Layered deposits are exposed in the walls of the troughs cutting the north polar cap of Mars. They consist of alternating ice and dust layers or layers of an ice-dust mixture with varying proportions and are found throughout the cap. However, the details of their formation process remain unknown. Extensive simulations of the LMD GCM water cycle (Forget et al., 1999; Montmessin et al., 2004) have been performed at various obliquities (15^o to 45^o with a 5^o step), eccentricities (0 to 0.12) and longitude of perihelion, to investigate the rates of water ice exchange between the northern cap and potential equatorial ice reservoirs. The corresponding rates were propagated over the last 10 Myr martian orbital and axial history (Laskar et al, 2002; 2004) in order to track the evolution of polar and equatorial ice thicknesses and test simple models for layers formation over orbital cycles. We found that the annual cap stability mainly depends on the summer solstice insolation. Above a critical insolation, the annual loss rates appear to be a marked exponential function of the insolation. Conversely, beyond this value, polar accumulation rates estimated from various sizes and locations of equatorial sources have found to be nearly unsensitive both to insolation values and remain close to 2 mm/yr. The evolution of the northern cap thickness was then tested for three scenarii.: (1) an infinite equatorial reservoir (2) The formation of a protecting dust lag reducing the further ice sublimation by a variable factor since ~ 10 meters of ice are sublimed (assuming that ice deposited at low obliquity contains about 10% of dust and that a ~1 m dust thickness is sufficient to strongly reduce the ice sublimation) (3) The previous scenario coupled with a realistic history of the equatorial reservoir. The exchange of ice between high-latitude deposits and equatorial reservoir (but not between the polar cap and high-latitudes reservoir) was thus simulated to ensure the global ice mass conservation. Our three-box model is then able to track the evolution of polar, high-latitudes and tropical ice reservoirs for arbitrary initial ice distributions. In the three scenarios, ice rapidly goes to the equator in the high mean obliquity regime (5-10 Myr) and the onset of the polar cap formation begins around 4 Myr during the transition towards the low-mean obliquity period. In the third scenario, more than 600 meters of ice could have accumulated at the north pole from the equator since 4 Myr, without major erosionnal episodes, allowing the formation of ~27 ice layers (or 54 dust-ice layers) with an averaged 22,0 m thickness and a 13.8 m standard deviation, consistent with current thickness observations (Milkovich and Head, 2004). These properties are not modified for moderate variations of model parameters. Our results implies that most of the current 3-km polar ice thickness must originate from other subsurface or surface reservoirs (south cap, high-latitudes ice deposits) acting when the equatorial reservoir disappears. Our model predicts that such periods could have occured recently (0-350 kyr and around 2.4 Myr) corresponding to periods of mininal obliquity variations.Conversely, we discuss the possibility of transient equatorial ice reservoirs during recent large insolation excursions and erosionnal periods for the northern cap.