**Abstract**

This chapter is concerned with first-best marginal cost pricing (MCP) in a stochastic network with both supply and travel demand uncertainty and perception errors within the travelers' route choice decision processes. To account for the travelers' perception error, moment analysis is adopted in this chapter to derive the mean and variance of total perceived travel time of the network. We then developed a Perceived Risk-Based Stochastic Network Marginal Cost Pricing (PRSN-MCP) model. Furthermore, in order to illustrate the effect of incorporating both stochastic supply and demand into the PRSN-MCP model, the calculation of the PRSN-MCP model is divided up into four scenarios under different simplifications of network uncertainties. Numerical examples are also provided to demonstrate the importance and properties of the proposed model. The main finding is that ignoring the effect of stochastic travel demand, capacity degradation, and travelers' perception error may significantly reduce the performance of the first-best MCP tolls, especially under high traveler's confidence and network congestion levels.

**Keywords:** marginal cost pricing, moment analysis, demand uncertainty, supply uncertainty, perception error
