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Let us have a simple FIFO M/M/1 queue. There is an initial poisson arrival stream with arrival rate $\lambda_1$.

Now after some time $t$ there is an additional stream with arrival rate $\lambda_2$, independent of the original stream. How do i analyze the waiting times after this new arrival?

Is it correct to simply assume the new arrival rate as $\lambda_1 + \lambda_2$ and do the analysis? Will it work even if the queue size is finite?

Note that there is no priority between streams, it is still FIFO,and the service time distribution still remains the same.

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Maybe the multiclass M/G/1 queue model is helpful. See example slides 50-62.

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