The effect of green time on stochastic queues at traffic signals

Figures & data

Table 1. Conditions for specified final queue in green period with capacity G.

Initial queue state	Arrivals in green period
Zero queue i = 0 at end of green period
0	Up to G
1	Up to G−1
J	Up to G−j
>G	Not possible
Non-zero queue i > 0 at end of green period
0	Exactly G + i
1	Exactly G−1 + i
J	Exactly G−j + i
>G+i	Not possible

Figure 1. Dependence of M/D/1[G] equilibrium p₀ (left) and mean queue (right) on ρ, G from simulation (i_max = 10,000). Points measured from Olszewski (1990) are shown (EVOL).

Table 2. Representation of recurrence relations for G = 5 lower queue states.

Figure 2. Errors in Cronjé–Newell factor (left) and relationship of slopes v. G to ρ (right).

Figure 3. Performance of normalised original and adjusted Cronjé–Newell methods.

Figure 4. Plots of Markov-simulated p_0e against link function z which depends on ρ and G.

Figure 5. Plots of link-function mapping for simulated L_e[G] (left) and V_e[G] (right).

Figure 6. M/D/1[G] simulation and estimation compared for 25 pairs of ρ and G.

Figure 7. Gamma fits to M/D/1[G] extended distributions for ρ = 0.8, G up to 20.

Figure 8. Fits between doubly nested geometric and Markov simulated M/D/1[G] distributions, with M/M/1 for comparison (lower graphs).

Olszewski, P. S. 1990. “Modelling of Queue Probability Distribution at Traffic Signals.” In Proceedings of the International Symposium of Traffic and Transportation Theory, edited by M. Koshi, 569–588. New York: Elsevier.

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