Location management or mobility management is a challenging topic in mobile computing environment.HLR (Home Location Register) and VLR (Visitor Location Register) are currently used in some Personal Communication networks (PCN)

such as GSM and IS-41

in many countries to support location management.In these networks

the basic location management scheme

called the basic HLR/VLR scheme below

updates the HLR whenever a mobile crosses the boundary of an LA (Location Area) regardless of whether the updating is necessary.As a result

this scheme produces enormous location updating cost

wastes substantial networks' resources

and reduces networks' performances.A ring search scheme with a threshold

where HLR is not updated until the number of LA rings crossed by a mobile reaches the threshold

an integer

is proposed to decrease the location updating cost.Both the probabilities of a mobile residing in LA rings and the number of LA rings crossed by the mobile between two successive call arrivals in the proposed scheme are derived on the assumption that the incoming calls to the mobile form a Poisson process and that the time of the mobile residing in each LA is a general distributed random variable.Besides

the conditions on which the proposed scheme outperforms the basic HLR/VLR scheme are given.