Constructing a Passenger Trip Delay Metric

Transcription

1 Constructing a Passenger Trip Delay Metric An Aggregate-level Approach Shin-Lai Tien Department o Civil & Environmental Engineering University o Maryland College Park, MD 2742, U.S.A. alextien (at) umd.edu Bargava Subramanian Institute or Systems Research University o Maryland College Park, MD 2742, U.S.A. sbargava (at) umd.edu Michael Ball Robert H. Smith School o Business and Institute or Systems Research University o Maryland College Park, MD 2742, U.S.A. mball (at) rhsmith.umd.edu Abstract The on-time perormance o passenger trips has received a great attention rom government agencies in recent years but lacks a systematic metric to measure or trace the impact o light delay to air travelers. The proposed model considers possible trip types o a passenger, utilizes system-wide light-based perormance metrics, and employs statistical approaches in order to develop an aggregate delay metric rom passenger s perspective. Its results can be used to analyze historical passenger schedule reliability and can also be used to predict passenger experience or uture aviation system. Keywords-delay, passenger trip, perormance metric, air travel I. INTRODUCTION The on-time perormance o lights is a key concern o carriers and administrative agencies o aviation worldwide. It can be easily quantiied or the U.S. National Airspace System (NAS) because all light arrival and departure inormation is well recorded and disclosed by the Federal Aviation Administration (FAA). For example, the FAA s Aviation System Perormance Metrics database (ASPM) provides individual light inormation rom all participating carriers at 75 major U.S airports. Arrival delay o lights can thus be calculated by comparing scheduled and actual arrival time [1]. With suitable aggregation methods, delay metrics at airports or at the NAS-wide level can easily be constructed. While light delay statistics are well-recorded and wellpublicized, they are not necessarily an accurate measure o a passenger s level o satisaction. In particular, a passenger s average trip delay can vary substantially rom average light delay due to trip disruptions due to cancelled lights or missed connections. Bratu and Barnhart [1] analyzed proprietary airline data and indicated that the average time penalty on passenger trip time due to light cancellations and missed connections is 33 minutes, while the average delay or nondisrupted passengers was only 16 minutes. However, acknowledging that passenger delay is also an important actor o system perormance, it is not easily measurable rom any publicly accessible data. Since ticket inormation is not released by airlines nor collected by the government due to privacy concerns, the delay o multiple-leg passenger trips can be traced only with great diiculty. Even through proper sampling and survey techniques, passenger delay can only be observed during the selected survey period. Considering a long term objective o quality assurance o air travel, it would appear that there exists a need or deining a passenger oriented metric to be used as a quantitative measure o system-wide light delay impact on passenger trips. There is limited research that models passenger delay most likely because o the relative unavailability o individual passenger trip inormation. The essential challenge is to quantiy the impact o light delay on passenger trip disruption. Wang [3] treated passenger delay by its causes: delay due to delayed lights and due to cancelled lights. To estimate the passenger delay rom cancelled lights, an algorithm was proposed that processed single-segment light data. The underlying idea was to assign cancelled seats to the temporally closest available lights. Intuitively, this approach should work well in cases where only direct lights are being considered or under the assumption that on multi-leg passenger trips, the passenger always maintains the same intermediate stopping point. It should also be noted that this research does not model the possibility o missed connections on multi-leg lights. The common characteristics o our paper and Wang [3] are: 1) both develop passenger-based perormance metrics, and 2) both quantiy the impact o light cancellations on passenger delays. However, while the Wang model is a detailed microscopic model that estimates delays at a light level, our model is macroscopic scope, attempting to directly estimate overall averages. The FAA s NAS Strategy Simulator (NSS) is a high-level policy analysis tool that predicts the impacts o uture demand growth, policy changes, increasing uel price, etc. [7]. Our research was speciically aimed at producing a perormance module or the NSS. In the NSS context, all input

2 and output data are maintained at an aggregate level and so it is assumed that light-level data are not available. Likewise, the required output should be NAS-wide average light delay and cancellation rates rather than similar light-speciic metrics. This paper is organized as ollows. In Section 2, the concepts o the proposed model are discussed, and statistical methods are perormed to estimate the probability o missing a connection light. Numerical examples are constructed to illustrate the model, and the trend o passenger delay since 2 is presented in Section 3. In Section 4, sensitivity analysis is conducted by analyzing the impact o key parameters on passenger delay. In Section 5, the potential usages and limitation o the proposed model are discussed. II. MODEL CONSTRUCTION AND ESTIMATION Passenger delays can be inherited directly rom delayed lights but also can result rom cancelled lights. Further, on multi-leg passenger trips, long light delays on the initial leg can result in missed connections and induced delays not equal to, or even proportional to the original light delay. In act, cancellations and missed connections very oten result in the most severe passenger delays. With these eects in mind, it can be seen that passenger delays depend on: Distribution o light delays Flight cancellation rate Average load actor Percentage o passengers with 2 or more light legs in their itinerary In order to accurately address the actual delay experienced by passengers, models and statistical analysis are required that transorm statistics related to these actors to passenger delay measures. A. Scenario Tree Model o Passenger Delay Our passenger delay model employs in a undamental way, the concept o a disrupted passenger, which was introduced in Bratu and Barnhart [1]. A disrupted passenger is a customer who must use a light other than the one on which the customer was originally scheduled due to a missed connection or light cancellation. Disrupted passengers incur delays not related in a direct way to the delays on any o the lights in their original itinerary. Such passengers might be able to recover quickly, e.g. by taking the next light scheduled to the missed destination or might incur a very long delay, e.g. requiring an unplanned overnight stay. In order to model passenger delays, we create a scenario tree that represents all possible outcomes o a passenger s trip. The database o Airline Origin and Destination Survey (DB1BMarket) contains directional market characteristics o each domestic itinerary o the quarterly Origin and Destination Survey [11]. The trip leg inormation o domestic markets rom 2 to 27 is summarized in Figure 1, indicating that on average over 97% o the passengers chose direct or two-leg lights. Thus, because o the relative inrequency o three or more leg trips in the U.S., we will represent itineraries as consisting o either one or two light-legs. 1% 95% 9% 85% 8% 75% 7% 65% 6% 55% 5% 2.7% 2.7% 2.8% 2.8% 2.6% 2.4% 2.4% 2.4% 32.6% 33.5% 34.2% 33.9% 32.3% 31.2% 3.% 29.7% 64.6% 63.8% 63.% 63.3% 65.1% 66.3% 67.6% 67.9% tosep Figure 1. BTS Survey Results on Passenger Trip Leg Inormation 3+ legs 2 legs 1 leg Our scenario tree is given in Figure 2. It represents the various events that can occur on a passenger itinerary, where or a 1-leg trip, the light is denoted by 1 and or a 2-leg trip the irst light is 1 and the second is 2. Each lea o the scenario tree represents a dierent outcome o a passenger trip and leads to a dierent type o passenger delay. Direct Trip Two-leg Trip Figure 2. 1 canceled 1 not canceled 1 canceled 1 not canceled 2 not canceled 2 canceled Disrupted Passenger Passenger Delay = Flight Delay Connection Made Connection Missed Scenarios Tree or a Passenger Trip Expected passenger delay could be computed by computing the expected passenger delay at each lea node in this tree and the probability o reaching each lea node. The sum o the product o the lea node probabilities times their expected delays would give the expected passenger delay. This would accurately compute expected passenger delay given the restriction to one and two leg trips. This is the approach we take; however, we must make several approximations in order to estimate the various probabilities and expectations. We hope that over time some o these approximations can be improved. In computing our estimate o passenger delay, we use the ollowing quantities: P_DIRECT: the raction o passenger itineraries that are direct lights

3 P_CANCEL: the raction o scheduled lights that are canceled F_DELAY: Average light delay DISRUPT: Average delay o disrupted passengers P_MISS: An estimate o the probability that a passenger misses connecting light (the method or computing this estimate is discussed in the next section) We now list all lea nodes in the scenario tree, give our approximations o the expected passenger delay at that node and the probability o reaching that node, and discuss the accuracy o these approximations. The various possibilities that can arise are: 1) Direct Trip, 1 canceled: Probability estimate: P_DIRECT*P_CANCEL Discussion: The probability estimate is airly accurate; however, P_CANCEL is actually a surrogate or the probability that a passenger is booked on a canceled light. To the extent that there is a greater propensity or airlines to cancel lights with ewer passengers, a more accurate estimate could be obtained by doing a calculation that weights lights by the number o passengers (or seats). In act there is not source o accurate statistics on the delay o disrupted passengers so the value we use or DISRUPT is a very rough estimate. Further, models could take into account whether a passenger is disrupted by a cancellation or a missed connection. DISRUPT also would be impacted by changes in airline policies and light characteristics, such as load actor, so these could be used in improving estimates. 2) Direct Trip, 1 not canceled: Probability estimate: P_DIRECT*(1-P_CANCEL) Delay estimate: F_DELAY Discussion: Subject to the caveats related to P_CANCEL mentioned above, both the probability estimate and the delay estimate should be highly accurate in this case. 3) Two-leg Trip, 1 canceled: Probability estimate: (1-P_DIRECT)*P_CANCEL Discussion: See discussion or previous two cases. 4) Two-leg Trip, 1 not canceled, 2 canceled: Probability estimate: (1-P_DIRECT)*(1-P_CANCEL)* P_CANCEL Discussion: See discussion or previous two cases. 5) Two-leg Trip, 1 not canceled, 2 not canceled, connection made: Probability estimate: (1-P_DIRECT)*(1-P_CANCEL)*(1- P_CANCEL)*(1-P_MISS) Delay estimate: F_DELAY Discussion: As will be discussed later, estimating P_MISS can be very challenging. Our approach is to estimate the probability that light delay exceeds a certain (constant) threshold. Clearly the required connection time varies substantially by light so in reality the required threshold itsel is a random variable. Further, it can be the case that both 1 and 2 are delayed so that even with a large delay on 1 the connection can be made. Assuming the connection is made the passenger delay equals the delay on 2 so that F_DELAY is a good estimate o passenger delay in this case. 6) Two-leg Trip, 1 not canceled, 2 not canceled, connection missed: Probability estimate: (1-P_DIRECT)*(1-P_CANCEL)*(1- P_CANCEL)*P_MISS Discussion: See discussion in previous case regarding P_MISS. As discussed earlier it is certainly the case that the expected delay experienced by a disrupted passenger could vary depending on whether a canceled light or missed connection was involved. Based on this scenario tree and the preceding analysis, our estimate o average passenger delay, Pax_DELAY can be computed as: Pax_DELAY = (P_DIRECT)*(P_CANCEL)*DISRUPT + (P_DIRECT)*(1 P_CANCEL)*F_DELAY+ (1 P_DIRECT)*(P_CANCEL)*DISRUPT+ (1 P_DIRECT)*(1 P_CANCEL)*(P_CANCEL)*DISRUPT+ (1 P_DIRECT)*(1 P_CANCEL)*(1 P_CANCEL)*(1 P_MISS)*F_DELAY+ (1 P_DIRECT)*(1 P_CANCEL)*(1 P_CANCEL) *P_MISS*DISRUPT B. Probability o Passenger Missing Connection Three o the inputs in the Pax_DELAY equation, i.e. F_DELAY, P_CANCEL and P_DIRECT, can be easily obtained rom historical NAS perormance statistics. For example, the monthly light arrival delay and cancellation rate or the NAS can be calculated rom ASPM individual light data; the percentage o direct trips can be estimated rom the quarterly market survey provided by the Bureau o Transportation Statistics, as shown in Figure 1. However, two inputs, i.e. DISRUPT and P_MISS, require reasonable approximation or urther modeling eorts since they are not readily available in any data sources or previous research. In order to provide a reliable estimate o P_MISS, we conduct a statistical analysis on the composition o P_MISS. I we denote by D, the random light delay, then we deine our estimate o the probability that a connection is missed because o a delayed light by:

4 P_MISS = Prob { D > Threshold } where Threshold = LAY CONNECT, LAY is a nominal light layover time or connecting lights, and CONNECT is an estimated minimum time required to connect between two lights. We assume that schedules are created so that i a light arrives on-time then it makes its connection. Here on-time is deined relative to the U.S. Department o Transportation standard so that a light is not classiied as delayed i it is no more than 15 minute late. Thus, i D is less than or equal to 15 minutes, then we assume the passenger makes the connection successully to the second light leg. The probability o passenger missing connecting light can thus be modeled as a conditional probability. Speciically, the probability that the connection is missed given that the light is delayed (more than 15 minutes) is represented as: Prob { D >Threshold Flight being Delayed} Prob { D >Threshold D >15 } = Prob (D >15) P_MISS = P_DELAY where P_DELAY = the probability that a light s delay > 15 = Prob (D. The probability o missing a connecting light >15) can thus be represented as: P_MISS = P_DELAY Prob {D >Threshold D >15} The irst term is the probability that a light is delayed more than 15 minutes. The second term is a conditional probability. P_DELAY can be estimated directly rom light delay data or the purposes o computing a metric. We also provide a way o estimating it using only an estimate o F_DELAY. This was done in order to derive estimates or uture years in the context o the FAA Strategy Simulator. Our approach to estimating the second term or a time period, e.g. one month, will be to estimate the distribution: Prob{ D > D D > 15} based on several years o historical data. The parameters o this distribution will be estimated as a unction o F_DELAY and P_CANCEL. The value o Threshold and these light perormance statistics or the time period in question will be plugged into the distribution unction to determine the estimate o the second term. C. Probability o a Flight Being Delayed As discussed above, P_DELAY can be computed directly rom historical data. However we also provide a way o estimating it rom light delay statistic. From the ASPM database [1], or each month rom January 2 to December 24, we computed the monthly values o F_DELAY and P_DELAY. Due to the obvious non-linearity in distribution unctions, we postulated a quadratic relationship between F_DELAY and P_DELAY. A simple regression produced the ollowing model with an R 2 o P_DELAY = [ (-.26)* (F_DELAY) * (F_DELAY) * (F_DELAY) ] / 1 D. Estimating Conditional Distribution o Flight Delays In this section we describe our approach to estimating the conditional distribution unction: Prob { D > D D > 15}. Individual light inormation stored in APSM database was used to compute the arrival delay o lights, which is deined as the dierence between actual and scheduled arrival time. For each o month, an empirical distribution o light delays > 15 was created. Speciically, each light delayed over 15 minutes was placed into a 15 minute bin (15-3, 3-45, etc.) based on its delay value. Empirical light delay distributions were obtained in this way or each month rom January 2 to December 24. These distributions were then itted with the Bi-Weibull distribution. The Bi-Weibull, which is a combination o two Weibull distributions, is widely used in reliability applications. The Bi-Weibull distribution assumes a dierent orm based on its shape parameters, which are: x : the point at which the parameters change, and (α 1, β 1 ) and (α 2, β 2 ) : the parameters o the two Weibull distributions. The parameter β 2 is a unction o the other parameters, so there are our parameters in total to be estimated. The itted distributions gave 6 sets o observations o (x, α 1, β 1, α 2 ). A regression was perormed on each o these parameters, respectively, by using independent variables F_DELAY and P_CANCEL. The results rom the regression are as ollows: x = * F_DELAY * F_DELAY * P_CANCEL (R 2 =.93) α 1 = * F_DELAY * F_DELAY + 3.2* P_CANCEL * P_CANCEL +.32 * F_DELAY (R 2 =.87) β 1 = * F_DELAY * P_CANCEL * P_CANCEL (R 2 =.91) α 2 = * F_DELAY * F_DELAY +.87 * P_CANCEL * P_CANCEL (R 2 =.82) Thus, the distribution Prob{D >D D > 15} was estimated as a Bi-Weibull distribution whose parameters are given as unctions o F_DELAY and P_CANCEL. III. MODEL APPLICATION AND DATA ANALYSIS The passenger delay model takes into account several major actors that impact passenger delay. Some model inputs are the results o aorementioned statistical models; some are available rom reliable data source or analysis. As the market survey results on trip leg inormation rom 2 to 27 shown in Figure 1, it is observed that on average two-thirds o the passengers take direct lights. Hence, or model application purposes, we set P_DIRECT = 66%. Disrupted passengers might be re-assigned to a later light and oten experience overnight stays. There are no publicly

5 available data about average delay o disrupted passengers. The research results o Bratu and Barnhart [1] based on a combination o proprietary data and simulation provide an estimate o 33 minutes as the average delay o disrupted passengers. Hence we set DISRUPT = 33 minutes. The delay threshold o not missing a connection light is the dierence between the average light layover time and minimum required connection time. Calculating average layover time experienced by a passenger requires detailed analysis on either passenger itinerary inormation or light schedule along with seat inormation, which are not publicly accessible. The minimum required connection time can dier among individual airlines or even airports. Thereore, we take a conservative estimate on these two inputs based on empirical experience and assume that LAY = 45 minutes and CONNECT = 15 minutes. Thus, the delay threshold o not missing connecting light is: Threshold = LAY CONNECT = 3 minutes. We now have provided models, estimation methods or approximation to obtain all required inputs or our metric. We use a simple example summarized in Table 1 to show how the passenger delay metric is computed. Given that Monthly NAS delay is minutes and cancellation rate is 3.8%, the probability o a light being delayed as well as the parameters o light delay distribution is determined. The probability o light delay more than connection threshold is computed by using the itted distribution. As a result, the probability o missing a connection light is.113, and the estimated monthly average passenger trip delay is minutes. The relation among major model components is shown in Figure 3. TABLE I. A NUMERICAL EXAMPLE OF PASSENGER DELAY MODEL Variable Name Value Source Avg Monthly NAS Delay o Flights Monthly NAS Cancellation Rate mins. Historical data or estimated rom other models 3.8% Historical data or estimated rom other models P_DIRECT 66% BTS DB1B Database DISRUPT 33 mins. Result rom Bratu s study Threshold 3 mins. Assumed P_DELAY 24% Estimated by this study x Estimated by this study α 1.57 Estimated by this study α 2.35 Estimated by this study β Estimated by this study Monthly NAS Cancellation Rate Flight Delay Distribution Probability o Flight Delay Longer than Threshold Monthly NAS Flight Delay Probability o Flights Being Delayed Probability o Missing Connection Flights Other System-wide Parameters Scenario Tree Formula Expected Monthly Passenger Delay Figure 3. Application Procedures o Proposed Passenger Delay Model Given the application procedures in Figure 3, monthly passenger delay metrics rom January 2 to May 27 are computed by using ASPM light delay and cancellation data. Figure 4 shows the time series o monthly passenger delay against light delay and cancellation rate. Most o the spikes o passenger delay trend are due to high cancellation rates in those months as more passengers are disrupted. This suggests that there will be large penalty or passengers in terms o delayminutes whenever a light is cancelled, and also provides an explanation or why passenger experience varies rom year to year as the overall cancellation rates change. Monthly Cnx Rate 1.% 8.% 6.% 4.% 2.%.% Flight Cancellation Rate (%) Avg. Flight Delay (Mins.) Avg. Pax Delay (Mins.) YYYYMM Figure 4. Time Series o Passenger Delays The comparisons o modeled passenger delay against cancellation rate and average light delay in the NAS are plotted in Figures 5 and 6, respectively. It can be also seen that as light delay increases the passenger delay increases in more than a linear ashion. This validates our claim that as light delays increase, more passengers are disrupted and the impact on passenger delays is much worse than actual light delays Monthly Delay Minutes β 2 = x *β 1 /(α 2 α 1 ) Estimated by this study P_MISS.1134 Estimated by this study Pax_DELAY mins. Calculated by using scenario tree ormula

6 Monthly Avg Pax Delay (mins) % 2% 4% 6% 8% Monthly NAS Cancellation Rate Figure 5. Monthly Passenger Delays vs. Cancellation Rates rom Jan. 2 to May 27 (Sept. 21 is excluded) Monthly Avg Pax Delay (mins) Monthly Avg Flight Delay (mins) the average delay o disrupted passengers. Certainly, DISRUPT is the most diicult to estimate input parameter. We see that P_DELAY increases with DISRUPT but that the sensitivity i airly modest and the unctional relationship between F_DELAY and P_DELAY generally retains its structure as DISRUPT changes. Figure 8 provides a similar sensitivity analysis or P_DIRECT. Note that the nonlinear structure o the curves in Figures 7 and 8 results rom the act that the probability o missing connections increases more than linearly with average light delay. Monthly Avg Pax Delay (min.) DISRUPT=25 DISRUPT=3 DISRUPT=35 DISRUPT= Monthly Avg Flight Delay (min.) Figure 7. Sensitivity o Increasing Average Delay o Disrupted Passengers 7 Figure 6. Monthly Passenger Delays vs. Flight Delays rom Jan. 2 to May 27 (Sept. 21 is excluded) IV. SENSITIVITY ANALYSIS As one o the modules in a high-level policy analysis tool, our model is designed to use light perormance statistics and to evaluate the passenger trip experience in response to changes in aviation system. The creditability o our model relies on proper inputs o parameters, either processed rom historical data or calibrated rom other modeling eorts. To better understand how passenger delays correspond to average light delay, sensitivity analysis is conducted by varying the values o several key parameters. The parameters o our base scenario are summarized in Table 2. Monthly Avg Pax Delay (min.) P_Direct=5% P_Direct=6% P_Direct=7% P_Direct=8% Monthly Avg Flight Delay (min.) Figure 8. Sensitivity o Increasing Direct Trip Percentage TABLE II. Variable Name PARAMTERS OF BASE SCENARIO Value P_CANCEL 2% P_DIRECT 66% DISRUPT 3 mins. Threshold 35 mins. Figure 7 illustrates the relation between light delay and passenger delay with increasing values o DISRUPT, which is Figure 9 shows the sensitivity o varying the light connection threshold. The choice o Threshold depends on the settings o minimum required connection time and average light layover time, which are related to airlines behaviors on schedule design and leet management and require urther exploration. This value is employed in determining the probability o missing a connection. The shorter the connection threshold, the greater the likelihood a light is missed. The P_DELAY growth rate exhibited in Figure 9 is explained by the rather drastic growth rate in the probability o missing a connection or F_DELAY over over 15 minutes as illustrated in Figure 1.

7 The multiplier eect o reducing Threshold on the probability o missing connection becomes more signiicant as light delay increases. When system perormance is getting worse, stringent connection times will increase the chances o missing connections and aggravate passenger trip delay. At 15 minutes o light delay, the probability o missing connections with Threshold=4 is about 17% o that with Threshold=1. At 25 minutes o light delay, the probability o missing connections with Threshold=4 is more 22% o that with Threshold=1. Monthly Avg Pax Delay (min.) Threshold=4 mins Threshold=6 mins Threshold=8 mins Threshold=1 mins Monthly Avg Flight Delay (min.) Figure 9. Sensitivity o Increasing Connection Threshold on Passenger Delays Prob. o Missing Connection (P_MISS) Threshold=4 mins Threshold=6 mins Threshold=8 mins Threshold=1 mins Monthly Avg Flight Delay (min.) Figure 1. Sensitivity o Increasing Connection Threshold on Probability o Missing Connections V. CONCLUDING REMARKS It is generally agreed that light-based delay metrics are not good surrogates o overall passenger experience o air transportation system. This study addresses the need or a quantitative measure o NAS passenger trip delays. The main contribution is that a passenger-based metric is modeled by considering a scenario tree or a passenger trip. This model allows the estimation o passenger delay based on existing light-based perormance metrics. A drawback o this study as well as other comparable research on passenger delays is that the results can not be validated because o the unavailability o comprehensive passenger trip records. The proposed model uses NAS-wide perormance metrics, i.e. average light delay and cancellations, in order to measure passenger delay rom a strategic perspective. The inputs o the passenger delay metric are obtained rom historical data analysis, statistical models, and reasonable approximation. Its intention is to provide an eicient but dependable estimate o passenger schedule reliability without much eort on analyzing detailed light activities. Using models that orecast NAS-wide perormance metrics, e.g. the light delay models in Wieland [8] and Subramanian [9] and the cancellation rate model in Subramanian [9], the results o this research can also be used to predict passenger experience o uture aviation system. ACKNOWLEDGMENT This work was supported by the National Center o Excellence or Aviation Operations Research (NEXTOR), under FAA cooperative agreement number 1CUMD1. Opinions expressed are solely those o the authors. They do not relect any oicial opinions or policies the FAA or the U.S. Department o Transportation. The authors would like to thank Dave Knorr, Stephanie Chung, and Anne Suissa o the FAA as well as three anonymous reviewers or their valuable comments and suggestions. REFERENCES [1] Bratu, S and C. Barnhart. An analysis o passenger delays using light operations and passenger booking data. Air Traic Quarterly, volume 13(1) 1-27, 25. [2] Bratu, S. Airline Passenger On-Time Schedule Reliability: Analysis, Algorithms and Optimization Decision Models. PhD. Dissertation, Massachusetts Institute o Technology, Cambridge, MA, 23. [3] Wang, D. Methods or Analysis o Passenger Trip Perormance in a Complex Networked Transportation System. PhD. Dissertation, George Mason University, Fairax, VA, 27. [4] Wang, D and L. Sherry. Trend Analysis o Airline Passenger Trip Delays. In the Proceedings o the 86th Transportation Research Board Annual Meeting, Washington D.C., 27. [5] Sherry, L., D. Wang, and G. Donohue, Air Travel Consumer Protection: Metric or Passenger On-Time Perormance, Transportation Research Record: Journal o the Transportation Research Board, No. 27, 27, pp [6] Wang, D., L. Sherry and G. Donohue. Passenger Trip Time Metric or Air Transportation. The 2nd International Conerence on Research in Air Transportation, Belgrade, Serbia and Montenegro, June 26. [7] Suissa, A. FAA NAS Strategy Simulator (NSS): Overview. Presented at National Airspace System Perormance Workshop, March 14-17, 26, Paciic Grove, CA. [8] Wieland, F. Estimating the Capacity o the National Airspace System. The 24th Digital Avionics Systems Conerence, Volume 1, November 25. [9] Subramanian, B. Aggregate Statistical Models or National Airspace System Perormance. Master Thesis, University o Maryland, College Park, 27. [1] Federal Aviation Administration, Aviation System Perormance Metrics (ASPM) Online Database. Retrieved on July 31, 27. [11] Bureau o Transportation Statistics. Airline Origin and Destination Survey Database. Retrieved on January 24, 27.