Moving average vs. exponential smoothing cost-updating filters for day-to-day dynamic assignment: fixed-point stability and bifurcation theoretical analysis

Deterministic process (DP) models for day-to-day dynamic assignment can be cast in the general two-equation assignment modelling approach, including the following: - the arc cost updating recursive equation in the case of day-to-day dynamic assignment; instances are exponential smoothing (ES) or moving average (MA) filters; - the arc flow updating recursive equation in the case of day-to-day dynamic assignment; instances are ES filters. Even though ES filters for cost updating may well approximate MA filters, somebody in the scientific community argue against the underlying hypothesis of infinite memory for ES filters with respect to MA ones; numerical results support significant differences for small memory depths, say 2 or 3 days. The main original contribution of this study is a formal fixed-point stability and bifurcation analysis of MA-ES DP models with memory depth 2, and a comparison with ES-ES DP. At this aim the Omega method 2.0, suitable for carrying out general fixed-point stability and bifurcation analysis has been developed and discussed. Extremely long proofs have not been included for brevity. This study focused on methodological aspects; thus, numerical examples were not included.