**Acknowledgements**

**7. Conclusions**

*PRSN-MCP tolls for each link at equilibrium state.*

**Table 5.**

**72**

To make pricing more efficient and effective, this chapter developed a reliability-based marginal cost pricing model. The new model explicitly accounts for both stochastic link degradation and stochastic demand of road network and perception errors within the travelers' route choice decision process. We consider that the stochastic demand follows a lognormal distribution and the capacity degradation follows a uniform distribution, and *VMR* across all OD pairs. Based on moment analysis, we derive the mean and variance of the expected total perceived travel time. After performing some derivations, we derived four analytical functions of

**Link Link toll Link Link toll Link Link toll Link Link toll** 19.37 20 23.16 39 33.54 58 45.96 12.81 21 17.97 40 68.29 59 20.13 19.37 22 37.02 41 38.43 60 35.53 16.08 23 95.53 42 22.83 61 20.13 12.81 24 17.97 43 59.94 62 23.86 34.19 25 37.12 44 38.43 63 32.55 78.43 26 37.12 45 22.83 64 23.86 34.19 27 33.15 46 29.97 65 7.68 39.22 28 59.94 47 37.02 66 15.86 125.82 29 17.53 48 17.53 67 29.97 39.22 30 30.77 49 14.00 68 32.55 46.12 31 125.82 50 3.07 69 7.68 95.53 32 33.15 51 30.77 70 18.04 16.08 33 18.94 52 14.00 71 22.83 46.12 34 68.29 53 45.96 72 18.04 73.25 35 78.43 54 15.33 73 5.24 23.16 36 18.94 55 3.07 74 33.54 15.33 37 24.96 56 35.53 75 15.86 73.25 38 24.96 57 22.83 76 5.24

*Linear and Non-Linear Financial Econometrics - Theory and Practice*

This chapter investigated possible defects associated with ignoring certain aspects of the stochastic behaviors of the network. Through numerical examples, we find that both link capacity degradation and stochastic demand play essential roles in the PRSN-MCP model, especially under high travelers' confidence level and network congestion. We further examined the effect of incorporating the travelers' perception error into the RSN-MCP tolls. The numerical example illustrates that travelers' perception errors have a significant impact on the performance of the

PRSN-MCP under different simplifications of network uncertainty.

PRSN-MCP tolls and, therefore, should not be neglected.

**A. Appendix: computation of the MGF of** *T*~*T*~

The MGF of *T*~*T*~can be represented as follows:

This research has been supported by the National Natural Science Foundation of China (Project No. 71701030 and 71971038), the Humanities and Social Sciences Youth Foundation of the Ministry of Education of China (Project No. 17YJCZH265), and the Fundamental Research Funds for the Central Universities of China (Project No. DUT20GJ210).
