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## Methodology

**Life cycle cost analysis (LCCA) method**

LCCA permits comparison between different project alternatives having similar level of service (LOS) (i.e. a range of operating conditions in a particular type of facility). However, BCA permits the application of different LOS. For instance, one project maintains existing road pavements whereas the other makes road stretches.

Real Cost LCCA passes through five different steps (FHWA, 1998). The first step is establishing design alternatives. LCCA is needed when a project is selected for improvement or reconstruction. At this time two or more mutually exclusive options have to be identified. As shown in Figure 1, the analysis period, which is the time period from the first project expenditure through the useful life of the project, should be the same for each project alternative. Furthermore, it should include at least one major rehabilitation activity. However, the frequency of maintenance or rehabilitation and the service life of each alternative may differ in order to compare the cost differences among alternatives.

The second step is to determine the activity timing; as shown in Figure 1 a typical road pavement passes through initial construction and periodic maintenance before reaching its minimum acceptable condition throughout its life time. Pavement preservation activities may reduce the frequency of maintenance or rehabilitation activity. As the matter of fact, prevention is always better than curing. The schedule of future work depends on the rate of deterioration in addition to existing performance records which can be found from historical data and the judgment of experienced engineer. Thus, alternative maintenance and rehabilitation activities are planned according to the service life of the project.

The third step is estimating costs; basically costs considered in LCCA are agency costs and user costs. In LCCA the costs which do not bring differences between the project-alternatives should not be evaluated (i.e. land costs that are common to all alternatives are not be considered in the analysis). User costs may differ among the alternatives.

The forth step is calculating the total life cycle costs (LCCs) for each project alternative and compare the results based on the net present value (NPV). NPV is calculated for the agency and user costs by using the real rate of return as shown in Equation (1).

In the last step, the results of LCCA will be analyzed and interpreted. Many analysts do not emphasis user costs. Consequently, the comparison between project alternatives is often made between agency costs. However, it is suggested to include the user costs in the analysis (FHWA, 1998).

**Aimsun-based microsimulation model**

This model uses microscopic simulation approach for calculating the user cost. The model uses different input data such as road type, work-zone type, traffic flows and heavy vehicle ratios (HVR). These are divided in to two categories i.e. road properties and traffic properties.

a. Road properties include the road type, the road geometry, the speed limit and area type. However, these can have insignificant effect on the result compare to traffic properties.

b. Traffic properties are traffic flow, heavy vehicle ratio, variation of traffic distribution and deployment time.

Traffic flow is the interaction between the vehicle and the road based on the flow capacity. If the flow is above the road’s capacity there will be congestion. During work-zone the delay starts to grow due to the limit of the passing lane. However, hourly traffic distribution can control the flow level by distributing the flow for each hour.

Heavy vehicle ratios: In comparison with cars, heavy vehicles travel with a lower speed. More cars drive fast to overpass heavy vehicles and prone to congestion near to work zone area. Since heavy vehicle ratios greatly affect the delay, it’s important to use various HVRs in the simulation.

Variations of traffic distribution: The weekday and weekend variation of traffic volumes and hourly distributions needs to be considered. The traffic flow depends on the condition of the road and different hours of the day. According to (Wennström 2010) the hourly traffic distribution is used in the simulation to account for average condition. It is classified as midday hours (9-16), peak hours (7-9, 16-18) and night hours (0-7, 18-24) and get 5%, 12% and 1% of the daily flow respectively.

Deployment time: The traffic flow during the midday hours and night hours is comparatively lower than the peak hours.

### Binomial lattice approach

This approach is used to evaluate future traffic as well as road user delay costs for three different types of roads. In this thesis the time step is assumed to be one month. The user cost is calculated for a rehabilitation activity at the 15th year. For the given AADT values 1000 number of iterations is carried out. The first value of AADT (AADT0) in the binomial lattice tree is the most likely AADT value in the first year after the completion of the project. The anticipated AADT value at the beginning of the 15th year or 180th month after the completion of the project is evaluated using binomial lattice formulation. The binomial lattice model is addressed in detail in the next section.

**Binomial lattice model**

A binomial lattice model is used to estimate traffic prediction uncertainties. Different researchers explained the binomial lattice model as a simple discrete time approach to characterize uncertainty about future traffic in highway projects (Ho and Liu, 2002; Garvin and Cheah, 2004, and Hull, 2008). It was observed that the variation between actual traffic and forecast ranged between 20 to 40 % for most examined projects (Lemp, 2009). This traffic uncertainty leads to traffic revenue risk, which is a main source of financial risk and one of the most significant risks in built operate transfer (BOT) contracts.

Public-private partnership (PPP) is a partnership between government and private sector in a way that the private party provides a public project by contributing financial, technical and other supports and the government may provide a capital subsidy or encourage the private investment by incorporating traffic revenue risk mitigation mechanisms. There are two types of risk sharing mechanisms: 1) Minimum Revenue Guarantee (MRG) is a common risk mitigation strategy in which the government guarantees a minimum income of the project 2) Toll Revenue Cap (TRC) for sharing the surplus revenue beyond the anticipated threshold. In different countries mostly government chooses MRG and TRC to mitigate traffic revenue risk (Kashani, 2012).

Net present value (NPV) is a traditional method in order to evaluate BOT road projects (Cheah and Garvin 2009). The selection of discount rate is up to the concessionaire interest in NPV analysis. The discount rate reveals the rate of return that the stakeholders expect from investing in the toll road project. NPV can be expressed as follows:

n CC N PR j OCi

NPV i (3)

1 i 1 j

i 0 j n 1

where,

n is the length of construction period (yr)

N is the total concession length (yr) from the initial construction to the return to the government

CCі (i=1, 2… n) is the annual construction costs throughout the construction period from beginning to end

OCj (j=n+1, n+2…N) are the annual operations, maintenance, and rehabilitation costs from the first year after the completion of the project until the end of the concession period

PRj (j=n+1, n+2… N) is the forecasted annual traffic revenues from the first year after the completion of the project until the end of the concession period ρ is the real rate of return (discount rate)

Even though NPV has merits in providing clear and consistent decision criteria, it has some drawbacks regarding future traffic uncertainty and cannot be used to establish an appropriate MRG and TRC minimum level.

Since inappropriate choice of MRG and TRC can lead to improper allocation of risks between the stakeholders and can cause huge unexpected costs to the government or the concessionaire, the real option theory is recommended for evaluating BOT projects. The real option model has been implemented by using a binomial lattice framework. A binomial decision tree uses a market-based option pricing approach which is known as risk-neutral probabilities to approximate the risk associated with traffic uncertainty in the project over time. There are several important characteristics that make it more useful than NPV models. It is a financial model to evaluate investments in highway projects under future traffic uncertainty. The real option analysis also helps the concessionaires to price MRG and TRC as well as to compare their financial risk profile and give chance to reduce the loss of the investment by conducting probabilistic life cycle cost and revenue analysis (Cheah and Garvin, 2009).

Traffic study for all major BOT projects can be carried out in stochastic manner to treat future traffic demand forecasts. The traffic study assumes AADT projections as pessimistic, most likely, and optimistic forecasts. Suppose AADTj where, j= n+1,n+2,…,N are the most likely forecasts of AADT from (n+1) which is the first year after the project is completed until (N) the end of concession lifetime. The expected annual growth rate of AADT (α) is computed based on Equation 4 (Luenberger, 1998).

1 AADTN (4)

ln

N ( n 1)

AADTn 1

In order to evaluate the future traffic level the annual traffic volatility (σ) should also be involved in the calculations. The annual volatility of AADT is the standard deviation of the expected annual growth rate of AADT. It shows how much variation exists in the expected annual growth of the traffic demand. Since volatility of traffic demand is the source of uncertainty for project revenue, the private sectors should give emphasis to mitigate the risk. However, the choice of volatility is not always easy since it is highly exposed to uncertainty.

There are three sources indicated by different authors to determine σ in toll road projects:

1) historical traffic demand data which has been applicable to similar toll road project in the region (Irwin, 2003), 2) the annual volatility of regional gross domestic product (Banister, 2005) and 3) the expertise opinion to estimate the annual volatility of the traffic demand (Brandao and Saraiva, 2008). The concessionaire uses one of the aforementioned methods to make an appropriate estimate. In order to reduce or to account for the uncertainty regarding the inappropriate estimation of σ, sensitivity analysis should also be carried out.

In the binomial lattice model usually a one month time step or a shorter period is considered to make it more powerful to characterize dynamic uncertainty regarding future traffic demands. In Figure 2 the AADT0 is equal to the most likely AADT value in the first year operation stage of the investment after the project is completed. The AADT value for the coming month would be one of the two multiples of AADT0, i.e., either u×AADT0 with probability p or d ×AADT0 with probability 1-p (Hull, 2008).

The upward movement multiple can be expressed by: u e t (5)

The downward movement can also be expressed by: d 1 (6) u where, both u and d are positive values. The probability of upward movement from any node in the lattice can be determined by: p e t d (7) u d 1-p is then the probability of downward movement from any node.

The above binomial distribution tree is used to generate random binomial parameters over the project life time. A series of continues random up and downside movements are along the sample path on the binomial lattice tree. The Monte Carlo simulation algorithm is then applied for binomial random variables in order to generate a significant number of random AADT paths along the binomial lattice.

This is a powerful feature of the proposed model for characterizing uncertainty about future traffic demands and paves the way to determine revenue streams for concessionaire. AADT0 is the initial AADT at the beginning of the n+1 year which is the AADT value of the root node in the model. The expected value of AADT at the beginning of n+2 year, n+3 year,…(N) year are summarized in the binomial lattice node of 12th month, 24th month,…12x(N-(n+1)) month, respectively. Any node in month m= 12, 24…12x(N-(n+1)) from root node can be reached upside movements by 0 ≤ k ≤ 1 and downward movement by 0 ≤ 1-k ≤ 1 along the binomial lattice. The AADT at the beginning of the mth month becomes AADT0 x ukd1-k (Hull, 2008).

#### Results and Discussion

**Factors that affect the delay costs**

In this study, sensitivity analysis is carried out to identify the most important factors affecting the road user delay costs. The analysis is carried out using the Real Cost software. All the input parameters are checked out to identify the influential inputs.

The following values are assumed to be constant in the calculations:

1. 1000 AADT in both directions

2. 10 % HVR

3. Value of time: $91 per hour for passenger cars, $ 578 per hour for single unit trucks, $578 per hour for combination trucks

4. 1km work-zone length

5. 1day work zone duration

6. 50km/h work zone speed

By changing one of the above input variables and keeping the other input variables constant, the impact of each variable is assessed in Figure 3.

**Table of contents :**

Abstract

Acknowledgment

LIST OF ABBREVIATIONS

LIST OF SYMBOLS

LIST OF FIGURES AND TABLES

**1 Introduction **

1.1 Life Cycle Cost Analysis (LCCA)

1.2 Traffic simulation models

1.3 Some of LCCA models

1.4 Objectives

**2 Methodology **

2.1 Life cycle cost analysis (LCCA) method

2.2 Aimsun-based microsimulation model

2.3 Binomial lattice approach

**3 Binomial lattice model **

**4 Results and Discussion**

4.1 Factors that affect the delay costs

4.2 Predicting uncertainty in traffic

**5 Conclusions **

**Bibliography**

Appendix