flow Interdiction

II. Mathematical Modeling: 2.2. Min-Cost Flow

II. Mathematical Modeling Min-Cost Flow Interdiction

III. Network System 3.1. Overall Data Description UCLA Beverly Hills & West Hollywood Burbank & Glendale Santa Monica & Del Rey LAX Airport Redondo Beach LA Downtown Hollywood

Table 1. Distribution of selected hotels near UCLA

3.2. Network 80 nodes and 182 arcs Nodes include hotels and intersections Each hotel node is connected to one super source, Start, UCLA serves as the destination of the network. Arcs present channels of flow connecting two nodes Shortest Path Flow Model Each arc between non-super nodes carries “driving time”, which is calculated using distance weighted by MPH. MPH comes from the Google Traffic Map as of Friday 17:00, where Friday 17:00 represents the busiest time. Measure of Effectiveness = driving time in minutes Driving time: – Distance / MPH * 60 – MPH: from the Google Traffic Map as of Friday 5:00 pm Black and Red lane = 5 MPH Red lane = 10 MPH Yellow lane = 20 MPH Green lane = 30 MPH

Google Traffic Map

Min-Cost Flow Model Each Node specifies Supply and Demand. The Start node is assigned the negative total number of rooms needed. The UCLA node is assigned the positive total number of rooms needed. Each arc carries Capacity and Cost. Capacity refers to the capacity of each hotel, i.e., number of rooms. Cost on arcs between Start and hotels represent room rates. Cost on arcs between non-start nodes refers to the money value converted from time, using conversion vectors = 1, or 5. Conversion vector = 5  10 miles means $50.

S T

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Network Interdiction The network interdictions is “to assess the vulnerability of network to various types of failures” and thus is “well suited to address problems arising in [such] contexts” (J. Smith, 2012).

3.3. Assumptions The network is coarse-grained. The road capacity is fixed. The number of lanes is constant across all roads. The traffic condition is fixed based on Friday 5:00 pm. The network uses the full capacity. All traffic is moving toward UCLA. An accident or other obstacle creates a fixed delay of 30 mins and 60 mins, and road closure.

VI. Results 4.1. Overall Results on the Shortest Path Flow a)The shortest path to UCLA is from the W Los Angeles Hotel. The driving time is 12 minutes. b)The network stops functioning with 4 attacks. Impact of interdiction varies depending on interdiction types. Road closure results in “no path,” whereas 30-min delays causes 372 minutes of driving time from the W Los Angeles Hotel to UCLA.

4.2. Overall Results on the Min-Cost Flow a)The Min-Cost Flow identifies hotels which are close to UCLA and which offer inexpensive room rates. The average room rate of the hotels on the Min-Cost Flow is $147.27, whereas the average of the 75 hotels on the entire network is $ b)The network remains functional with two attacks. c)The network becomes malfunctioned with 3 attacks. Impact of interdiction varies depending on the size of supply/demand.

Comparison of Operator Resilience Curves Shortest Path Flow Interdiction Min-Cost Flow Interdiction

Min-Cost Flow without Interdiction vs. with one attack

Min-Cost Flow with two attacks vs. with three attacks

Table 2. Hotels on the Min-Cost Flow Without Interdiction (n = 3000, conv = 5)

Comparison of Interdiction Patterns: Shortest Path Flow vs. Min-Cost Flow Shortest Path Flow Interdiction Min-Cost Flow Interdiction

4.3. Impact of Time Factor in Min-Cost Flow interdiction (conversion vectors = 1 vs. 5) a) Conversion Vectors did not change the network malfunction points. Regardless of whether the conversion vector is 1 or 5, the network system stops functioning with 4 attacks and 3 attacks, when n = 100 and n= 3000, respectively.

4.3. Impact of Time Factor in Min-Cost Flow interdiction (conversion vectors = 1 vs. 5) b) Conversion vector does change the order of attacks. The larger the conversion vector, the more likely the attack pattern is similar to the one in the Shortest Path Flow. Number of rooms needed = 3000, conversion = 1 Number of rooms needed = 3000, conversion = 5

Comparison of Time Factor in Interdiction Patterns: (conv = 1 vs. conv = 5) Number of rooms needed = 3000, conversion = 1 Number of rooms needed = 3000, conversion = 5

Hotel (Cap, Room Rate, Driving Time to UCLA, Driving Time to UCLA with Conv = 5) UCLA W Los Angeles (258, $215, 12, 60) Bel Air (103, $415, 19.31, 96.6) Angeleno (209, $161, 13.84, 69.2) Beverly Hills (80, $405, 17.7, 85.37)

Conclusion and Limitations The Min-Cost Flow selects hotels that are located near UCLA and offer inexpensive room rates. The network interdiction model shows that the network requires protection from the malfunction of three road to UCLA. Ceremony guests can be recommended to select hotels that are safe from attacks. Those who value time, that is, those who put higher conversion vectors, need to select the shortest path flow interdiction plan. Wider applications of the project to real world should be considered, given that the applications can invoke both civilian and military scenarios. Pattern of attacks.

Thank you very much!