Segment information: (Tables)

6 Months Ended

Jun. 30, 2023

Segment information:

Schedule of service revenue by geographic region and product class and long lived assets by geographic region

Three Months Ended June 30, 2023
Revenues	On-net		Off-net		Wavelength	Non-core		Total
North America	$	99,822	$	95,239	1,585	$	8,531	$	205,177
Europe		22,120		5,070	—		22		27,212
South America		1,652		203	—		—		1,855
Oceania		3,894		1,447	—		19		5,360
Africa		177		25	—		—		202
Total	$	127,665	$	101,984	1,585	$	8,572	$	239,806

Three Months Ended June 30, 2022
Revenues	On-net		Off-net		Wavelength	Non-core		Total
North America	$	86,686	$	31,839	—	$	173	$	118,698
Europe		20,458		4,046	—		20		24,524
South America		1,330		57	—		—		1,387
Oceania		3,321		320	—		—		3,641
Africa		180		20	—		—		200
Total	$	111,975	$	36,282	—	$	193	$	148,450

Six Months Ended June 30, 2023
Revenues	On-net		Off-net		Wavelength	Non-core		Total
North America	$	188,519	$	128,115	1,585	$	8,669	$	326,888
Europe		43,967		9,090	—		38		53,095
South America		3,297		236	—		1		3,534
Oceania		7,649		1,774	—		28		9,451
Africa		376		51	—		—		427
Total	$	243,808	$	139,266	1,585	$	8,736	$	393,395

Six Months Ended June 30, 2022
Revenues	On-net		Off-net		Wavelength	Non-core		Total
North America	$	173,128	$	63,548	—	$	312	$	236,988
Europe		41,954		8,320	—		29		50,303
South America		2,722		115	—		1		2,838
Oceania		6,462		657	—		3		7,122
Africa		343		28	—		—		371
Total	$	224,609	$	72,668	—	$	345	$	297,622

	June 30,		December 31,
	2023		2022
Long-lived assets, net
North America	$	1,505,413	$	397,434
Europe and other		158,095		147,005
Total	$	1,663,508	$	544,439