Segment information: (Tables)

9 Months Ended

Sep. 30, 2020

Segment information:

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

Three months Ended September 30, 2020
Revenues	On-net		Off-net		Non-core		Total
North America	$	82,730	$	32,416	$	107	$	115,253
Europe		19,966		4,422		12		24,400
South America		599		14		—		613
Asia Pacific		1,786		240		—		2,026
Africa		10		—		—		10
Total	$	105,091	$	37,092	$	119	$	142,302

Three months Ended September 30, 2019
Revenues	On-net		Off-net		Non-core		Total
North America	$	80,176	$	33,172	$	104	$	113,452
Europe		17,921		4,053		4		21,978
South America		139		5		—		144
Asia Pacific		1,180		188		—		1,368
Africa		—		—		—		—
Total	$	99,416	$	37,418	$	108	$	136,942

Nine months Ended September 30, 2020
Revenues	On-net		Off-net		Non-core		Total
North America	$	247,679	$	97,951	$	369	$	345,999
Europe		58,433		12,781		32		71,246
South America		1,344		34		—		1,378
Asia Pacific		4,880		692		—		5,572
Africa		10		—		—		10
Total	$	312,346	$	111,458	$	401	$	424,205

Nine months Ended September 30, 2019
Revenues	On-net		Off-net		Non-core		Total
North America	$	236,636	$	98,670	$	300	$	335,606
Europe		53,889		12,192		45		66,126
South America		244		8		—		252
Asia Pacific		3,300		582		—		3,882
Africa		—		—		—		—
Total	$	294,069	$	111,452	$	345	$	405,866

	September 30,		December 31,
	2020		2019
Long-lived assets, net
North America	$	305,648	$	269,364
Europe and other		115,619		99,582
Total	$	421,267	$	368,946