This is like the microwave problem at work though. My food only needs 30 seconds to microwave, but Slow Joe brought thanksgiving to work and needs to use the m

This is like the microwave problem at work though. My food only needs 30 seconds to microwave, but Slow Joe brought thanksgiving to work and needs to use the microwave for 4 minutes. We have 2 microwaves M1-2. With your system this is what happens: - Slow Joe blocks M1 with a 4 minute meal - Several 30-60 second users cycle through M2 - Another Slow Joe blocks M2 - The queue grows until M1 is free - The feedback loop gets worse the next iteration Basically, you need a dedicated "express lane" for quick people to use. If there are no quick people in the queue, then a slow joe can use it. Otherwise you need to increase N such that there is always at least one unblocked lane, which might not be viable.