Channels in cellular systems: To borrow or not to borrow...

This note develops an analytic model to answer the question whether it is advantageous to borrow a channel in cellular mobile communications systems. Such questions arise dynamically, whenever there is a pending call which will be blocked unless a channel is borrowed. The expected number of calls which will be blocked in the donor cells is calculated assuming that the channel is borrowed and held for the call holding duration. The resulting borrowing rule is simple — the channel should not be borrowed if this number is more than one and borrowed otherwise. If there is an option of borrowing from one of several donor groups, then the donor group which suffers the minimum number of expected blocked calls should be borrowed from. This approach provides a simple practical solution to a rather complicated problem. The results apply to any layout of cells. Channels could have been assigned to the cells via any method and not all channels may be borrowable.