This paper explores the perceptual effect of network delay jitters on consumers' quality of experience during packet-based VoIP conversations. Novel parametric speech quality models are proposed to faithfully capture speech quality impairment caused by network delay jitter and de-jittering buffer settings. The proposed models have been rigorously conceived following a regression analysis approach using a wide range of network delay jitter traces and de-jittering buffer settings. The network delay traces were synthetically produced by a stochastic generator, widely used by the research community. Moreover, new speech quality models, which quantify the individual and mixed perceptual effect of network random packet losses and delay jitter, are proposed and validated. The packet layer key parameters of proposed speech quality models, namely mean network delay jitter and de-jittering buffer delay, are easily accessible at run-time. Experimental results show that our no-reference speech quality models correlate very well with the standard full-reference speech quality models. Indeed, our performance evaluation shows correlation factors equal to 0.97 and 0.94 for, respectively, the G.711 and the G.729 CODECs. The proposed speech quality models should help design optimized schemes for network delay jitter removal, thus improving the perceptual speech quality for a given network delay jitter intensity. Moreover, the speech quality models can be used to accurately measure in a non-intrusive way the perceptual effect of network delay jitter and packet loss, separately. This constitutes a desirable feature, as it enables the smart mitigation of the sources of speech quality degradation.