Many researchers argue that autonomous vehicles (AV) will create a safer and more efficient transport infrastructure. However, some studies have drawn attention to potential problems in relation to how AVs and human-driven vehicles will co-exist. We investigated the effect of speed compliance behavior of AVs on an urban two-lane road section with alternating speed limits of 50 and 30 km/h. A Vissim microsimulation model was used where we gradually increased the traffic volume and the market penetration rate (MPR) of AVs. We found that under low traffic flow conditions the increase in MPR will lead to a decrease in the average speed and worsening of the average travel time. Under medium and, specifically, under saturated conditions, a high share of AVs can bring stability to the system. They can also significantly improve the speed compliance rate.