Rehoming Strategies for a Relief Toll Machine

When an existing toll machine exhausts and a relief toll machine is added, rehoming of existing trunk groups is necessary. The intent of this paper is to determine rehoming programs whereby the present worth of the total trunk rearrangement cost is minimized while the total number of trunks to be rearranged at any stage of the program is constrained to lie within specified lower and upper limits. The rehoming program will specify the amounts of trunks to be rearranged and their corresponding timings for the rearrangements to take place. It is found that the choice of a proper rehoming strategy is critically dependent on the relative magnitude of the monetary discount rate compared to the traffic growth rate. When the discount rate matches the growth rate, any feasible rehoming strategy for any type of existing and relief machines is appropriate. If the discount rate is lower than the growth rate, it is more economical to rehome the maximum allowable amount of trunks as early as possible. On the other hand, if the discount rate is higher than the growth rate, the rehoming strategy is completely reversed. This case calls for a delay of as much rehoming as possible. However, the number of trunks to be rearranged during each stage of the rehoming program is bounded by the specified minimum allowable limit.