Insensitivity of network performance to the traffic details is a desirable property, since it facilitates robust traffic engineering.
Example: Erlang B call blocking formula
How about 3G cellular data networks? Are performance measures sensitive to the detailed traffic characteristics (e.g., flow size distribution, flow inter-arrival time, number of flows, correlations) or not?
Downlink Model for a Cellular Data Network flow arrivals feasible rate of flow j at slot t realized throughput of flow j up to slot t schedule flow i at slot t propagation loss, shadowing, fast fading data flow 1 data flow 2 data flow n MS MS MS PF scheduler current feasible rate: r( i ) TDM ... ... 1.667ms frame forward link C(t) CAC
Poisson flow arrivals without blocking [Cohen; Kelly]
Poisson session traffic with infinite capacity [Bonald et al. 2001abc; Bonald 2006; Borst 2003]
We prove that the joint queue length distribution, mean number of active flows, and blocking probabilities are insensitive to the session structure in the finite-capacity EPS queue fed by Poisson session arrivals .
Model the system by a queueing network with a restricted state space.
Apply results from stochastic queueing network theory for the proof. (see paper)
Value? Assuming homogenous rate variation in the cellular system, we can replace the complicated Poisson session traffic with simple Poisson flows with exponentially distributed flow sizes. The simplified model will suffice for provisioning purposes.