The Walmart checkout manager has a task, walk up and down the different counter and change the 'items per basket' sign, one counter at a time. Clerks and customers arrive at random intervals from the shelves, where they put stuff up and take stuff down.
All customers and all clerks have equal view of the check out stands and the checkout manager.
What is the condition when all queues are stable? My algorithm says this is a matching problem between compact generators, a compact generator akin to a generalized Huffman tree. The generator converts a uniform sequence indices into typical arrivals, at stability. The store manager is, in fact, a dual Huffman encoder, running real time adaptive. The manager is adiabatic, one node at a time, access to the queues round robin, there is no party with biased access.
Since there is flow, it is implied in the quantization process, there is queue asymmetry. In particular, at the minimum there will be zero to one clerks, the customer queue backed up to one or two. This algorithm is likely optimal, any time two or three customers a see the counter vacant, they will migrate to the next available queue, tracking the manager , causing an inefficient loop..
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