The study proposed a methodology based on queueing theory for travel time assessment over multiple routes with unsignalized traffic junction in tandem network. The work carried out in the study gives an approach for best route selection between two points based on minimum traveling time. The queuing theories used in the study took the M/M/1 model over the unsignalized junction and evaluated the traffic performance on different mean arrival rates of the vehicles. The proposed methodology is analyzed in a pilot study with observed data of mean service rates for each of the junctions for all route choices. The study can be used as a decision-making tool for formulation of route selecting strategies based on minimum traveling time.