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in a checkout system, customers arrive according to Poisson rate λ. The system consists of two parallel boxes, in Box 1 time is exponential of rate μ1 and box 2 exponential of rate μ2.

There is only one common queue. If both boxes are empty, clients prefer the box 1. You want to study the number of customers in the system at any steady-state.

Under normal conditions, customers choose the shortest line.

Formulate a model for these effects and obtain the average wait in the common queue.

this is not homework, im studying for a test and I'm resolving lots of problem, but this seems to beat me, im not sure if it Jackson or M|D|S, what complicates me is the two different μ

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