Analytic Queuing (QA) models assume that a Poisson arrival rate (lambda) is constant during a steady-state time period. If it is not constant, QA results could be very misleading. Because the arrival rate lambda is included non-linearly in the exponential term of a Poisson distribution formula, lambda cannot be averaged first and then substituted in the exponential term. (This is because for non-linear functions, the average value of a function is not equal to the function of average values of its arguments). Thus, a steady-state queuing model with constant lambda and mu is inappropriate in this situation. A discrete event simulation model will be far more accurate and recommended.

Sometimes QA model is used by dividing the total time into time periods in which lambda (and mu) is approximately constant. Then a series of M/M/s models is constructed, one for each period. This approach is called SIPP (Stationary Independent Period-by-Period). However the SIPP patch was found in the literature to be unreliable This is because in many systems with time-varying arrival rates the time of peak congestion significantly lags the time of the peak in the arrival rate. There is a modification called Lag-SIPP that incorporates an estimation of this lag. This approach has been shown to often be more effective than a simple SIPP. Nonetheless this approach still makes QA models application cumbersome if there are many time periods with different arrival rates because many different M/M/s models need to be constructed and stitched together to describe one process.

The bottom line: the best approach is the use of the discrete event simulation DES models. DES easily and elegantly handles non-steady state processes, as well as time-varying arrival rate lambda and the various service rate mu.

Please see detailed examples of comparison QA vs. DES in the attached book (section 2.3.2 ...non-steady-state operations, and section 2.3.4 ...Time varying arrival rates, as well as multiple other relevant examples). The link is:

https://www.amazon.com/Healthcare-Management-Engineering-Methodology-Quantitative/dp/1461420679/ref=sr_1_2?keywords=healthcare+management+engineering&qid=1558995566&s=gateway&sr=8-2

You may want to have a look at "Introduction to Queuing theory" [1]

[1] https://www.bookdepository.com/Introduction-Queueing-Theory-Lothar-Breuer/9789048169139

The time varying arrival rate queueing models can be easily done with Discrete event simulation software. I strongly recommend "ARENA".

Time varying arrival rates form a non-homogeneous Poisson process. The underlying queueing model becomes a non-homogeneous CTMC. There is PCA (piecewise constant approximation) method that can be adopted -- see the chapter on NHCTMC in my 2017 book with Bobbio. I am attaching two relevant papers.

Also two types of customers can be handled via a hyperexponential service time distribution -- see my queueing and Markov chain book with Bolch (second edition 2006). So it is possible to handle what you are faced with using analytic-numeric solutions aided by a software package such as SHARPE or spnp. Of course, simulation is always possible as suggested by Gulab Patel above. But you can do simulation via SPNP also.

I think taiking daily data will give you more accuracy, but computationally complex.

Is it so that your customers also arrive during working hours of the facility? If yes, the input is even more complex, as is the analysis. Simulation is one of the options (and an alternative to ARENA, I recommend R package with various extensions, e.g. queuecomputer), other options depend on the goal of analysis. If you want to optimize something, take a look at queueing games (e.g. the book by Hassin&Haviv).