Mixed monotonicity of partial first-in-first-out traffic flow models

Abstract

Abstract-In vehicle traffic networks, congestion on one outgoing link of a diverging junction often impedes flow to other outgoing links, a phenomenon known as the first-in-first-out (FIFO) property. Simplified traffic models that do not account for the FIFO property result in monotone dynamics for which powerful analysis techniques exist. FIFO models are in general not monotone, but have been shown to be mixed monotone-a generalization of monotonicity that enables similarly powerful analysis techniques. In this paper, we study traffic flow models for which the FIFO property is only partial, that is, flows at diverging junctions exhibit a combination of FIFO and non-FIFO phenomena. We show that mixed monotonicity extends to this wider class of models and establish conditions that guarantee convergence to an equilibrium.

On Sufficient Conditions for Mixed Monotonicity

“…Secondly, we give two sufficient conditions that can be used to verify mixed monotonicity of a function defined on ndimensional Euclidean space. These sufficient conditions are more general than the ones given in [3], [5]. By our first sufficient condition, all continuously differentiable functions with bounded partial derivatives are mixed monotone.…”

“…Moreover, it remains unclear how to verify the mixed monotonicity of a function or a system in general. Instead, there are only some sufficient conditions [3], [5] available for checking mixed monotonicity. Aimed at solving these challenges, we present two main contributions of this paper.…”

Formal Synthesis of Control Strategies for Positive Monotone Systems

“…By assuming fully non-FIFO models, system becomes monotone in the whole state 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 space. For a more thorough discussion on physical aspects of monotonicity in traffic networks, see [15].…”

Safety control of monotone systems with bounded uncertainties

“…Consequently, an increase in the occupancy of link 3 may actually decrease the occupancy of link 10. The authors in [17] studied this phenomenon and showed that traffic networks are mixed monotone, which is a weaker property than monotonicity. We desire that links do not impede the vehicular flow from their upstream links, i.e.…”