Mobility Management in Cellular Telephony

In the world of cellular telephony there is a hierarchy of controlling devices. Cellular telephones communicate with Base Transceiver Stations (BTS) or transceivers, which in turn are assigned to Base Station Controllers (BSC) or controllers. All controllers are connected to a Mobile Switching Centers (MSC). As a user of a cellular telephone moves around, the call must be transfered from transceiver to transceiver, and sometimes from controller to controller. We are interested in the problem of minimizing the cost of these transfers from controller to controller. In the above hierarchy, we consider a subtree emanating from one Mobile Switching Center. The two sets corresponding to the subtree are I, the set of transceivers, and J , the set of controllers. The problem is to assign each transceiver from the set I to a controller from the set J optimally subject to certain constraints. We introduce |I||J | binary variables xij . If the i-th transceiver is assigned to the j-th controller then xij = 1, otherwise xij = 0.