A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters’ Route

Table 2

Comparison of the average waiting times in phase-1 and phase-2 for four different interarrival time distributions: uniform, triangular, normal, and exponential. Constant rate refers to deterministic interarrivals. Mean interarrival rates for all distributions in phase-2 are 75 tertias.

Input parameters				Simulation output results
	Phase-1	Phase-2	Both phases	(average of 30 replications)
	Arrival rate	Arrival rate	Departure rate
	80	48	60	Phase-1	Phase-2
Constant	Interarrival time	Interarrival time	Constant interdeparture time	Average waiting time	Average waiting time
	45.00	75.00	60.00	36,000.00	36,000.00
Uniform	Interarrival time	Interarrival time	Constant interdeparture time	Average waiting time	Average waiting time
Min:	27.50	51.60	60.00	35,944.36	35,818.27
Max:	62.50	98.40
Triangular	Interarrival time	Interarrival time	Constant interdeparture time	Average waiting time	Average waiting time
Min:	20.25	33.60	60.00	35,933.22	35,801.87
Mode:	45.00	75.00
Max:	69.75	116.40
Normal	Interarrival time	Interarrival time	Constant interdeparture time	Average waiting time	Average waiting time
Average:	45.00	75.00	60.00	36,025.72	36,122.18
St. deviation:	10.125	16.85
Exponential	Interarrival time	Interarrival time	Constant interdeparture time	Average waiting time	Average waiting time
Average:	45.00	75.00	60.00	36,067.42	36,714.35