Set-up:
Travelers are waiting in line to be processed by immigration officers. There are N officers, each with their own counter. No assumptions about line-switching, constant processing speed, homogeneous processing speed, or homogeneous entrance rate of travelers.

Scenario A: Travelers line up in one of 3 lines, each line leading to one of the 3 counters.

Scenario B: Travelers line up in a single line. The person at the head of the line will be directed to the next available officer.

Additional assumption: All officers will be at 100% utilization rate. 

I argue that average queue time will be the same in both scenarios. Many co-workers, friends, and the following quotes disagree and believe that Scenario B (single-line) will result in a shorter average queue time. 

Who's right?

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"Finally, a single-line, multiple-server system has better performance in terms of waiting times than the same system with a line for each server." - Reid, Sanders; Operations Management

"Research has proven that a single line, multi-server waiting system is faster than the multiple line approach." - <http://blog.lavi.com/2014/08/07/single-line-queue/>

"A Long Line for a Shorter Wait at the Supermarket" - <http://www.nytimes.com/2007/06/23/business/23checkout.html>