This work deals with the problem of balancing traffic (load) amongst mobile switching centers (MSCs) when the cluster of cells to be connected to an MSC is decided during the design of a Personal Communication Services Network (PCSN). Our aim is to assign cells to MSCs in such a manner that the traffic handling capacity of each of the MSCs is utilized uniformly, thereby precluding the possibility of unfairness in loading of MSCs. This, in tum, makes all the MSCs equally scaleable against the increase in either mobile user density or per user traffic. A conventional cell to switch assignment (CSA) algorithm attempts to optimize only the total cost, comprising cable cost and handoff cost, without taking into account the utilization of the traffic handling capacity of MSCs. To obviate this limitation, we propose a new CSA algorithm with load balancing (CALB) which emphasizes equally on the load balancing as well as on cost optimization. As shown in this work, CALB performs extremely well in balancing the traffic amongst the MSCs present in the network thereby helping in increasing the overall scalability of the system. Although, it outperforms CSA in terms of load balancing, it does so obviously at the expense of slightly increased total cost (i.e., the solution obtained is a sub optimal one in terms of cost only). But the increase in cost is never overwhelming (5%-14%) vis-&vis the improvement in the system scalability (0.5%-19%).