Abstract
Congestion-prone service systems(or simply, service systems) refer to service production systems that exhibit or have the potential to exhibit congestion causing economic losses to its customers due to limited service capacity. While such congestion causes economic loss to customers, the decision to avoid congestion sometimes leads to excess capacity. Excess capacity, of course, brings its own adverse effects, including uneconomical investments and excessive operating costs to suppliers. It can therefore be said that service time, congestion in particular, is an important factor that affects both supplier and consumer choice, even though service time itself is not a factor contributing to supplier monetary costs.
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Notes
- 1.
The queue length of this queuing system is estimated in Boudreau, Griffin, and Mark Kac (1962). The estimated queue length is not a closed-form solution.
- 2.
The approximation formula, known as the Davidson formula, is available in many books dealing with transportation planning such as Manheim (1982).
- 3.
Assume that \( ATC \) is supposed to include the time cost of additional throughput \( e \). Then, (6.25) would be amended as follows: \( \bar{v}(s + e)\,T\left( {s + e,c(s + e)} \right) - \bar{v}sT(s,\hat{c}) \). For this amended cost function, the marginal full cost is equal to the social marginal cost. This confirms that the social marginal cost estimates the additional time cost of all users, including one additional user.
- 4.
From (6.41) and (6.42), we readily deduce the following: an improvement in service quality has the effect of reducing various costs affected by the social or private value-of-time. However, this does not mean that a service system with a higher quality has a smaller marginal full cost. These aspects of the full cost approach will be thoroughly explored in Sect. 10.4.
- 5.
In the case of quantitative competition, the fact that the interval \( [\,\min \;{L_{mn}},\;\max {L_{mn}}] \) is "short" implies that the thickness of \( {D_{mn}} \) is small, as can be deduced from Fig. 5.1. In contrast, in the case of qualitative competition, the interval can be large even though the thickness is small, as shown in Fig. 5.7.
References
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Transportation Research Board (1999) Highway capacity manual, special report 209. National Research Council, Washington DC
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Moon, DJ. (2011). Cost Analyses for the Basic Service System. In: Congestion-Prone Services Under Quality Competition. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20189-9_6
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DOI: https://doi.org/10.1007/978-3-642-20189-9_6
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