Matrix Theory is not the name of a movie

By Noel T. Braymer, Editor, Western Rail Passenger Review — The late Dr. Adrian Herzog was a very smart guy. It helps to be smart when you’re a college professor at Cal State Northridge. This is even more so when you teach Astronomy and Physics. Adrian’s love for trains seems to have been his birth right, inherited from his native Switzerland which has more trains per capita than almost any other country. As a college professor, one of the benefits of the job was the right to conduct independent research. This research doesn’t have to be directly related to the professor’s normal field of study.

Adrian’s independent research was to create a computer simulation program of long distance rail ridership in America using the University’s mainframe computer. Using existing ridership on Amtrak to calibrate the simulation, Adrian created a mathematical model to see what happens as you add routes, stations or connections to the rail network in terms of passenger miles. Passenger miles are important because this is a better measure of ridership revenue than simple head counts. The work that Adrian did was vastly more sophisticated than anything that had been done before or since.

Has this “theory” been put to the test? It was with the extension of the PALMETTO.

“Amtrak’s Board of Directors, at the urging of the United Rail Passenger Alliance, forced the extension of the Palmetto on a reluctant management. Management objected to the additional costs associated with operating the train the additional 140 miles to Jacksonville, and did not recognize the revenue potentials from the extension. Management’s forecast of revenues associated with the extension were based only on management’s perception of the local traffic that would be generated between Jacksonville and Savannah, which was by any reckoning very low.

“Once the train was actually extended, however, the results were telling. Although the Palmetto ordinarily carried only 40 to 50 passengers into or out of Jacksonville, those passengers tended to travel longer distances than had been forecasted even by the advocates of the extension based on matrix theory. These passengers more than paid for the extension, and represented a significant improvement in the Palmetto’s operating ratio. Ridership and output could have been higher still, because ridership yields at Jacksonville were sharply capped by limited capacity on the Palmetto through its peak loading point in northern Virginia. Empirical experience indicated that high revenue, long distance, traffic between Jacksonville and the Northeast could have been expanded by 50 to 100% had additional lift capacity been provided. A serendipitous additional benefit from the extension was the unforecasted availability of a daily mail contract with the U.S. Postal Service once the train was extended to Jacksonville.”

Amtrak Marketing learned nothing from this, and allowed cut backs to the Palmetto to “save money”.

Another example of the power of the Matrix Theory can be seen from this work of Dr. Herzog sponsored by URPA.

“In 1984, the United Rail Passenger Alliance sponsored a simulation, using matrix theory, of Amtrak’s Southwest Transcontinental Corridor (Chicago-Kansas City-Albuquerque-Los Angeles) by the Surface Transportation Systems Institute (“STSI”). This route is served by a single daily long distance train, the Southwest Chief. It has no rail connections anywhere between its endpoints other than an unpublicized connection at Kansas City to an all-coach local train to St. Louis. STSI compiled actual ridership data for Trains 3 and 4 from the preceding year in order to calibrate a computer model of the route using actual origin-destination data for all en-route stations. Assuming constant levels of market penetration, the STSI computer model was then calibrated and extended to ask what ridership results would obtain if the Southwest Transcontinental Corridor were modified in three respects: (1) a section of the train, i.e., a through sleeper and coach, were to drop from the train at Flagstaff, Arizona for Phoenix and Tucson (providing second-morning arrivals in Arizona’s premier destinations from Chicago and the Upper Midwest); (2) the remaining train were to be split in half at Barstow, with half continuing to Los Angeles as the actual train did, but with the second half proceeding north over Tehachapi Pass to Bakersfield, and then displacing an existing San Joaquin valley train (i.e., only 90 incremental train miles were involved) up the valley through Fresno to Oakland and terminating at San Jose; and (3) on the east end, the train were split in half between Chicago and Kansas City, with half operating over the existing direct route to Kansas City, and half operating between those two points via St. Louis (again, displacing an existing local train).At that time, actual ridership onboard Train No. 4 eastbound out of Flagstaff on average was 212 passengers per day. The STSI model, assuming constant levels of market penetration but with the three incremental changes described, forecast an average daily ridership load onboard eastward out of Flagstaff of approximately 1,260. Because a long distance passenger train even in a peak load environment cannot accommodate 1,260 passengers, it immediately became apparent that multiple frequencies, at least three and probably four, would be necessary to accommodate that volume of traffic. The model did not analyze the further incremental demand generation (i.e., deeper market penetration) resulting from having four daily frequencies available in each direction, rather than merely one.”

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