An analysis of expansion and reduction speeds of traffic jams on graph exploration

One of the representative problems of multi-agent systems is the graph exploration for package delivery. In this paper, we analyze the effect of the number of agents and network structure on efficiency of exploration on warehousing systems. In the package delivery, not only overcrowding but also stopping of agents for loading and unloading package cause traffic jams. This paper motivates to evaluate a relationship between stopping of agents and exploration efficiency. In this paper, we introduce the incident ID which expresses the stopping of an agent and formulate outbreak, merging, and splitting conditions of traffic jams from model of movement and stopping of agents on ASEP network, and two dimensional grid exploration. With the formulated conditions, we represent the area of traffic jams as Wait-for graph. The novelty of this paper is to evaluate the scale of the traffic jams based on the length and width of the Wait-for graphs. We also derive the expansion and reduction speeds for the derived length and width of traffic jams. The first result is to derive the cancellation conditions of the traffic jams using its expansion speed of length. The second result is to evaluate influence on exploration efficiency decrease due to the traffic jam using its expansion and reduction speed of width. For the verification of the derived cancellation conditions, expansion speeds, and reduction speeds, we show the numerical experiments.