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between values of k by "births" and "deaths" which occur at rates given by various values of λi and μi, respectively. for a queueing system, k is the number of jobs in the system (either being serviced or waiting if the queue has a buffer of waiting jobs). further, for a queue, the arrival rates and
departure rates are generally considered not to vary with the number of jobs in the queue so that we consider a single average rate of arrivals/departures per unit time to the queue. hence, for a queue, this diagram has arrival rates of λ = λ , λ , ..., λk and departure rates of μ = μ , μ , ..., μk...
https://en.wikipedia.org/wiki/Queueing_model