A Model of Rush-Hour Traffic in an Isotropic Downtown Area

A strategic model of job arrivals to a single machine with earliness and tardiness penalties

“…By part (b) of Assumption 9 c i (t) is decreasing for all t < d i ; therefore by part (c) there exists some t i such that 1 n − 1 n−1 j=1 c i (t i + j) = c i (t i ) , and 1 n−1 n−1 j=1 c i (t + j) < c i (t) for all t < t i , where t i is given by (6). Similarly, c i (t; t) ≤ c i (t + n − 1) ⇔ 1 n − 1 n−2 j=0 c i (t + j) ≤ c i (t + n − 1) , and as c i (t) is increasing for t > d i there exists a t i such that 1 n − 1 n−2 j=0 c i (t i + j) = c i (t i + n − 1) , and 1 n−1 n−2 j=0 c i (t + j) < c i (t + n − 1) for all t > t i , where t i is given by (5). Furthermore, (6) We conclude that the boundaries of the interval τ = [t, t] are as stated in the proposition statement.…”

“…Work in transportation (which rarely cites the work on queues) considers a bottleneck, such as a bridge, with a commuter's costs increasing with the time he spends on the road, and incurring a cost if he arrives at his destination too early or too late ( [41] and [4]). The choice of departure time in transportation is analyzed in [5], who introduce a model with masses of customers departing together. They assume a fluid population with the Greenshield's congestion dynamics (e.g.…”

“…We conclude that τ 2 = − 7 6 , − 5 6 . Applying ( 6) and (5) yields t 1 ≥ t 2 if β ≥ 2.125 and (5,46] then there is a non-empty (and non-singular) interval τ e ⊆ − 7 6 , − 5 6 of equilibrium arrival times. Lastly, if β < 5 there is no pure symmetric equilibrium.…”