Supplementary Material to Resolving Policy Conflicts in Multi Carrier Cellular Access

(Necessity⇐) We show in three steps that, if an inter-carrier switching sequence contains an N-carrier loop, then it contains the sequence (∗) C1↦→ C2↦→···↦→ CN↦→ C1. Suppose the phone initially connects to carrier C0’s RAT0. We denote the highest preference (carrier, RAT) combination in carrier Ci as Pi max= maxj Pi, j. Step 1. We show that under any initial condition (C0 that phone is connected to), the device will be served by C1 after finite switching steps. We prove it by cases. If C0= C1, then the conclusion holds. If C0