User Cost (C u )

In light of the user cost which is the summation of feeder bus and train cost, Equation (3.3) can be re-written as given:

Cu= (CaF+ CaT) + (CwF+ CwT) + (CuiF+ CuiT)

(3.3)

Generally, all elements of the user cost can be formulated as the product of an hourly demand, average time spent in each travel time category (i.e. access time, wait time, and in-vehicle time), and the users‘ value of time, which is explained in the following subsections.

Table ‎3.3: Derivation of all cost terms in proposed transit service model

Cost terms Literature Improved Proposed

Total cost

Feeder and train passengers who have access to stops and stations mainly incur the access cost. The access cost is generally experienced by local and train passengers accessing the transfer station. This cost is discussed by previous researchers such as Ciaffi et al., (2012); Cipriani et al., (2012); Chien, (2005); etc.

The access cost for feeder bus passengers is the product of local demand, qi, whose average access time t_aF and value of time μ_a, where t_aF can be estimated from average distance divided by average access speed. The average access time for train passengers (t_aT) can be formulated similarly. t_aT is dependent on the distance between the platforms of bus and train services and access speed. Assume that access speed and value of time

for feeder bus and train passengers are identical. Thus, the access cost for feeder route k can be formulated as (Chien, 2005):

 

a a k aF k aT

C  Q t Q t (3.4)

The users‘ value of time (μ_a) is an important parameter in determining the user cost, and is usually dependent on the economic situation (e.g. annual income).

3.4.1.2 Waiting cost (C_w)

The waiting cost includes passengers waiting for the buses and trains, which is the product of average wait time, demand, and the value of users‘ wait time (µw). Numerous studies have been conducted to describe waiting cost, such as the studies by Kuah and Perl (1989); Kuan et al. (2004), (2006); Ciaffi et al. (2012); Shrivastava and O‘Mahony (2006), etc.

Average wait time can be estimated by the fraction of the headway, so in this model the average wait time for feeder bus at the stops and for trains at the stations are assumed to be one half of headway. Hence, the user waiting cost can be represented using Equation (3.5) (Kuan et al. 2004, 2006).

1 1

where Fk and FT are respectively the frequency of feeder buses and trains.

3.4.1.3 User in-vehicle cost (Cui)

Similarly, the product of demand, in-vehicle time, and value of time can define the user in-vehicle cost (Cui). The Cui is formulated based on the average journey time and is calculated in two main parts: the run time and the dwell time.

Running costs for all passengers (Crui,), which is equal to the link travel distance from stop i to station j in route k (L_ijk) divided by the average bus real speed (V_k). Many studies considered this concept for determining Crui, such as the researches by Kuah and Perl (1989); Kuan et al., (2004), (2006); Shrivastava and O‘Mahony (2006);

Mohaymany and Gholami (2010); Gholami and Mohaymany (2011); Shrivastava and O‘mahony (2007), etc. In the current study, Crui, was determined using the same concept.

The dwell time is the boarding and alighting time at the feeder bus stops (tdF) and rail stations (t_dT). The observation of feeder bus stops and rail stations realised dwell time is important part of in-vehicle travel time. This time will increase the user, operation and social costs in both modes of feeder bus and train, as well as consequently has significant effect on total cost of transit network. Dwell time will increase user costs by increasing the in-vehicle time for on boarding passenger. In addition, this time costs will increase operation costs by increasing fuel consumption, maintenance, and personnel costs. Accordingly, with the increase in pollution, noise, and greenhouse gases, etc., the social costs will also be raised. The literature survey also revealed that there had not been a substantial work for calculating dwell costs in transit services.

Since spending time for boarding and alighting have got an important role in user in-vehicle time, it was tried in this study to present a new concept for determining such costs. Moreover, because of the variety in spending time which is dependent on the dwell time at each of the bus stops, the geometric series equation has been adopted to develop a more accurate model for distributing dwell cost of the bus stops along the routes. The average cost of dwell time (C_dui) is determined by demand multiplied by passenger boarding and alighting rate. The derivation of the dwell cost for feeder buses and trains are discussed in Appendix A.

Therefore, the in-vehicle cost, including in-bus and in-train cost, for each route k, is given as:

C_ui =C_rui+C_dui (3.6)

where Crui is running cost for all passengers (Kuah and Perl 1989; Kuan et al., 2004, 2006; Shrivastava & O‘Mahony, 2006; Mohaymany & Gholami, 2010; Gholami &

Mohaymany, 2011; and Shrivastava & O‘mahony, 2007)

1 1

and C_dui is the average cost of dwell time as described in Appendix A.

 

1( 1)

dui I 2 k k dF k dT

C  ^^ n  Q t ^ Q t ^ (3.8)

The first and second terms in Equations (3.7) and (3.8) respectively denoted the feeder bus and train user cost. In Equation (3.6), Crui represents the running cost for all passengers which is equal to the link travel distance from stop i to station j in rout k (Lijk) divided by the average bus real speed (Vk). Moreover, tTj denotes riding time between station j and the destination of the train regardless of boarding and alighting times, and n_k stands for the number of stops in route k. The sensitivity analysis performed in section 4.2.6 showed the relations between proposed cost terms in transit system, as well as the importance of this related cost significantly.