A Queuing Model for Mixed Traffic Flows on Highways considering Fluctuations in Traffic Demand

Modelling the mixed traffic flows of autonomous vehicles (AVs) and human-driven vehicles (HVs) on highways is challenging. Randomness, fluctuations, and congestion exist in the mixed traffic flows. This paper extends the current literature by proposing an M/G(n)/c/c state-dependent queuing model operating in a random environment. The fluctuating traffic demand is addressed by arrival rates modulated by the random environment. Meanwhile, a Markovian arrival process (MAP) is incorporated to describe the platoons. We investigate the performance of the mixed traffic flow under the I policy (AVs and HVs travel together in all lanes) and the D policy (one lane is designated to AVs). Numerical experiments reveal the following interesting findings: (1) the fluctuation degree of traffic demand, the traffic intensity, and the penetration rate of AVs play essential roles in determining the performance of mixed traffic flows. (2) The I policy should always be adopted if the travel time is more valuable. In terms of output rate, the choice between the I and the D policies depends on the traffic intensity, SCV of arrival rates and penetration rate. (3) A larger penetration rate is required to completely eliminate congestion on a longer highway segment.