can someone help me please solving this?

Consider a switch with two input links and one outgoing transmission link. Data packets arrive at the first input link according to a Poisson process with mean $\lambda_1$ and voice packets arrive at the second input link also according to a Poisson process with mean $\lambda_2$. Determine the total transit time when a packet arrives at either input until its transmission completion if the service time of both the data and voice packets are exponentially distributed with mean rates $\mu_1$ and $\mu_2$, respectively.

Since there are any assuntions about which one of the queue is the higher priority queue, I can't go on and find formulas needed. Should I make my assumption that voice channel is preferred and then

$W_v = R / (1-\rho_v)$


$W_d = R / ((1 - \rho_v)(1 - \rho_v - \rho_d))$,


$R = \rho / \mu$, $\rho = \rho_1 + \rho_2$, $\mu = \mu_1 + \mu_2$,

and calculate

$T_i = W_i + \bar x_i$?

Or should I consider that, because no priority is specified, and due to memoryless propriety of exponential distribution for service times, we simply have

$N= N_1 + N_2 = \lambda_1/(\mu_1 - \lambda_1) + \lambda_2/(\mu_2-\lambda_2)$

and then, for Little's formula,

$T_1 = N/\lambda_1$, $T_2=N/\lambda_2$.

Am I wrong? What do you think? Thank you all



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