This thesis addresses the mathematical modelling of end-to-end packet delay for Quality of Service (QoS) provisioning in multi-hop wireless networks. The multi-hop wireless technology increases capacity and coverage in a cost-effective way and it has been standardised in the Fourth-Generation (4G) standards. The effective capacity model approximates end-to-end delay performances, including Complementary Cumulative Density Function (CCDF) of delay, average delay and jitter. This model is first tested using Internet traffic trace from a real gigabit Ethernet gateway. The effective capacity model is developed based on single-hop and continuous-time communication systems but a multi-hop wireless system is better described to be multi-hop and time-slotted. The thesis extends the effective capacity model by taking multi-hop and time-slotted concepts into account, resulting in two new mathematical models: the multi-hop effective capacity model for multi-hop networks and the mixed continuous/discrete-time effective capacity model for time-slotted networks. Two scenarios are considered to validate these two effective capacity-based models based on ideal wireless communications (the physical-layer instantaneous transmission rate is the Shannon channel capacity): 1) packets traverse multiple wireless network devices and 2) packets are transmitted to or received from a wireless network device every Transmission Time Interval (TTI). The results from these two scenarios consistently show that the new mathematical models developed in the thesis characterise end-to-end delay performances accurately. Accurate and efficient estimators for end-to-end packet delay play a key role in QoS provisioning in modern communication systems. The estimators from the new effective capacity-based models are directly tested in two systems, faithfully created using realistic simulation techniques: 1) the IEEE 802.16-2004 networks and 2) wireless tele-ultrasonography medical systems. The results show that the estimation and simulation results are in good agreement in terms of end-to-end delay performances
