Network throughput and end-to-end delay time are two important parameters in the design and the evaluation of routing protocols for wireless ad hoc networks. Network throughput and routing protocols have been studied for some time. To be able to estimate the end-to-end delay time, the process induced by the random position of every node has to be known, that is, a mobility model for the nodes has to be specified. It has been proved that if a mobility model for the nodes is based on a Brownian motion on a flat 2-torus the expected end-to-end delay time has logarithmic growth. In this paper we propose a different, although related, mobility model for the nodes based on a discrete-time Markov chain on a flat 2-torus: a standard symmetric Random walk. We prove that under this mobility model the end-to-end delay time of a wireless ad hoc network with k user is ⊖(k log k).