In recent years, several perimeter control strategies have been proposed for traffic management in cities. The common factor found in these works is the use of Macroscopic Fundamental Diagram (MFD) models to describe the dynamics of the network and optimize traffic inside the perimeter by manipulating perimeter inflows. Perimeter gating control strategies are attractive for traffic management inside the inner city. However, it inevitably creates a negative impact on the traffic outside. Most of the works in this research area have neglected vehicle re-routing outside the controlled perimeter, i.e., they do not consider demand elasticity to the central region resulting from gating and the related queues. In this paper, we propose a global modeling framework capable of assessing the effect of perimeter gating control (in terms of queue, emission, and total time spent) on the full network, considering demand elasticity resulting from Dynamic User Equilibrium (DUE). Classical Proportional-Integral (PI) control scheme is used to control traffic congestion inside a central region (reservoir). The modeling framework is comprised of: (i) an accumulation-based MFD model to reproduce traffic dynamics inside the reservoir, (ii) point queue model to represent queuing vehicles on inbound links to the gating points, and (iii) a time dependent travel time profile based on a steady-state approximation of MFD dynamics to characterize the alternative road network (bypass). DUE is then implemented, considering instantaneous predicted travel time. This determines how the demand to the inner region is affected by the gating. The functioning of the global system is assessed by total time spent and NOx and CO2 emissions inside the reservoir and for the full network. The presented simulation results show that the perimeter gating control helps to maintain congestion at the desired level with significant improvements in the total time spent and the mean speed in the network. However, it shows a slight increase in the queues. As expected, deviation to the bypass alternative is significant and should not be neglected when carrying out a global assessment of gating system performance.