Modelling and Simulation in Engineering

Research Article

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

Table 4

Results of hypothesis testing for constructed paired -tests to compare phase-1 and phase-2 average waiting times for four interarrival distributions: uniform, triangular, normal, and exponential. Mean interarrival rates for all distributions in phase-2 are 75 tertias.


Paired -test results of the simulation replications ()

Constant	Phase-1	Phase-2
	Average waiting time	Average waiting time
	36,000.00	36,000.00
Uniform with 30 replications	Phase-1	Phase-2	Paired differences
Uniform with 30 replications	Average waiting time	Average waiting time	Average waiting time
Average	35,944.36	35,818.27	126.09
st. deviation	537.86	889.07	663.35
		-statistics ()	-1.0411
			Ok! Accept
Triangular with 30 replications	Phase-1	Phase-2	Paired differences
Triangular with 30 replications	Average waiting time	Average waiting time	Average waiting time
Average	35,933.22	35,801.87	131.35
st. deviation	526.48	1,244.89	957.34
		-statistics ()	-0.7515
			Ok! Accept
Normal with 30 replications	Phase-1	Phase-2	Paired differences
Normal with 30 replications	Average waiting time	Average waiting time	Average waiting time
Average	36,025.72	36,122.18	-96.46
st. deviation	528.59	1,292.84	919.57
		-statistics ()	0.5745
			Ok! Accept
Exponential with 30 replications	Phase-1	Phase-2	Paired differences
Exponential with 30 replications	Average waiting time	Average waiting time	Average waiting time
Average	36,067.42	36,714.35	-646.93
st. deviation	2,118.31	3,735.59	2,501.07
		-statistics ()	1.4167
			Ok! Accept