Positive congestion effect on a totally asymmetric simple exclusion process with an adsorption lane

We propose a type of asymmetric simple exclusion process by introducing an adsorption lane. In the system, each particle can be adsorbed by the adsorption lane only once per travel. The adsorption and desorption probabilities control the density of adsorption sites and the number of adsorbed particles. The ratio of the adsorbed particles shows reversal dynamics for congestion of the system, which is called the positive congestion effect. We analyze this phenomenon by simulations and an approximation and successfully derive its critical condition. The spatial distribution of particles controlled by the adsorption and desorption probabilities is also investigated through balance equations of particles.