lec10 (1)

lec10 (1) - Queueing Systems: Lecture 6 Amedeo R. Odoni...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Queueing Systems: Lecture 6 Amedeo R. Odoni November 6, 2006 Lecture Outline Congestion pricing in transportation: the fundamental ideas Congestion pricing and queueing theory Numerical examples A real example from LaGuardia Airport Practical complications Reference: Handout on “Congestion Pricing and Queueing Theory” (on course website)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Congestion pricing: The basic observation The congestion costs due to any specific user have 2 components: (1) Cost of delay to that user (internal cost) (2) Cost of delay to all other users caused by that user (external cost) At congested facilities, this second component can be very large A congestion toll can be imposed to force users to experience this cost component (to “internalize the external costs”) Economic principle Optimal use of a transportation facility cannot be achieved unless each additional (marginal) user pays for all the additional costs that this user imposes on all other users and on the facility itself. A congestion toll not only contributes to maximizing social economic welfare, but is also necessary to reach such a result. (Vickrey, 1967, 1969; Carlin + Park, 1970)
Background image of page 2
Two hard technical problems In practice it is very hard to: (1) Estimate external marginal delay costs (extensive data analysis and/or simulation have been typically needed – subtle issues); (2) Determine equilibrium congestion tolls (trial- and-error approach that may take long time to converge) Queueing theory has much to offer (especially with regard to the first problem) under certain conditions. Computing Internal and External Costs Consider a queueing facility with a single type of users in steady-state. Let c = delay cost per unit time per user C = total cost of delay per unit time incurred in the system Then: C = cL q = c λ W q and the marginal delay cost, MC , imposed by an additional (“marginal”) user is given by: dC dW q MC = = cW + c d q d Marginal Internal External cost cost cost
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Numerical Example Three types of aircraft; Poisson; FIFO service _ Non-jets: λ 1 = 40 per hour; c 1 = $600 per hour _ Narrow-body jets: 2 = 40 per hour; c 2 = $1,800 per hour _
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 14

lec10 (1) - Queueing Systems: Lecture 6 Amedeo R. Odoni...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online