the standard models of queuing theory of operations research is concerning with allocation of resources.The operation research models like queuing theory,linear programming dynamic programming and inventory was developed after the success in the second World War where the military has to allocate resources to various military operations and to the activities within each operations in an effective manner. These models are still applicable in the field of operational research.the standard theory of queuing are applicable everywhere when the facilities required to provide service are inefficient.Kibaha weighbridge in Tanzania is among the place where the facilities available cannot accommodate the vehicles requiring the service of weighing.The standard models of queuing theory are proposed to be used in the this place to reduce the congestion especially during the peak hours.