The success and increasing deployment of mission-oriented sensor networks has required sensors to collaboratively accomplish many complex real time tasks. In this paper, we focus on many-to-one mission-oriented sensor networks, where data are collected from multiple resources to one data sink. A critical component in realizing real-time services over such a network is the estimation of end-to-end delay. This problem has been widely investigated for wireless sensor networks under various assumptions such as Poisson packet arrivals or infinite queue length. In this work, we consider a more practical network setting in which the packets need to be forwarded to a data sink along multi-hop communications, the packet arrival rate and service rate are both generally distributed, and the queue length is finite. Our analytical expressions of the G/G/1/K queuing model under the popular protocol interference model when CSMA/CA is adopted for MAC control are carefully derived. An extensive simulation study is carried out and the results indicate that the proposed G/G/1/K queueing model outperforms M/M/1/K and G/G/1 under a high network load while it provides competitive results when the network is lightly loaded.