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This is a real-world question. I'm trying to convince people to consider changing this process to improve service.

There are 20 servers, each fed by it's own queue. Each queue has 30 customers when the process starts. No new customers are added, and none leave or switch queues, so that at the end, 600 customers will have been served. Service time is exponential. Currently, when a server finishes its 30 customers, it goes out of service.

If I combine the queues so that we have one queue feeding all 20 servers in FIFO order, what is the impact on average wait time?

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When I simulate this situation, I get that the isolated queue approach takes around 41 time units, while the communal queue takes around 32.50 They remain in this ratio regardless of what the exponential parameter $\lambda$ is. (The time is inversely proportional to $\lambda$.)

So you can save around 1/5 of the time by using a communal queue approach. That's the good news.

From a psychological perspective, if the servers are human, the communal queue may create a discouraging work environment. Some people may want to finish their work as soon as possible. When the queues are isolated, this means there's a finite, controlled amount of work which you can watch diminish, and which you can finish faster by working faster. When the queue is communal, the faster you work, the more work you have to do—which people may find discouraging. If this difference were supplemented by rewarding people for the quantity of the work they do, this may help the situation.

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  • $\begingroup$ Are the 41 and 32.5 time units the total time it takes the last queue to finish the last item, or is it the average wait or in-system time? $\endgroup$ – L. Blanc Feb 17 '18 at 11:50
  • $\begingroup$ It is the total amount of time it takes the system to be done, i.e. the amount of time it takes the last queue to finish the last item. $\endgroup$ – user326210 Feb 17 '18 at 18:51

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