To Save On Gasoline Expenses Edith And Mathew Agreed To Car ✓ Solved

To Save On Gasoline Expenses Edith And Mathew Agreed To Carpool Toget

To save on gasoline expenses, Edith and Mathew agreed to carpool together for traveling to and from work. Edith preferred to travel on I-20 highway as it was usually the fastest, taking 25 minutes in the absence of traffic delays. Mathew pointed out that traffic jams on the highway can lead to long delays making the trip 45 minutes. He preferred to travel along Shea Boulevard, which was longer (35 minutes), but rarely had traffic jams. Edith agreed that in case of traffic jams, Shea Boulevard was a reasonable alternative.

Neither of them knows the state of the highway ahead of time. After driving to work on the I-20 highway for 1 month (20 workdays), they found the highway to be jammed 3 times. Assuming that this month is a good representation of all months ahead, should Edith and Mathew continue to use the highway for traveling to work? How would your conclusion change for the winter months, if bad weather makes it likely for traffic jams on the highway to increase to 6 days per month? How would your conclusion change if Mathew purchased a new smart-phone app that could show the status of the highway traffic prior to their drive each morning, thus reducing the probability of them getting into a jam down to only 1day per month (where on this day, the app showed no traffic jam, but a jam developed in the meantime as they were driving along the highway).

Sample Paper For Above instruction

Introduction

This analysis evaluates whether Edith and Mathew should continue using I-20 highway based on their observed traffic jam frequency, considering future seasonal variations, and the potential impact of technological aids such as a traffic app. Using basic probability and decision analysis, we examine their expected travel times and make recommendations accordingly.

Analysis of Current Traffic Conditions

During their current month-long observation, Edith and Mathew encountered 3 traffic jams out of 20 workdays. Assuming each day’s traffic condition is independent, the empirical probability of a jam on any given day is:

p_jam = 3 / 20 = 0.15

This suggests that, on average, there is a 15% chance of experiencing a traffic jam on I-20 on any given day, with the remaining 85% being free-flow days.

Expected Travel Times

Using these probabilities, we compute the expected travel time when choosing I-20:

  • In case of no jam (85% chance), travel time is 25 minutes.
  • In case of a jam (15% chance), travel time is 45 minutes.

Expected commute time (E) is:

E = (0.85 × 25) + (0.15 × 45) = 21.25 + 6.75 = 28 minutes

For Shea Boulevard, assuming a consistent travel time of 35 minutes with virtually no jams, the expected time remains constant at 35 minutes.

Therefore, based on current conditions, using I-20 yields a lower average commute time (28 minutes) compared to Shea Boulevard (35 minutes). This indicates that, despite occasional delays, I-20 is the preferable route, as it saves approximately 7 minutes per trip on average, assuming current traffic patterns persist.

Seasonal Variations and Their Impact

In winter months, bad weather increases the number of jammed days to 6 per month. The new empirical jam probability becomes:

p_jam_winter = 6 / 20 = 0.30

The expected travel time on I-20 during winter then is:

E_winter = (0.70 × 25) + (0.30 × 45) = 17.5 + 13.5 = 31 minutes

While this is higher than in the current scenario, it still remains less than Shea Boulevard’s fixed 35-minute travel time, suggesting that I-20 remains a better choice even amid winter weather.

Impact of Traffic Monitoring Technology

If Mathew adopts a smartphone app capable of accurately predicting traffic jams, reducing the chance of getting caught in a jam to only 1 day per month, the jam probability drops to:

p_jam_app = 1 / 20 = 0.05

The corresponding expected travel time becomes:

E_app = (0.95 × 25) + (0.05 × 45) = 23.75 + 2.25 = 26 minutes

This significantly reduces the expected commute time from 28 minutes to approximately 26 minutes, providing a stronger incentive to use I-20 with traffic app support, especially considering unpredictable traffic conditions.

Conclusion

Based on empirical data, current traffic conditions favor using I-20 highway due to lower expected travel times. During winter, although traffic jams are more frequent, I-20 still offers a better average commute time than Shea Boulevard. The introduction of a traffic prediction app further improves decision-making, reducing expected delays and making I-20 the optimal route. However, in a hypothetical scenario where traffic jams are always present on I-20 and Shea Boulevard is always clear, this would suggest always choosing Shea Boulevard as a consistent route with predictable travel times. While this scenario is idealized and less reflective of real-world variability, it demonstrates that the regularity of traffic conditions greatly influences route choice, emphasizing the importance of real-time traffic information for effective commuting decisions.

References

  • Small, K. A., & Verhoef, E. T. (2007). The Economics of Traffic Congestion. Journal of Urban Economics.
  • Lu, J., & Lin, Z. (2014). Traffic variability and congestion dynamics. Transportation Research Part B.
  • Hadi, M. M., & Azar, M. (2017). Impact of weather on traffic flow. Journal of Transport Geography.
  • Davis, G. A., & Nihan, N. (2015). Traffic modeling and prediction. Accident Analysis & Prevention.
  • Chen, C., & Wang, J. (2019). Smartphone apps and real-time traffic management. IEEE Transactions on Intelligent Transportation Systems.
  • Fagnant, D. J., & Kockelman, K. M. (2018). The impact of autonomous vehicles on travel behavior. Transport Policy.
  • Schrank, D., et al. (2020). Urban Mobility Reports. Texas A&M Transportation Institute.
  • Transportation Research Board. (2019). Traffic flow theories and models. TRB Special Report.
  • Meyer, M. D., & Miller, E. J. (2014). Urban Transportation Planning: A Decision-Oriented Approach. McGraw-Hill.
  • Hensher, D. A., & Button, K. J. (2000). Handbook of Transport Economics. Elsevier.

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