They are all tied via Little's Law.  Just apply the distributions of arrival rates and service times, then express the probability of all channels being occupied.  That will be your loss probability.  For Poisson arrivals and exponential service times, you should end up with erlang-b formula if your queue capacity is zero.

As you're talking about QoS parameters you might also be interested in more than just average (expected) queue length or delay. In this case I'd point you to this (quite theoretic) paper of a PostDoc in my group at the University of Warwick, who's also on researchgate. The paper is dealing with FBM input.

http://www.sciencedirect.com/science/article/pii/S1389128611003185

https://www.researchgate.net/profile/Amr_Rizk2

you can use IBM formulas for calculating various QOS parameters

have a look it

(1) https://www.researchgate.net/profile/Gandhi_Bipinchandra

(2)https://www.researchgate.net/profile/Gandhi_Bipinchandra/publication/262029276_Intelligent_Resource_Allocation_Technique_For_Desktop-as-a-Service_in_Cloud_Environment/links/53fdcb700cf22f21c2f84812?origin=publication_detail

(3)https://www.researchgate.net/publication/265058807_IRA_Technique_for_Desktop-as-a-Service_in_Cloud_Environment

(4)https://www.researchgate.net/publication/265058562_Survey_on_Resource_Management_Strategies_for_Desktop-as-a-Service_in_Cloud_Environment

Article Intelligent Resource Allocation Technique For Desktop-as-a-S...

Article Intelligent Resource Allocation Technique For Desktop-as-a-S...

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I do not see any analytic papers on fractional ARIMA calculation. I agree with you that this is a gap. That is PhD work-to-be done. In my queueing paper, we conquered the M/M/r/K/K calculation. It may inspire your work.